The Official Guide for GMAT Review 12th Edition Part1-3



  

             



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

  

 

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          

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THE OFFICIAL GUIDE FOR GMAT® REVIEW, 12TH EDITION                                                         



          

          

          

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     

     

     

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      

      

      

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    

    

    

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     

     

     

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     

     

     

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      

      

      

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      

      

      

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        

        

        

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         

         

         

       

       

       

                       

  

 

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

                    

          

 

            

                

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

          

                                  

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                      

 

                  

  





     

      

 

     

  



       





 











      

                    

                 



 

      

     

  

 

  

 

         





              

           





       



 





          

                            

               





               

        

   

       

    

   





 

       

           

       

          

                    

                     



 





         



  

 

                         





 

            







        





































    





       

   







 



 



 



 

      



  













































      



















        

 



 



 



 



 

          





 



 



 









    



















 







    

 



 

















   

   





































          

   























 







 









       



















          





















  



 



 



 



 



 



    



















   































      





  

 



       



















         







 



 



  



















     

 



 



 



 



    

  









   











          

    

  

   







  







                       





    

  

   





 

 

  

  

















      

    

  







   



    

      



  

 





 





      

 



 

  







    







   

 

 





     

 



 

    







     







 

  









   

 

  

   





 



  

 

     

 



 

   





 



 

   

  



 

     



   









 

   















                                 





  

 



 



 



 



 

 

  



  



 



  



  







   







      



     

   



   



  



   



   



   



   



   

   

    



    



  



  



   





















                                             







 



















  

 



 



  



  



  

   

  



  



  



  



  







   

 



 



 



 



 

    





 



 



 



 

   









 



  



  



 

















                               

  

 



 



 



 



  

   

 



 



 



   



  

    

 



 



 



 



  





    

   





 





 

 





 

 





 

 





  

 

   







  



 



   



   



  





   

          

          

  

 







   

 



  

  



  

  



 



  



  



  

           











 



 



 



   

           

                 

  



 



   



   



  

  





  



  



   



 



   



             

   



  



  



 



  

        

  



  



 



  



 





              







             

  



  

  



   

  



 



   

   



  



  

          

 



 



 







 



           

   

  



 



  



 



 



   



 



  



  



  

          

            

   



 



 



   



  





           



           

 



 



   



  





   

  



 



  



  



  



  



           

  



 



   



 



  

            

 



   



   



 



 







       

      

   



   









           

      

    



    



   



   



    



       



     



  



  



  

       



   



   



   



   



   

      



















        

 



 



 



 



  



        



  



 



 



 





 

  





 

  



 



  

     



     



 



 



 



 



  

       

   



   



   



   



   



     



   



   



  



  



  



  



  



  



 



 

       



  



 



    

    



   





   

 



 

   



 



 



 







     

   



   



  



  



  



  



  

  



  



  



  



 



        





   



   



   

      

      

 



 



 



 



 



 



  





 

  

 



  

 

 

  

 

 

  

 

 

  

 

 

  

 

 

  

 

 

  

 





  

 

 

  

 

 

  

 

 

 



 

 

 



 

 

  

 

 

  

 

 

  

 

 

  

 

 

 

 

 

 

 

 

 





 

 

 



 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 





 

 

 

 

 

 

 

 

 





 

 

 





   

































































  



      



        









































      

       

 







        

  

   

 



 























          

    















       

    

  



 



   

 

      

      





















   







   

    

 



  









 



  



  







   

 





 

 

   

     

       

























         

























    

       

        

  







  

       



       

          

        

     



                                                  







    

 



 



 





















      

 





               



   



 

   

 



 















 



    

 



  

      























                



 

























    

       











       





















 

 

    





 



 









        



 

 







            

    

    

 





          



 









    































 



             



 

   





















          

  

  



   





























        

    





















      

         



  



    





















 



 





 

 



 



 

     



  

       

       

 





    

   



 







  









        



  

 















 







         





















      

       



     



  



 











  

      

     





 



 



 





























       



  



   

 

 

       

  







 









 



    







      

   

  



 



                   

                 

 



  



  

   

    

  

       

 















                









                         

  



 



                              

  



 

 

      





                                           





 



            



     



       









                                   



 











     





  

If 5x < 1, then =

< 1 since x

= 5 ; SUFFICIENT.

   x+2<2 add 2 to both sides 5x + 2 < 52 <1  

because a < b implies 5a < 5b divide both sides by 52 = 25;

          

   

                       











    

   

 

  

 

  

 





    









         



 



 



  



 

     

 If D is the distance Paula drove then

  

 

  









                



    

D > 200 and

>

=

so t >

and

t may or may not be less than 3; NOT sufficient.

<

<



 <

<

        











                                    









      

        

















          



                   

       



 

   









                          

 



  



   



                 



 



           



      



  





     

 



 

        



    

                                     

 



 

      

   

 



 



    





























          



               







       

 

      



  

 





        







                 



 







   



 

      

  

 

  

 



 



 



 



 

   



    



     

 



              





 

  



  



 



  



  







                   

 



            

 





   

  



   



  



   



   



              



    

               



             

  

   

   



         



  



  



   

   

     

    

 







     



   



   



   



   



   



 



      



   



 

    

 

















            







             





     



   

   

  

   



  



 



     



  

  



  

  



  

  



  

 



 





 







    

     

 



       



          







                         



                  

         



     



    

     

   

 



 



 



 



 

       





   

   











 



 



 





 

  



  



 



 



         

      



     

  



   

  



 

  



    

  

    

     





 



 

  

 



 



 





 

   



 





  

 



                     



 

     

 



 



 



   



  



       





   



     



         



    

    



   

  



   

     

           



 

 





 

 





 

 





 

 





  

  



         







           

  



 



    



  



  

    

  



 



   



   



  



         

 

  

          



   

 







   





 



 



 



 



          

 



 



   



  



    

 







     

        









 







 





  



       

  

          

 





       





 

















  



     



        



    

 





      

















 





   



        

   

      

 





       





 



 







 





   



     



             

 





        









 



 



 





  



     

   

   



 



 



 

 





      

 







 













  



    



   



        

 





    













 









   



        



 



 



     



 



  

 





       

 



 



 













  



      

   

    



     

 





      

 



 











 





  



     



 



   



       

 





     























    



        

        

       

 





      





 

















  



    

        

 



   

 





       









 













 



     

  

     



   

 





      

 











 









   



       

    

      

 





       

 



 







 



 





    



     



   



     





 





      









 













  



       

   

      



   

 





      









 













  



        

    

       

 





      





 



 













  



     

   

      



   

 







     

     

     



   





   



   

     



   



   



            

   

                   

    









        



   



    



              

 



     







       



  

         

  



  



  



  



  



         

  

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     



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  

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  

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  



        

   

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  

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  

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  

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     

          

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



                   

        

























                 

  



   



 



     



      

         





 



 



 



 



 



            

   



  



      



    

 



         

 



 



 



 



 

      

        

 



 



 



 



  



                      

   



  



   

    



            

   







  



    



    



  

 



         

 



  



         

      

  



 



  



  





  

     

  

         

   



   





   



   



   



                      

 



    



        

               

  



  



  



  



  



               

  



   





  



  



   

          

   



   



   



   



   



                    

   



    

                   







     

  



 



 



  



 



               



               



    

       

 



 



 



 



 



            





 













 





      

  



  



  



  



  



   



   



 

          

   



   



   



   



   



                   

        







       

    



   



    



   



   



  



  



 



           

  



  



   



  



   

         

  



  

 





      

 



 



 



 



 



                 

 



 



 



   



    

 





 

 





           

     

     

    

    

      

   

          

   

   

         

    

    

    

    

      

    

    

    

    





 

                    

 

                       

 



 





                     

                                                                                    

                                                    





                             

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   



















                                              

           





           

          

   

       

            

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

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           







           

                                                           

        

  

 



   





     



       



 



















  





   

  

                            



                               

              

     

           



           

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     

               

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           





                               



































    





 



    

         

 

                          



 

 





























     

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                            

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    



                 

                                                            





        









    



 

                             ({  }) =

{  }

=             



                               {   }            (    ) = =       

   

                      

 

=

{}  =  { } 

                

 

=

{}

=  {   }  

     



                  

     





            

                    

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        



  



 

  



             

               

       

 

   

  

  







                     

  

     

    



        

 

 

 

          





 

 

   

                                        

 

  

  

          



               

           







 

 

 

 

    



     

 



       

  





        



      

  

 



      





                

 

                               



 

        

              

        





                     



   

 

  

       

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   

    







   

      



  

           



          

     

      





     

      



      



 

     

















    

 





       

  





 



 







                   



  



             







      

   







         





      

 

 





            



 





            









 







            



                        







       





  

 

           





       







 









   













 



         

     

   



  



     

                



 

 



 

     





 



 

   















             





   

          

 

   





 

         







 

    

      





 

 

 

  

  







                                                                           

    



 

    







  

  



  

                 

 

 

        

     

               

                              

  

 

   



    

 



















 





 

 



  

 







       



 









      





    



         

 

                           

     

   



  





                

                                                                                  







      

 

   

            

   





       

 

   

     

   





  



                    



      

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 

            







 





          





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 

 

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   









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

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

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



   



    

   





 

 

 

 



 



            

     

 





















 

 







         

 

  

      

      

   

    

   

        





 

 





                                         

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

 



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 







 







 





 

    









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



            





 



             



     



    







    



 



 







    

















  



 



































  



















 

 

    























       









 













    



      

  















 















 



      

 

 



 

 





  





 

































  



















 









     











 

























 

  

     

  

     

 



 



 



 















































  





    

           



 

     

 



   



 



 

   













   



   



  

 



 



 









  

     









































 +   







 



 











 +  







      











    



   



 



















 







   

  











































    



















     



















      



















    



     

 



 



 









      

     



  



        















 



















    













   



 





 





       







 







 





 





 





 







 

 

        











 





 



 



 

   

     







 



 















 

   

   

   











































  



















     

   













 



 

 

 



       

 





 



 



 











   



 







 



 



 



    







   



 

























 

     





 





    



   



     





















   

 







    

 



 



 































   





















 

   





















    

 







 







 











 







 

    















































      

 



    

   



  



   



  



 



 



 



 





     

  







 































 

    

 















 







 



 



 





        



 





















 

  





    

   





  

        

 





  

   



  





   

      



  



  













     

 



































     

     





















 

           





 



 



 



 





    

      







 





    



















   =    







































   

       



            

 



 



  







  



  









   











  















 



 



 



        





















      



















   



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

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

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



     























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

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







  



  



  



  

(  )( ) (  )( )(  )  





 



















     

   

     



    













   



















        























         

 



















   

  













 







 

    





















 

  

   





       

















 

     



       





















       



















    



  

         



  



  



  



  





    



 



 



 



 



 



 



 

























    

 



 



 



 





        





















        

 

     

  









 









 

   





        

 











 



 

   



















     

 















 

      























   

 



 



 









       



















   



















      





















         















       



















      

  





















        

 

















    



















     

    



    



    



 



   

    

    

 







 











































   







     



 













  

















 



  





     +   









 + 



 + 



 +



 + + 

  



















    



      



     

 



 

















 







 



 





     





 

      







  









 





    



  











  











  







  



  

     



















     



















       

            

 

   

 

   





      

 





 





 



     



 



  



 

      

        











         

    







 





   









































          





      

 



































 



      































        























 



 

    

  



 























 



 



     

   

 









         









 









 

 



 

 



 



 

 



      



 



 





    

   







































      



















 

  











 



 



 



 

    











    





























   

























          





















     







  



 +  



  





  



  + 

 





        

 



 







  

  





   

  







 









 

 



   



















 



   

      

 



 



 



 









    







 

     

  



  



 



 





    

 

















      

























 



 



 



 

      

 



 



 



 





   (  + )       



















     



  





























 



     

 



 

  











 







 







 

















        



  +



  + 



  + 

      

 



 



 



 



 

        





 +



  + 

 

   

 









 





 





 







   







  

















 





 





 



 







      





























 



 



   









 





 

  

 

      

 



 













   

     

   

     





















  



    



 



 













    

 



 



  



  



  



        



 





 





     













 



 

 

 









  











             

      



 





































         

 



   

 





































 



  



  



 





    

















 

         

    













  

   

 









  













 



 

 







  







    



  











   







 



  

   

   



 

           



 





 



  





 



  



 

 



 



















 



  

          

 



 



  









      









      





  

































  





















     



       





      

























     





      





     

      

 







  

























   

     





















     



  



 

  



 



   







 

    

























  



 























      

       









































     





  



   







    













            













     

         















       























    





   







     

           







     

   



   























   



   

      

 

      

 





   

 







 





   



















    





 

    

 



     



      







  







  

 



 



 



 



 

    

              



























    

                  



















 















      

    



 

 

   

  



 



  







 



 

 





         

 



      





   



























 

   

       



















       

 



 



 









 



















      







    



     

     

       

       

      









 

  









































  











 

 

 







 









   

   

 











  

              



















           





      















 



 



 



  

 



 



 



  

 



 



 



  

 



 



 



  

 



 



 



  

 



 



 



  

 



 



 



  

 



 



 



  

 



 



 



  

 



 



 



 

 



 



 



 

 



 



 



 

 



 



 



 

 



 



 



 

 



 



 



 

 



 



 



 

 



 



 



 

 



 



 



 

 



 



 



 

 



 



 



 

 



 



 



 

 



 



 



 

 



 



 



 

 



 



 



 

 



 



 



 

 



 



 



 

 



 



 



 

 



 



 



 

 



 



 



 

 



 



 



 



 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 





     



 



 



 





































        

       

     

 







   

 



         















         







          



         





         













 







   +    +  =  +              



         





 

















    

   





  



(   ) +  (   ) + (   ) + (   )    +   +   +     





  

  



    ()() = ()(  )( )    



    

    





 



















       



     

    





  

 















                 





















               























       

 







 





 

 



 

 

      





  

 



 













 





           

 



  





















  



     

 













 



  

     

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

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

      





















    



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

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  

   



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

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

      









 







 





     











                                     

 

    





















     



















 

          



          



 



 



 













 



 



 



 

      









     





     

     

  

    

 



  

 



 



 











    



               



()()   ( )() 











 





    

    

    









































    



                     





 



 









     























  





       



                        

  









 



 



       





  



     + +      







 

 

        













  





















       



    



















 +        

  



        

       

 































 















      





       





















       +    

 

        





















    









 



 



       



  

 



 

 

  

  



     

 

 



  

 

   





 

     

 



 



 











 

    







         















 











    





             



    

()( ) + ()( )  ()( ) + ()()

     

()(  + )







   + 



  







  



   



 



 







 

    

 









   





 

 

 

                      



    

























          

 

        







 



 



 



 



   

    



 



 

































 

         









 









 





  



 



 



 







 























 





 



   









    



    

  

  

  

     







 













 



  



     

  

 







 

  

















 







 





  

  

 

   





   







   







 



 

   



 



 



   



  

 



          



 

  

   

     



 





 







     



   

   



 



 













 

                                                      



 







  



 

























  









        



  

    

  

  





 





 







 

 



    























     







       





   

     



















 







  

   

 



 



 









 

   



            







          

   



















 

      



                  

        

    





















             

         

 

 



  



 





  









































 



  





          



















 





     

    

 



 



 







  

     





 

        (  )  (  )        

(

)( ) (



   



 







    









)(  )



 

      

   









































            



             







         









 

     

    























                 





























  

           

 



 



 



 







              



      



















    





    



                 



    

  







   



   



   



 



   

 



 



 



 





 



 

 



 





      



    

       

























                



















 

     

        





 



 



 



 



       =  =          =                                              

  

 

                

  













     





















 

 

     

     

 

  

   

  







   











  























 



 



 



 





 





    



 

 



         

           

           

  



  fi        





 



  







   











 

 

















 



 



 



     

     



























 

   

  

   



          =    























 



     

   



               





















                 







  



   



  



  



                                                

                          





















        







 

    







    



















                 

 

     

 

   

  





  





  

   



   











  

  

 

(  )( )  (  )( )( ) 





 



 



 



 



            









  



  



  



  

  

( )( ) ( )( )( )       





 

   

  

     

          



















   





















 

      



               

    



 



 

   







      





















   



  

 



 



 



 



 

  

 



 



 

                          

              





















                          

    





  





 

              



















  

















 



             



       

     

 









                    























             





    















 

 







   



       









   

     









  







  

 







    





















       



  

  











  



       













                  

 







   

 









    



    

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 





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

          



















    

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







    

 



 



 



 







            





        



















 

                 



   



 



 



 



 



   



  

     

 



 















  

 



 





          +            

  



 

 













  





































 



  









     

 

 

 + ( + ) + ( +  ) + ( +  ) + ( + )

 



                 













 



 

  +    



      



 



 















 



    







    

 



 

 

  





   





















  





         



















    



          

          

     





      



 

     







































  











       

 

             









     





















         



                      

















                                      



       



















 





 





 



 





 

  



 









      





   



















    

 

             

 



















 







 

                     



 



 



 

 



    

   



    



    



    



 



   

      























     

                    



         

         

  fi   

    

     

 







 











             





 



























      



  







  

 



   

    















 



 



 





 







                       



 

             











 



























 







  



        

 

















      



                   



     

 



















   

   



 





 

  



     







                                 





   



   

 

             

  



  



  



  



  

 

     



     





















                       





   



 



  







  





  









       



















 

                                  



















                      



   

       



     

   

                



 



  



  





          

    

                                                        

        

 







 



         





















       



   





 



 



 

 

                          

   



           

      





             



















        =          =       



  =                 

    



    



    



    



    



      

    







 





    





















                        







 

















              

    

 

 

  



          

 

             

 

       

     

 



















     

 

 







 



















 

          



  

     



 





 

 





 

  







   

 





                       

         













 



 



    



( )( )  ( )( )() 









 

      



 





































    



     

()( ) ()()(  )





  





 



 









 

 



          





       



               

 

















    











    





































   

 



                   







     

 





 



    

 



 



   









 



  

 









        





















         

    

        ()()( )     =   

    





















     















            





















       

  



       

  











 



 



 

       





 



 





       

      

 



 

  







   

        

       























          





















                  



           

 

 

 

  





   



























        

 



 







   







   

              

                    







      



      +   

   



   



  



 



 

         

           

  



     

           +   +    

     

  

  



  

 



 

  

 

 +  



 

 

  









  







  + 





   

 



   

 

            

 

  

 





 





  







      

 





 

      (  )            



 

 + (



 



  +   



  +   

)

 



 







  





   

     

                      





     

  



  



 



 







  























 

 

                  





  





   

  

     



            

















 





        

                         

        









             

 



 



 





 









 



      

 





 



 





 



 





      

     (  + )     





























 



 

  

           

             

 

  

 

  



  







































         





     





  

 

 

  







     



    

 



 



 



 



 











 



 



 



         



                   

            

   















 



















   









 





    

       



                       



   







  





 



          (  +  )  +    



  



 





    



 

  



    

     



 

 























 





  

   

     







 



 







 







               

    

  

 





      









 



 



 









 

     











   





  







 



                    

 

 

      

















 

 







        













 



 







     

  



     

   

 



 







 







 



















 



       















    

           





















 



 





  





      















  

                         











           

 



 





 





 



  



                                         

 

















   











 





 

 























  

                      





                        





 

    =   =    ()( ) ()( )



       





 













       





















 













       



















 

     

       

  





   











 

 



 

 

              



     



      

    

  

      

 



  

 





 



          





 





 



  



      

















 

 

               



           



    



 





     



   













 



 



             

    





  











  



     



  

      

                            



  

 





  



  



     





                      

 















 



  

  





   

 

 



 

 





     



 



            



















 

   

              

 



 



  



 









  









 

  





       

  



 

  

 



  



     





  

 



 





          

      













  

 































    

        





















      

   





















        



   

 



     





 

      























             



    

    

 



         



















        

 

















   

 

    



 

 





 

   

          



 

    













   







      





















        











  



 

 

          

 



 



 



 







       



  

 

  



  





 

     

 







 







































       

       



 

























             



 

















 

                       

 

 

    



   

      























           

     

       



















     



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

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

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

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



              + (  ) +   = =                

                    





















                                    







                      







    

        

















                



 



 



 



 



 

                         



 

        











    





   

   







             









          

       





















                        

     



 



 

     

       

 

       



         

 

 

  

                    







       



   

    



   

  









     

   



   

 

 

         

























           





     





  

 

 

  











                      

 





 



               





         

  











           

      

     

 





   

    



















     



       





 

 



 



 

  



 





 

 

 

 

 

 





  





  









 

 





  

  





    

     



 



      



  

 



    

  







     



     



                                  



          

                       

   













 













                

        

   









   





   









   

   



 

   



                 

 

 

  



  =    (  + )  +   

 

 

 







 





 





       





 



 



 



 





   

 



    



 



    



 



 

 





 







 



 



  



 

 





 







 

  



 



 

  



 



  







 



 

 







 

 



  

    



 





 

 



        



       























 

 

 

           

 

























      





 

  







 









                            



       

















        



 







      



 



 



 











                





  









 

  























 

          













  







               



    

      





   











   



          



     







    

      



 



                     



   





















                  



 

   



     

       

       

      



 

  

  

  

  

 

 

       













  

  





  





















  



  



        







 

 

  



 





  

   

         

  











 

 



 



      

           

  





  

  

  

 





























 



          

   

   

           

      

    

 

                

     





  



   

















   













 



 



 



  







 

 





                             





 

  



      



    



     



      





       

 



 

  



  

 



  

  

  



  





           

 



 



 







 

           





 



         

    

  

   







  







                   









 









 



  



 





 

  

 









   

  

  

 





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 







 

   

 



 

  

 



 

      

 



     

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  







 







  

  



 

  







      

  



 



        

   



 

  







    

 



 





  



  





 

     













 







 



 









     

   

 

 

    



    





 

   

  









 

   







    

 



 



           

        

    

 



  

       





 

   

  



  

 

    







  







       





      

    

 



 

     











   







  







    

 





      







   

  



  

















































     





 



  





     

 





                    







   









  

  

  





 







    



    

    

  



 

    







     

 



 

  







   



    

       



      







  







   







      

 



  







      

  

 

   

   

    







 

  

 



 

      



 



 



 



  

    

 



  

     

  



  

  



  



 



 

      

  



  









   









       

    





     



     

   







      

  





      

 









   

      

   

     

   













 

 



  









     





     

  

       



















  



 







 











   

  







  

 



 



 



 

       

           



      

    

 



 

    







    



  

















  







      

 



 











    









   

 



 







   

  









 

  



























   









     





    

  



    





 

     





 

     



      

    

 



  





   

 



 

     







      





 

    







   

   

      

       





      



 





 



      

  



 

       





 

             





 



         

     



 







 



  

     







     

     

  



  

 

       





 



       







     

   

    









  

 



 

   





 



























        

 

   

 



 

   

 



 

 

      

    















  

   

 



 

     







       





     

  







   







    

 



 









 



  

  





         





  

   







   

 

  

     

   



 

  



 



 



 



  

     







            

      

 



     

 



 











 







    

    





 



     



  



 

 



 

      

 



 

      













   









      

    

   

     





 



    







   



  

    







 



   

 





       

 



 

   

 



  

   

 





    





 

   

     



 

          

 



 

        







       

 









   







  







      

     





  

 













  









  







   

       

    

   



 



















   





     







  



 





  



 



 











 



 



 











 



 



 









 

 



 



 









 



 



 











 



 



 











 



 



 











 



 



 











 



 



 











 



 



 











 



 



 











 



 



 











 



 



 











 



 



 











 



 



 











 



 



 











 



 



 











 



 



 











 



 



 











 



 



 











 



 



 











 



 



 











 



 



 











 



 



 











 



 



 











 



 



 











 



 



 











 



 



 











 



 



 











 



 















 



 















 



 















 



 















 



 















 



 















     



                 

 









          

  



  

 



 

   











  

            

            





      





  

   

 



 

   







  

 



 









 



                                  

            

 









           







      

  

  



 

       



                    

    

  



  



           

   

       

 



 



                                               





 



     





                    

 

  



                             

  





  









              



                    









 



    

        

   



 

       



             

   

 



                      

 





















    





         

    





          

 



        



              

      

 

      

  



  





  



 



    

 

 

               

                                              

                         













 

     

                 

 



 



                       



     

 







                               

 



 





     

                       







             





    

 



 



 

 

            





 



   





 



  

 

 















 



  



 





 

  

  

   



     

           

        



                                                         

 



 



         

               

 

    









                



  







 

                       

 



 

 

            

       





 



                               

  





   

  



  



       



                  

         

        









      

      









 

  

  

   

       





