PREFACE NTS, a project of its own kind is aimed at setting standards of excellence in educational testing. NTS is a rapidly growing and credible entity of national repute. Its context and potential coincides with the expressed need of the Government for the establishment of a National Accreditation Council and Testing Service. Establishment of this set-up has been necessitated by the prevailing lack of credibility and absence of standardized testing facilities in our national Institutes. Institutions waste massive amount of work hours in preparing and conducting diverse kind of entrance tests with least credible and authentic consequences. NTS has made a bid to restore some order to the growing chaos in the field of testing. It has developed the capability to offer the testing services to all national institutes providing education. Its content is aimed at identifying the ability-oriented strengths among prospective candidates for IT education. NTS is a multifaceted and comprehensive facility that can provide services at an enormous scale in all dimensions of testing. Based on a vision aimed at providing quality services in educational testing and assessment mechanisms for various stakeholders, NTS is committed to promoting the overall quality of education as a value-added adjunct. It also extends Services for the employed & unemployed professionals to get satisfactory jobs in their relevant fields through an assessment of their knowledge base, skills, and professional expertise & abilities. NTS is a unique and trend-setting venture that has shown great promise.
Student Guide
1
1
NTS – INTRODUCTION
NTS was formed in 2001 with the basic objective of establishing a credible testing system to evaluate the knowledge level of students against a consistent and standard yardstick. It was felt that although our universities and other educational institutions are producing a large number of qualified professional and nonprofessional manpower, there is no single standard for quality evaluation of this educated human resource. Since there is no single syllabus right from basic to the advanced levels of education, the normal performance evaluation procedures fail to measure the quality as well as the extent of discrepancy between the existing and the desirable quality for individual candidates. Similarly, a big variation in syllabi and the apparent status of the educational institutions have created a huge gap between the haves and have-nots of the society. The students from big name institutions always have an added advantage where mediocre students are preferred over excellent students from low status institutes because of the brand name of the institutions they carry with them. NTS addresses these important issues by providing testing procedures that evaluate the knowledge and skills of individuals on a unified scale using standardized measures that are independent of class differentiation. In a short period of three years, NTS has made a significant contribution by developing and implementing training and testing programs for individual students, educational institutions and the potential employers of the country. The hallmarks of the NTS system are its consistency, transparency, reliability and efficiency. Being a non-profit organization, it takes pride in offering a cost-efficient system that could meet the needs of individuals and organizations to their utmost satisfaction. NTS continues to strive for excellence through research and development in its testing system and related services. The goal of the organization is to keep contributing towards improvement in education by building standards for educational and professional testing. Its ultimate aim is to be recognized nationally and internationally as a credible and reliable name in the field of testing.
1.1
NTS – BACKGROUND
Th e re is a n e ve r- in c re a s in g dem an d o f qu ality prof e s s io n als aro u n d th e glo be . O u r u n ive rs it ie s a n d o th e r e duc atio n al in s ti tu t io n s are pro du c in g large qu a n tit ie s o f prof e s s io n a ls , ye t th e re appe ars to be n o s in gle s tan dard f o r th e pe rf o rm a nc e e va lu a tio n o f th e se prof e s s io n als an d th e ir qu ality as s u ran c e . S in c e th e re is n ’t a s in gle s tan dard s yllabu s , th e pe rfo rm an c e e valu atio n pro c e du re s f a il to m ea s u re th e qu ality as we ll as th e e xte n t o f dis c re pan c y be tw ee n th e exis tin g a n d th e de s irable qu ality o f in div idu al c an didate . Th is s itu a t io n is ra is in g a la c k of c o nf ide n c e amo n g th e c an didate s an d th e e n tre pre n e u rs . To a lle via te th is , th e re is a n im m e diate ne e d fo r in c o rpo ratin g an au to no mo u s a n d a so ve re ign bo dy, wh ic h s ho u ld c ate r to th e n ee ds o f th e e n tre pre n e u r an d h a rn e s s th e in div idu a l ta le n t. Th is bo dy s h o u ld be m ade re s po n s ible f o r bridg in g th e ga p be tw ee n th e edu c atio n in du s tr y an d th e prac tic a l/ pro f e s s io n al in du s try by pro vidin g a n e valu at io n an d te s tin g s tan dard. Th is No n G o ve rn m e n t O rga n iza tio n ( NG O ) , u n de r th e n ame o f NTS “Nat io n al Te s tin g S e rvic e ” f a c ili ta te s th e e va lu a t io n o f gradu ate o r u n de rgradu ate c an didate s fo r a dm is s io n to a n y u n ive rs it y. NTS w ill n o t on ly le ad th e edu c atio n al in du s try to
Student Guide
2
a he a lth y co m pe tit io n bu t in s ti tu t io n s in a ll f ie lds .
1.2.
a ls o
im pro ve
th e
s tan dards
of
th e
e du c atio n al
NTS – Objectives
W ith in th e o ve ra ll prem is e o f c o n tribu t in g to th e im pro ve me n t o f th e qu ality of e du c a tio n in Pa kis ta n , th e im po rtan t obje c tive s o f NTS in c lu de : •
To im pro ve u po n th e sh o rtc o m in gs in o u r pre vailin g pe rf o rm an ce e valu atio n s ys te m of c an dida te s th ro u gh es tabl is h in g a c re dible , te c h n ic all y a ppro pria te a n d a c c u ra te s ys te m of pe rf o rm an ce e valu atio n fo r s tu de n ts o f dif f e re n t e duc a tio n a l in s ti tu t io n s at vario u s le ve ls .
•
To pro vide a s ta n da rdize d an d u n if o rm c rite r io n f o r se le c tin g c an didate s s ee kin g a dm is s io n to va rio u s u n ive rs it ie s in th e c o un try an d abro ad an d a ls o to pro vide a ba s is on w h ic h s tu de n ts , in dividu a ls an d in s titu tio n s c an a s s e s s pe rf o rm a nc e fo r pre paratio n o f vario u s type s o f te s ts c o n du c te d by dif f e re n t in te rn a tio n a l te s tin g age n c ie s .
•
E n a blin g a s s e ss m en t a n d ran kin g n o t on ly in a partic u l ar s u bje c t on a ge ne ra l co m pe te n c y le ve l bu t als o h e lp in ide n tif ic a tio n of are as o f s tre n gth s a n d w e a kn es s e s in its s u b- c o n te n ts on a dis aggre gate d bas is .
•
To pro vide a re lia ble a n d ef f ic ie n t s ys tem fo r e valu atin g th e kn o w le dge bas e a n d s kills of c a n dida te s in c lu din g pro fe s s io n als - e mplo ye d an d u ne m plo ye d.
•
E s ta blis h in g a c re dible a n d re liable me as u re of as s e s s in g th e s tu den ts ’ kn o w le dge in c om m on ly ta u gh t pro gram s f o r re lative ran kin g.
•
To bridge th e ga p be tw ee n ac ade m ic pre paratio n an d th e prac tic al m arke t n ee ds in a h igh ly dyn a m ic an d co m pe tit ive e n viro n me n t.
1.3
NTS – COMMITMENT
National Testing Service (NTS) is a non profit, autonomous organization established with the basic objective of developing a credible, technically appropriate and accurate system to evaluate the knowledge level of students of different educational institutions at various levels. It thus assists in carrying out an estimated ranking of students for admissions in various educational institutions and also provides potential employers with a credible yardstick for evaluation and induction of quality human resource. NTS operates on national level and is committed to:
1.3.1
Promoting Overall Quality of Education
B a s e d o n a vis io n a ime d a t pro vid in g qu ality S e rvic e s in e duc atio n al te s tin g a n d a ss e s sm e n t me ch a n is m s fo r vario u s s take h o lde rs , NTS is co mm itte d to pro mo tin g th e o ve ra ll qu a lity o f e du c atio n as a valu e - adde d adju n c t.
1.3.2
Performance Evaluation
NTS u n de rta ke s pro gra m s th a t are aim e d at e s tablis h in g a c re dible , te ch n ic al ly a ppro pria te and a c c u ra te s ys tem of pe rfo rm an c e e valu atio n of s tu de n ts / c a n dida te s of va rio u s e du c atio n al in s titu tio n s at dif f e re n t le ve ls .
1.3.3
Assessing Knowledge, Skills & Professional Abilities
Student Guide
3
I t a ls o e xte n ds se rvic e s f o r th e e m plo ye d an d u n em plo ye d pro fe s s io n als to ge t s a tis f a c to ry j o bs in th e ir re le van t are a th ro u gh an ass e s sm e n t o f th e ir kn o w le dge ba s e , s kil ls , a n d pro f e s s io n al abili tie s .
1.3.4
A Rapidly Growing & Credible Entity
NTS is a ra pid ly gro w in g a n d c re dible e n tity o f n atio n al re pu te . I ts c o n te xt an d po te n tia l co in c ide s w ith th e e xpre s se d ne e d o f th e Go ve rn me n t fo r th e e s ta blis h m e n t of a Na tio n a l Ac c re ditat io n C o u n c il an d Te s tin g Se rvic e .
1.3.5
Conducting Various Types of Tests
W h ile th e be gin n in gs we re made by c o n du c tin g Ge ne ral Te s ts th ro u gh an I Tf oc u s e d th ru s t, NTS h a s e xpan de d its se rvic e s to o th e r dis c ipl in e s o f e du c a tio n a l te s tin g. I t no w pro vide s se rvic e s f o r co n du c tin g Su bje c t Te s ts by pro vidin g fa c ili tie s bo th fo r in div idu al c an didate s an d in s titu tio n s . Th e se te s ts a re pre pa re d a n d a s se s s e d by e xpe rts an d pro f es s io n als f ro m re le van t f ie lds .
1.3.6
Linkages & Networks
NTS n ow h a s grow in g lin kage s an d as s o c iatio n s w ith edu c atio n al an d pro f e ss io n a l o rga n iza t io n s & I n s titu tio n s , in c lu din g th o se en gage d in tale n t s e a rc h a n d c a ree r & e du c a tio n al pro mo tio n ac tiv it ie s , at bo th n atio n al an d in te rn at io n a l le ve ls .
1.4
NTS- BENEFITS
NTS a im s a t be in g be ne f ic ia l f o r bo th s tu den ts an d in s ti tu te s .
1.4.1
Students
NTS Te s ts e n a ble s tu de n ts to draw be n ef its in a n um be r o f w ays : • • • •
•
I t pro vide s a s in gle s ta n dard f o r me as u rin g kn o w le dge bas e an d als o s kil l le ve l eva lu a t io n o f c a n dida te s . C a n dida te s c a n h a ve a m o re tran s pare n t, c re dible an d s tan dardi ze d a s s e s sm e n t of th e ir kn o w le dge. B es ide s be in g e co n om ic a l, NTS dec lare s th e te s t res u lts in ju s t a fe w days tim e . NTS ’ s co re s a re a re lia ble so u rc e to m e as u re c an didate s ’ kno w le dge in c om mo n ly ta u gh t a c a de m ic co u rs e s . Te s tin g th ro u gh NTS a u tom atic al ly le ads to s tan dardiza tio n at a n atio n al le ve l, wh ic h e lim in a te s c h an ce s o f large dro po u ts du rin g th e c o u rs e of e du c a tio n .
1.4.2
Institutions
B es ide s s tu de n ts , NTS is a ls o u se f u l f o r th e e du c atio n al in s titu te s an d s im ilar e n titie s : • • •
I ns titu te s , w is h in g to ge t a dm is s io n te s ts pre pare d f o r th e ir c an didate s , an d a ls o w a n tin g to ge t th e m s c o re d in a m o re tran s pare n t an d in a le s s tim e c o n s um in g m a n ne r c a n re ly o n NTS . Th is te s tin g se rvic e is h igh ly re liab le , ef f ic ie n t an d s tan dardize d; so an y of th e in s titu te s c an s h a re th e ir re s po n s ibil ity w ith NTS . Th e pre pa ra t io n a n d h o ldin g o f te s ts c o ns u me a lo t of tim e an d ef fo rt. Th e in s ti tu te s c a n le s s e n th is bu rde n o f re s po n s ibi li ty of co n du c tin g te s ts by s h a rin g it w ith NTS . Pre paratio n of re gis trat io n fo rm s, ro ll n um be r s lips , qu e s tio n pa pe rs , a n sw e r s he e ts , s atis f ac to ry arran ge me n ts f o r in vigi lat io n , pa pe r m a rkin g, re s u lt de c laratio n e tc . are arran ge d by NTS .
Student Guide
4
•
Th e I ns titu te s c a n to ta lly re ly o n NTS f o r e ff ic ie n c y of S e rvic e s in c lu din g tra n s pa re n c y o f re s u lts .
•
Th e I n s titu te s a re pro vide d w ith a c re dible s ys te m of pe rf o rm an ce ran kin g.
1.5
NTS – SERVICES
NTS provides its services in vast areas:
1.5.1
National Aptitude/General Testing
NTS conducts General Tests so as to evaluate the critical thinking skills of analytical reasoning and also performance assessment of candidates with regard to quantitative & verbal ability. General Tests also called National A p t i t u d e T e s t s , h e l p e s t a b l i s h i n g a r e l i a b l e a n d c r e d i b l e m e a s u r e o f ju d g i n g the knowledge base of students in commonly taught programs.
1.5.2
Services - Measuring Knowledge Base and Skill Levels
T h e N T S S u b j e c t T e s t s a r e p r e p a r e d a n d de s i g n e d w i t h a v i e w t o a s s e s s i n g the qualifications, knowledge base, competency and skill level of the c a n d i d a t e s i n a s pe c i f i c a r e a o f s t u d y .
1.5.3
Services for Test Preparation
NTS provides complete guidelines with regard to Test Preparation. A guide for users is available on our website as well as in the market in printed form. M o de l Q u e s t i o n s a n d S a m p l e T e s t s a r e a l s o a v a i l a b l e o n t h e w e b s i t e f o r helping the candidates to practice and be well prepared for the test. Furthermore Reference Books are also recommended by NTS to be an a d d i t i o n a l s o u r c e o f h e l p f o r t h e t e s t t a k e r s f o r c o m p u t e r S c i e n c e S u b je c t Tests.
1.5.4
Administrative Services
NTS provides an administrative service for not only the candidates but also t h e i n s t i t u t i o n s . A l l a dm i n i s t r a t i v e a r r a n g e m e n t s r e g a r d i n g r e g i s t r a t i o n , t e s t center selection, test execution, result preparation and then its reporting etc, are taken as a responsibility by NTS.
1.5.5
Admission Test Services for Institutions
NTS conducts Admission Tests for various institutes and institutions, all s e r v i c e s l i k e t h e a r r a n g e m e n t s o f t e s t r e g i s t r a t i o n , p a p e r ge n e r a t i o n , t e s t e x e c u t i o n , p a pe r m a r k i n g , r e s u l t d e c l a r a t i o n e t c . a r e p r o v i d e d b y N T S f o r these entities.
1.5.6
Services for Online Testing
NTS also conducts Online Tests for the candidates’ efficient and credible evaluation of their knowledge and skills. Arrangements like the availability of l a b s , c o n t e n t d e ve l o p m e n t f o r t h e a s s e s s m e n t , o n l i n e p a p e r g e n e r a t i o n a n d t e s t e x e c u t i o n a n d o n l i n e r e s u l t f o rm a t i o n i m m e d i a t e l y a f t e r t h e t e s t , a r e made by NTS.
1.5.7
Establishing Performance Ranking
NTS also assists in carrying out an estimated ranking of students as well as p r o f e s s i o n a l s . T h i s r a n k i n g i s n o t o n l y i n a p a r t i c u l a r s u b je c t o n a g e n e r a l competency level but also helps in the identification of areas of strengths and weaknesses in its sub-contents on a disaggregated basis.
Student Guide
5
1.5.8
Services for Score Reporting
F o r G e n e r a l T e s t s , N T S d e c l a r e s i t s r e s u l t s e le c t r o n i c a l l y w i t h i n s e v e n d a y s o f the test being conducted, the results of each candidate are sent to their homes through a fast and reliable courier service. The result of Online Subject Tests is displayed online immediately after the c a n d i d a t e c o m p l e t e s h i s / h e r t e s t . T h e s c o r e o f c a n d i d a t e s i s a l s o r e po r t e d i n the form of a certificate at their respective addresses.
1.5.9
Services to Facilitate Employment
NTS extends its services for employed and unemployed candidates to get s a t i s f a c t o r y j o b s i n t h e i r r e l e v a n t a r e a s t h r o u g h a ve r y e s t i m a t e d a n d c a r e f u l j u d g m e n t o f t h e i r k n o w l e d ge b a s e a n d s k i l l s . I t f a c i l i t a t e s a c c e s s t o j o b o p po r t u n i t i e s f o r v a r i o u s p r o f e s s i o n a l s a n d c a n d i d a t e s bo t h w i t h i n t h e c o u n t r y a n d a b r o a d o n t h e b a s i s o f t h e i r s c o r e s i n NTS Subject Tests.
1.5.10 Statistical Analysis and Reports
NTS by virtue of it’s flexible and user friendly solution can better help the institutions and organizations to have statistical analysis and report for administrative tasks and it will ultimately lead to true decision making and managerial tasks.
1.5.11 Survey
N T S h a s v e r y r o b u s t a n d a c c u r a t e s y s t e m f o r p r o c e s s i n g f o rm s a n d s u r v e y s . In addition to the educational and professional testing services NTS has the survey facility for different organizations, government data collection and other methods to get feedback from people.
1.6 1.6.1
NTS – PARTNERS COMSATS Institute of Information Technology
COMSATS, through a notification in 1979, setup the COMSATS Institute of I n f o rm a t i o n T e c h n o l o g y ( C I I T ) , w h i c h b e c a m e f u n c t i o n a l i n A p r i l 1 9 9 8 . C I I T is a world-class teaching institute, creating knowledge base and advanced technologies that are intended to shape the new direction of the country and educate its future leaders for the 21st century. The aim of the Institute is to train the country’s human resource in the field o f I n f o rm a t i o n T e c h n o l o g y s o a s t o e q u i p t h e m w i t h e m e r g i n g I T t r e n d s . T h e C I I T i s f u l l y e q u i p p e d t o c o pe w i t h t h e n e e d s o f a g r o w i n g a n d f a s t - p a c e d I T industry, flexible enough to adapt to the challenges of the future. The CIIT has a mission to deliver new ideas and products through research, development and education in strategic partnership with IT industry and organizations. CIIT has a total of five campuses across the country, two in Islamabad, one e a c h i n W a h , A b bo t t a b a d a n d L a h o r e .
Online Test
Student Guide
6
N T S i s c u r r e n t l y c o n d u c t i n g o n l i n e e x am ( 2 0 % ) f o r t h e s t u d e n t s a t C I I T A b b o t t a b a d a n d i t w i l l l i k e l y t o b e a do p t e d i n a l l t h e c a m p u s e s i n n e a r f u t u r e . S t u d e n t s w h i l e t a k i n g t h i s k i n d o f t e s t c a n h a v e a b e t t e r v i s i o n a n d f ro m academic and teaching point of view NTS can prepare different statistical a n a l y s i s a n d r e p o r t s t o i m p r o v e t h e q u a l i t y o f e du c a t i o n , p erformance and
knowledge.
A d m issio n Test s for CI I T N a t i o n a l T e s t i n g S e r v i c e ( N T S ) h as be e n c o n d u c t i n g A d m i s s i o n T e s t s f o r C I I T across all its campuses since July 2002. The General Tests are conducted for admissions at both Graduate and Post-Graduate levels catering for candidates from different educational backgrounds.
1.6.2
Virtual University
Virtual University (VU) is one of the priority projects of the Ministry of Science and Technology (MoST), which participates as a key contributor in t h e s o c i o - e c o n o m i c de v e l o p m e n t o f t h e c o u n t r y . V U i s b a s e d o n a n e x c e l l e n t telecommunication infrastructure and provides educational facilities on a nationwide basis.
N TS Co nd uc t s Ad m issio n Test s fo r VU NTS conducted admission tests (NAT-IS) at various Private Virtual Centers (PVCs) of VU in August ’02. To facilitate the conduct of these Tests, NTS provided Services on a countrywide basis simultaneously in 135 centers spread over 51 major cities of Pakistan. O n b e h a l f o f t h e s a t i s f a c t o r y a n d s u c c e s s f u l s e r v i c e s p r o v i de d b y N T S , V i r t u a l U n i ve r s i t y r e p o s e d i t s c o m p l e t e t r u s t i n t h e a u t h e n t i c i t y a n d c r e di b i l i t y o f NTS’ initial testing for the university which they reconfirmed by their pledge to continue availing the services of NTS for any further testing. We certainly view this with great appreciation and encouragement.
1.6.3
Higher Education Commission (HEC)
The Higher Education Commission has been setup to facilitate the d e v e l o p m e n t o f t h e u n i v e r s i t i e s o f P a k i s t a n t o be c o m e w o r l d - c l a s s c e n t e r s o f e d u c a t i o n , r e s e a r c h a n d d e v e l o pm e n t . A critical additional challenge is to vastly increase access to higher education in Pakistan so that our talented p e o p l e a r e n o t d e n i e d a v e n u e s f o r pe r s o n a l a n d p r o f e s s i o n a l g r o w t h . The H E C i n t e n d s t o p l a y i t s p a r t i n s pe a r h e a d i n g t h e b u i l d i n g o f a k n o w l e d g e based economy in Pakistan. People are the real assets of Pakistan however it i s o n l y t h r o u g h e d u c a t i o n a n d r e s e a r c h t h a t o u r c o u n t r y c a n p r o f i t f ro m t h i s great asset. A well-educated graduate is the building block of a knowledgebased economy, and it is for this reason that the HEC is focusing on the issue of “quality” of higher education.
Co nd uc t ing Sc ho la r ship Test s fo r H EC In February 2003 NTS successfully conducted Subject tests for various areas of study across Pakistan on behalf of the Higher Education Commission and since then all the scholarship tests (Subject/General) offered by HEC are carried out by NTS.
1.6.4
Pakistan Telecommunication Corporation Limited (PTCL)
Student Guide
7
P a k i s t a n T e l e c o m m u n i c a t i o n C o r p o r a t i o n ( P T C ) s e t s a i l s f o r i t s vo y a g e o f g l o r y i n D e c e m b e r 1 9 9 0 , t a k i n g o ve r o p e r a t i o n s a n d f u n c t i o n s f r o m P a k i s t a n T e l e p h o n e a n d T e l e g r a p h De p a r t m e n t u n de r P a k i s t a n T e l e c o m m u n i c a t i o n C o r p o r a t i o n A c t 1 9 9 1 . T h i s c o i n c i d e d w i t h t h e G o v e r n m e n t ' s c o m pe t i t i v e policy, encouraging private sector participation and resulting in award of l i c e n s e s f o r c e l l u l a r , c a r d - o pe r a t e d p a y p h o n e s , p a g i n g a n d, l a t e l y , d a t a communication services. S i n c e t h e n , P T C L h a s be e n w o r k i n g v i g o r o u s l y t o m e e t t h e d u a l c h a l l e n g e o f t e l e c o m d e v e l o pm e n t a n d s o c i o - e c o n o m i c u p l i f t o f t h e c o u n t r y . T h i s i s c h a r a c t e r i z e d b y a c l e a r a p p r e c i a t i o n o f o n go i n g t e l e c o m s c e n a r i o w h e r e i n convergence of technologies continuously changes the shape of the sector. A measure of this understanding is reflected by progressive measures such as e s t a b l i s h m e n t o f t h e c o m p a n y ' s m o b i l e a n d I n te r n e t s u b s i d i a r i e s i n 1 9 9 8 . The telecom sector of Pakistan has also entered into a new era. The monopoly of PTCL is now over and the sector is moving towards liberalization. While liberalization and competition are synonymous, the future scenario also poses some challenges to the market dominance of PTCL. The Company is ready to face this challenge and maintain its dominating position, while guarding its r e v e n u e s t r e a m s i n t h e f a c e o f f o r t h c o m i n g c o m pe t i t i o n .
Recruitment Test for PTCL Being an elite client, PTCL uses the services of National Testing Service [NTS] f o r h i r i n g pe o p l e f o r t h e o r g a n i z a t i o n . A ro u n d t h o u s a n d s o f c a n d i d a t e s a p p l y for jobs in PTCL through the testing services of NTS.
1.6.5
Bolan Medical College
Bolan Medical College as seat of medical Balochistan has a remarkable history.
education
in
the
province
of
Admission Test for BOLAN Medical College
N T S h a s b r o a d e n e d i t s s e r v i c e s a n d h a s a l s o c o n d u c t e d a dm i s s i o n t e s t f o r Bolan Medical College Quetta, the conduct and outcome of which was to the entire satisfaction of all candidates. The students could tally their score with the key displayed afterwards.
1.6.6
Engineering University Khuzdar
N T S do e s n o t l i m i t i t s s e r v i c e s t o a s p e c i f i c e d u c a t i o n a l g r o u p b u t h as a l s o p r o v i d e d i t s s e r v i c e s f o r t h e c o n d u c t o f A dm i s s i o n T e s t s a t E n g i n e e r i n g University Khuzdar.
6.6.7 Federal Urdu University of Arts, Science and Technology, Islamabad T h e g o v e r n m e n t h a s e s t a b l i s h e d a F e de r a l U r d u U n i v e r s i t y o f A r t s , S c i e n c e s and Technology Islamabad through an ordinance with Urdu to remain the main language of instruction and teaching. The university will have its p r i n c i p a l s e a t a t I s l a m a b a d a n d w i l l h a v e t h e F e de r a l G o v e r n m e n t U r d u Science College, Karachi, and Federal Government Urdu Arts College, Karachi, as constituent institutions. Under the rule, the university will have academic, financial and administrative autonomy, including the power to employ o f f i c e r s , t e a c h e r s a n d o t h e r e m p l o y e e s w h i l e t h e u n i v e r s i t y w i l l be c o n t r o l l e d b y a s e n a t e , a s y n d i c a t e a n d a n a c a de m i c c o u n c i l .
Student Guide
8
Recruitment Test for Urdu University The National Testing Service [NTS] provided its services to the University for t h e h i r i n g p u r p o s e s o f t h e i r f a c u l t y m e m b e r s i n e i g h t s u b je c t s t h u s m a k i n g the selection transparent.
6.6.8
Board of Intermediate and Secondary Education, Abbottabad
Recruitment Test
Abbottabad Educational Board signed up the services of NTS for hiring e m p l o y e e s . A C o m pu t e r S c i e n c e s u b j e c t t e s t w a s c o n d u c t e d f o r t e s t i n g t h e academic skills of the candidates. The assessment was later used to determine the merit for final selection.
6.6.9
Others
NTS now has growing linkages and associations with many educational and p r o f e s s i o n a l o r g a n i z a t i o n s a n d i n s t i t u t i o n s , i n c l u d i n g t h o s e e n g a ge d i n t a l e n t s e a r c h , c a r e e r a n d e d u c a t i o n a l p r o m o t i o n a l a c t i v i t i e s , a t bo t h n a t i o n a l a n d international levels. As a rapidly growing and credible entity of national repute, the context and potential of NTS coincide with the expressed need of the Government for the establishment of a National Accreditation Council and Testing Service.
1.7
NTS – Tests
N T S ge ne r ally co nducts tw o kinds o f te sts: • •
General Tests Subject Tests
T he se are co nducte d bo th as co mpute r - aide d, pape r base d and o nline te sts, as re quir e d.
General Tests NTS co n du c ts dif fe re n t u n de rgra du a te s tu de n ts ;
type s
of
Ge n e ral
Te s ts
for
th e
gradu ate
an d
T h e G e n e r a l T e s t c o m p r i s e s Q u a n t i t a t i v e , A n a l y t i c a l R e as o n i n g a n d V e r b a l Sections for assessment.
Subject Tests Subject Tests are designed to evaluate the educational skills in a specific a r e a o f s t u d y . S o f a r N T S h a s c o n d u c t e d t h e S u b je c t T e s t i n d i f f e r e n t subjects:
1. 2. 3. 4. 5.
Physics Electronics/Engineering Biology Chemistry Pharmacy
Student Guide
9
6. Computer Science 7. Mathematics 8. Telecommunication 9. Biochemistry 10. Management Science 11. Health Sciences 12. Environmental Science 13. Earth Science 14. Statistics 15. Veterinary Science 16. Economics 17. Agricultural Science 18. Islamic Studies 19. Pakistan Studies 20. English
1.8
NTS – TEST CENTERS
NTS’ Head Office is in Islamabad, it conducts tests across Pakistan, for any Institute or institution requesting our services, providing sufficient time is provided for preparation.
1.9
SCHEDULE AND INFORMATION
There are several sources for obtaining information and schedules on the NTS Tests.
i ii iii iv
Advertisements through Printed Media Advertisements through Electronic Media NTS Allied Institutions NTS and its Allied Institutions' Website
1.10 CONTACT NTS For Tests and Test Center queries related to Score Reporting, and also for other reasons like putting complaints or providing Feedback, you may: Visit NT S at its w e bsite i.e . htt p :/ / w w w .nt s.o r g .p k W r ite to N T S at Sec r et a r y N at io na l Test ing Ser v ic e (N TS) Offic e # 10 – 11, Fir st Flo or Pla za 2000 Plo t # 43, Ma r kaz I- 8, I slam a b a d . Email Dir e cto r NT S at
Student Guide
d ir ec t or nt s@c iit .net .p k d ir ec t or nt s@nt s.o r g .p k
10
Email N T S at
nt sc o or d @c iit .net .p k sup p o r t @nt s.o r g .p k
TECHNICAL REVIEW
Student Guide
11
2.
Technical Procedures and Operations
2.1 Content Collection As NTS is an autonomous body following a set of SOPs, trying to maintain the National and International state of the art technology and standards. Keeping this vision in mind, NTS team would like to share the most important and central activity that is how the contents are being gradually increased, updated, the template upon which questions are being collected and after carefully collecting the questions how quality is controlled. Template creation and paper generation for individual tests is flexible and fair enough to meet the requirements of different clients and produces results is different scenarios reliably. NTS test engine and paper processing mechanisms are matured and error prone and we are still trying to introduce new features. NTS is highly conscious about the sensitive issue of contents. To date, NTS has conducted
The Subject Test in several subjects and has formulated Subject Committees for each of those subjects. The committee members consist of subject specialists from various institutes and organizations, providing valuable input in building up an authentic and reliable database. Subject Committees These committees are made for each subject i.e. Engineering, Biology, Physics etc., comprising of a Chairperson being a PhD doctor and at least four members who have a Masters Degree. Making curricula, policies, identifying other subject experts for the Review and Question Making Committee are all responsibilities of this working group. Other committees formulated by the Subject Committee are: i. Review Committees ii. Question Making Committees NTS operations and methodology for content collection and improved quality is very secure and protected. We put the contents in encrypted/coded format into the central database along with other precautions to make the system safe and fool proof. NTS has huge central database in different areas of study. The method of question collection is of two types.
• •
Paper Base Content Collection Online Content Collection
2.1.1 Paper Based Content Collection For paper based content collection a template has been designed with some fields and attributes, and information required are associated with each question. Some are narrated • Education Level of the Question • Difficulty Level of the Question (Easy, Moderate, Difficult) • Reference Information As the question can be obtained from the book, own creativity (self-made), website etc., in any case the additional information is required. As an example in case a question is picked from the book the following information will be linked with the question • •
•
Title & edition of the referenced book Publisher of the referenced book Topic & subtopic the questions belong to
Student Guide
12
•
Page No. of the Book.
Student Guide
13
The Sample Template for Content Collection Field Subject: Section: Branch/Topic Sub-Topic Type:
Conceptual Practical logical
Statement:
Difficulty Level:
Easy Moderate Hard
Max/Min Time Correct Answer: Possible Choice: (Min 4, Max 5) A
B C
D
E
Author: Website: Book:
Student Guide
Details:
14
After collecting the paper based question it is carefully entered into the central repository by skilled Data Entry Operators. Each Question passes through different stages of Quality Control and undergoes the detailed review to ensure the Quality and finally it becomes the part of NTS Question Bank.
2.1.2 Online Content Collection As it is the age if IT and internet so NTS has also the online mechanism for building question bank we have the user friendly web based front end to collect the questions in different disciplines. The requirement is almost the same i.e. to ensure the quality of questions.
The Snapshot of the Front End for Online Content Collection is Give Below
Student Guide
15
2.2 Review Process 2.2.1 Review by Reviewer As soon as question is added by the data entry operator, it becomes available to the reviewer for review. Reviewer takes care of the typing mistakes, spelling, and formatting (font face, font size) of the question. Questions that are marked as reviewed by reviewer become noneditable for this operator.
1.2
Technical Review
Student Guide
16
After review from reviewer, it is then viewed technically by a person/committee nominated by the peer committee relevant to that subject for the verification of the educational level, difficulty level, quality, correct answer, time, etc., regarding each question
2.2.3 Grammatical Review The grammatical reviewer takes care of all the questions for grammatical and language point of view. Note: in both cases either paper based or online content collection, all the question passes through the same review process.
2.3
Paper Generation Process
NTS information system is capable of generating fully-formatted paper by selecting questions randomly and/or according to the template requirement. The Following can be specified as an input while generating the Paper
Education level of the paper Subjects/Topics/Subtopics to be included in the paper. No. of easy, moderate, difficult questions to be included from each subject Selection of the questions can be controlled by including or excluding topics/subtopics. Selection of a question can also be limited on the basis of “No. of times question used”
Note: By default, the system automatically selects 30% easy, 40% moderate and 30% difficult questions to generate a paper. However this can be changed. After the template is defined, as many sample papers can be generated as required having the following in it;
Each sample paper can be a distinct one. Each sample paper can be re-randomized to change the sequence of the question.
If the No. of questions selected from a topic or subtopic is not according to requirement, then same template can be redefined on topic or subtopic level by limiting the No. of questions from each topic or subtopic. The discussed process of paper generation is for both Paper based and online test. For online test the questions are picked randomly from the template constructed from the question bank and the test engine manipulates the sequence of questions for every candidate
Test Engine For online test NTS has developed a very robust, user friendly, stable and secured Test Engine for online test. It has very distinguished features like on spot registration, shuffling the questions randomly for each candidate, result display immediately after the completion of test, tracking of user session, flexible enough to cope with the requirement of a particular exam, continuous time monitoring, pass box for placing questions temporarily, pictures handling in the question statement and question choice, can accommodate multiple true answers, manage scenario based questions, and toggle freely between Question Box and Pass Box.
Student Guide
17
Glimpse of the web based online test application is given below User Registration Process
Instructions for the Test
Student Guide
18
Question Box
Pass Box
Student Guide
19
Paper Checking and Result Preparation NTS has very reliable, error free, efficient and transparent system for paper checking and result preparation. It is fast enough and flexible to cope with the requirements of any client. As a reference we are quoting the Bolan Medical College, Quetta “Entry Test” we meet the requirement of delivering the result after few hours on the same day the test was conducted. The result was handed over along with merit lists in their required format and the notable feature was “display of answer key on the spot” form where any candidate could calculate his/ her result because the carbon copy of answer sheet was given to the candidates after they finished their test. Despite all these facts there was not a single error in the result which shows the competency, reliability, transparency of NTS Paper Checking and Result Preparation System. We are continuously improving our System day by day by introducing new features and customization. A team of skilled professionals are dedicatedly working on the task.
Student Guide
20
Sample of an Answer Sheet is shown.
Student Guide
21
PATTERNS AND PRACTICE
Student Guide
22
Quantitative Ability
2
The Quantitative section measures your basic mathematical skills, understanding of elementary mathematical concepts, and the ability to reason quantitatively and solve problems in a quantitative setting. There is a balance o f q u e s t i o n s r e q u i r i n g b a s i c k n o w l e d g e o f a r i t h m e t i c , a l g e b r a , ge o m e t r y , a n d data analysis. These are essential content areas usually studied at the high school level. T h e q u e s t i o n s i n t h e q u a n t i t a t i v e s e c t i o n c a n a l s o be f r o m • •
•
Dis c re te Q u a n tita t ive Q ue s tio n Q u a n tita ti ve C om pa ris o n Q u e s tio n Da ta I n te rpre ta tio n Q ue s tio n e tc.
The distribution in this guide is only to facilitate the candidates. This distribution is not a part of test template, so, a test may contain all the questions of one format or may have a random number of questions of different formats. T h i s c h a p t e r i s d i v i d e d i n t o 4 m a jo r s e c t i o n s . T h e f i r s t d i s c u s s e s t h e s y l l a b u s /contents in each section of the test respectively and the remaining three s e c t i o n s a d d r e s s t h e q u e s t i o n f o rm a t , g u i d e l i n e s t o a t t e m p t t h e q u e s t i o n s i n each format and some example questions.
2.1
General Mathematics Review
2.1.1
Arithmetic
The following are some key points, which are phrased here to refresh your knowledge of basic arithmetic principles.
Basic arithmetic
•
F o r a n y nu m be r a , e xa c tly o ne of th e f o llo w in g is tru e : o a is n e ga tive
o o
a is ze ro a is po s itive
a = −a only if a = 0 )
•
Th e on ly n um be r th a t is e qu al to its o ppos ite is 0 (e . g.
•
I f 0 is mu ltip lie d to a n y o the r nu m be r, it w ill m ake it ze ro ( a × 0 = 0 ).
•
Pro du c t o r qu o tie n t o f two n u m be rs of th e s am e s ign are alw ays po s itive a n d of a dif f e re n t s ign a re alw ays n e gative . E. g. if a po s itive n u m be r is m u ltipl ie d to a ne ga tive n um be r th e re s u lt w ill be ne gative an d if a ne gative n u m be r is divide d by a n o th e r n e gative n u m be r th e re s u lt w ill be po s itive .
S ee th e f o llo w in g ta ble s fo r a ll co m bin atio n s .
Student Guide
23
+
÷ or ×
+
=
+
+
÷ or ×
−
=
−
−
÷ or ×
+
=
−
−
÷ or ×
−
=
+
•
Th e s um of tw o po s itive n um be rs is alw ays po s itive .
•
Th e s um of tw o n e ga tive nu m be rs is alw ays ne gative .
•
S u btra c tin g a n u m be r f rom an o th e r is th e s am e as addin g its o ppos ite
•
1 Th e re c ipro c a l of a n u m be r a is a
•
Th e pro du c t o f a n um be r a n d its re c ipro c al is alw ays on e
a − b = a + ( −b )
a×
•
1 =1 a
Div idin g by a n um be r is th e s ame as m u ltip lyin g by its re c ipro c al
a ÷b = a ×
1 b
•
E ve ry in te ge r h a s a f in ite se t o f fac t o r s ( divis o rs ) an d an in f in ite s e t of mul t i p l ie r s.
•
I f a a n d b a re tw o in te ge rs , th e fo llo w in g fo u r te rm s are s yn o n ym s o a is a di vi so r o f b
o o o
a is a f a c t or of b b is a di vi si b l e b y a b is a mul t i pl e of a
Th e y a ll m ea n th a t wh e n a is divide d by b th e re is no re mai nd e r . •
Po s itive in te ge rs , o th e r th a n 1, h ave at le as t two po s itive f ac to rs .
•
Po s itive in te ge rs , o th e r th a n 1, wh ic h h ave e xac tly two f ac to rs , are kn o w n a s pr i me numb e r s.
•
E ve ry in te ge r gre a te r th a n 1 th at is no t a prim e c an be w ritte n as a pro du c t o f prim e s . To f in d th e prim e f a c to riza tio n of an in te ge r, f in d an y tw o fac to rs o f th at n u m be r, if bo th a re prim e s, yo u are do ne ; if no t, c o n tin u e f ac to riza tio n u n til e a c h fa c to r is a prim e . E . g. to f in d th e prim e fa c to riza tio n of 48, tw o f ac to rs are 8 an d 6. Bo th o f th e m a re n o t prim e n um be rs , s o co n tin u e to f ac to r th em . F a c to rs o f 8 a re 4 a n d 2, a n d of 4 are 2 an d 2 ( 2 × 2 × 2) . F a c to rs o f 6 a re 3 a n d 2 ( 3 × 2) . S o th e n um be r 48 c a n be w ritte n as 2 × 2 × 2 × 2 × 3.
Student Guide
24
•
Th e L e a s t Co mm o n M u ltip le ( LC M ) of two in te ge rs a an d b is th e s m alle s t in te ge r wh ic h is divis ib le by bo th a an d b, e . g. th e LC M o f 6 an d 9 is 18.
•
Th e G re a te s t Co mm o n Divis o r (G C D) o f tw o in te ge rs a an d b is th e large s t in te ge r wh ic h divide s bo th a an d b, e. g. th e G C D o f 6 an d 9 is 3 .
•
Th e pro du c t o f G C D a n d L C M of two in te ge rs is equ al to th e pro du c ts of n u m be rs its e lf . E. g. 6 × 9 = 54 3 × 18 = 54 ( w he re 3 is G C D an d 18 is LCM o f 6 an d 9) .
•
E ve n nu m be rs a re a ll th e mu lt iple s of 2 e. g. (… , − 4, − 2, 0, 2, 4, … )
•
O dd n um be rs a re a ll in te ge rs no t divis ib le by 2 ( … , −5, −3, −1, 1, 3, 5, … )
•
I f tw o in te ge rs a re bo th eve n o r bo th o dd, th e ir s um an d dif fe re n c e are e ve n.
•
I f o n e in te ge r is e ve n a n d th e o th e r is o dd, th e ir s um an d dif fe re n c e are o dd.
•
Th e pro du c t o f tw o in te ge rs is e ve n u n le s s bo th o f th e m are o dd.
•
W h e n a n e qu a tio n in vo lve s m o re th an o ne o pe ratio n , it is im po rtan t to c arry th e m o u t in th e co rre c t o rde r. Th e co rre c t o rde r is P are n th e se s , E xpo ne n ts , Mu ltip li c a t io n a n d D ivis io n , A dditio n an d S u btrac tio n , o r ju s t th e f irs t le tte rs P EMD A S to re me m be r th e pro pe r o rde r.
Ex p o nent s a nd Ro ot s
•
R e pe a te d a dditio n o f th e s am e n u m be r is in dic ate d by mu ltip lic at io n : 17 + 17 + 17 + 17 + 17 = 5 × 17
•
R e pe a te d m u ltipl ic a t io n of th e s ame n um be r is in dic ate d by an e xpo n e n t: 5 17 × 17 × 17 × 17 × 17 = 17
5 I n th e e xpre s s io n 17 , 17 is c alle d b ase an d 5 is th e e xp o ne nt. 1
n
•
F o r a n y nu m be r b: a s f a c to r.
•
F o r a n y nu m be rs b a n d c a n d po s itive in te ge rs m an d n : o b m b n = b m +n o o o
•
= b an d b
= b × b × … × b, wh e re b is us e d n tim e s
bm = b m −n bn (b m ) n = b mn b m c m = (bc) m
I f a is n e ga tive , a
Student Guide
b
n
is po s itive if n is eve n , an d n e gative if n is o dd.
25
•
Th e re a re two n um be rs th a t s atis f y th e e qu atio n x = 9 : x = 3 an d x = −3 . Th e po s itive on e , 3, is c a lle d th e ( prin c ipa l) s qu are ro o t o f 9 an d is de no te d 2
by s ym bo l
0 =0 ,
•
9 . C le a rly, e a ch pe rfe c t s qu are h as a s qu are ro o t: 9 =3, 36 = 6 , 169 =13 , 225 = 25 e tc .
F o r a n y po s iti ve n u m be r a th e re is a po s iti ve n u m be r b th at s atis f ie s th e
a =b .
e qu a tio n
•
2 F o r a n y po s iti ve in te ge r, ( a ) =
•
F o r a n y po s iti ve n u m be rs a an d b:
ab = a × b
o
o
•
a +b ≠ 5=
as
a = b
and
b
a+ b 25 = 9 +16 ≠ 9 + 16 = 3 + 4 = 7
( −5) 2 =
n 2
F o r a n y nu m be r a ,
•
F o r a n y nu m be r a , b a n d c :
a =a n
a (b + c ) = ab + ac a n d if
a 2 = a is tru e on ly if a is
25 = 5 ≠ −5
•
•
a
2 A lth o u gh it is a lw a ys tru e th at ( a ) = a ,
po s itive a s
•
a× a =a.
.
a (b − c ) = ab − ac
a ≠0
(b + c) b c = + a a a
(b − c) b c = − a a a
I neq ua lit ies
•
F o r a n y nu m be r a a n d b, e xac tly on e o f th e fo llo w in g is tru e :
a >b
a =b
or
or
a
•
F o r a n y nu m be r a a n d b,
a > b m ean s
th at
a − b is
po s itive .
•
F o r a n y nu m be r a a n d b,
a < b m ean s
th at
a − b is
n e gative .
•
F o r a n y nu m be r a a n d b,
a = b m ean s
th at
a − b is
ze ro .
•
Th e s ym bo l
≥
me a n s gre a te r th an o r equ al to an d th e s ym bo l
le s s th a n o r equ a l to. E . g. th e s tate m e n t n u m be r gre a te r th a n 5. Th e s ta te m e n t
Student Guide
2 < x < 5 is
x ≥ 5 me an s
a n abbre viat io n of
≤
m e ans
th at x c an be 5 o r an y
2 < x an d x < 5 .
26
•
A ddin g o r s u btra c tin g a n u m be r to an in e qu ality pre s e rve s it.
•
If
a
a + c < b + c and a − c < b −c .
th e n
e . g. 5 < 6 ⇒ 5 +10 < 6 +10 •
•
A ddin g in e qu a li tie s in s am e dire c tio n pre se rve s it: If a < b
and
c
a +c < b +d .
th e n
M u ltip ly in g o r dividin g a n in e qu alit y by a po s iti ve n u m be r pre s e rve s it. I f
a < b and
•
5 −10 < 6 −10
and
c is
a po s iti ve n u m be r, th e n
a ×c < b ×c
an d
a b < c c.
M u ltip ly in g o r dividin g a n in e qu alit y by a ne gative n um be r re ve rs e s it. I f
a < b and
c is
a ne ga tive n um be r, th e n
a ×c > b ×c
an d
a b > c c.
•
I f s ide s o f a n in e qu a lity a re bo th po s itive an d bo th n e gative , takin g th e re c ipro c a l re ve rs e s th e in e qu alit y.
•
If
0 < x < 1 a n d a is
•
If
0 < x < 1 a n d m and n a re
•
If
0 < x < 1,
•
If
th e n
0 < x < 1 , then
po s itive , th e n
xa < a .
in te ge rs w ith
m>n,
th e n
xm < xn < x .
x > x.
1 1 >x >1 x and x
Pr o p er t ies o f Zer o •
0 is th e o n ly n um be r th a t is ne ith e r n e gative n o r po s itive .
•
0 is s m a lle r th a n e ve ry po s iti ve n u m be r an d gre ate r th an eve ry n e gative n u m be r.
•
0 is a n e ve n in te ge r.
•
0 is a m u ltiple o f e ve ry in te ge r.
•
F o r e ve ry n u m be r
a
:
•
F o r e ve ry n u m be r
a
: a×0 = 0.
•
F o r e ve ry po s itive in te ge r
Student Guide
a + 0 = a and a − 0 = a .
n : 0n = 0 .
27
a 0
•
F o r e ve ry n u m be r
a
( in c lu din g 0):
•
F o r e ve ry n u m be r
a
( o th e r th an 0) :
•
0 is th e o n ly n um be r th a t is e qu al to its o ppo s ite :
•
I f th e pro du c t o f tw o o r m o re n um be rs is 0, at le as t o n e o f th e m is 0.
a ÷ 0 and 0÷a =
are un de f in e d s ym bo ls .
0 = 0. a
0 = −0 .
Properties of One F o r a n y nu m be r
a : a ×1 = a a n d
a = a. 1
n : 1n = 1 .
•
F o r a n y nu m be r
•
1 is th e divis o r o f e ve ry in te ge r.
•
1 is th e s m a lle s t po s itive in te ge r.
•
1 is a n o dd in te ge r.
•
1 is n o t a prim e .
Fractions and Decimals •
W h e n a w ho le is divide d in to n e qu al parts , e ac h part is c alle d on e n th of th e w ho le , w ritte n
1. n
Fo r e xam ple , if a pizza is c u t ( divide d) in to 8 equ al
s lic e s , e a c h s lic e is on e e igh th (
1 ) 8
o f th e pizza; a day is divide d in to 24
e qu a l h o u rs , s o a n h o u r is on e twe n ty- fo u rth
1 ) of 12 8 tw e n ty- fo u rth ( ) 24 o ne tw e lf th (
1 ) 24
o f a day an d an in c h is
a fo o t. I f on e wo rks f o r 8 h o u rs a day, h e wo rks e igh t of a da y. I f a h o c ke y s tic k is 40 in c he s lo n g, it
(
m ea s u re s fo rty tw e lf th s
•
(
Th e n um be rs s u c h a s
1 , 8
40 ) of a 12 1 8 , 24 24
f oo t. an d
40 , 12
in wh ic h on e in te ge r is w ritte n
o ve r th e s e co n d in te ge r, a re c alle d fr ac t i o ns. Th e c en te r lin e is c alle d th e f ra c tio n ba r. Th e n um be r abo ve th e bar is c alle d th e nume r at or , an d th e n u m be r be lo w th e ba r is c a lle d d e no mi nat or . •
Th e de no m in a to r o f a f ra c tio n c an ne ve r be 0.
•
A f ra c tio n , su c h a s
1 , 24
in w h ic h th e de n om in ato r is gre ate r th an
n u me ra to r, is kn ow n a s a p r o pe r fr ac ti o n. I ts valu e is le s s th an on e.
Student Guide
28
•
A f ra c tio n , su c h a s
40 , 12
in w h ic h th e de n om in ato r is le s s th an n um e rato r, is
kn o w n a s a n i mpr o p e r f r a c t i o n. I ts valu e is gre ate r th an on e .
•
A f ra c tio n , su c h a s ,
12 12
in w h ic h th e de n om in ato r is e qu al to th e n u me rato r,
is a ls o kn o w n a s a n i mpr o p e r fr ac t i o n. B u t, I ts valu e is on e .
•
E ve ry f ra c tio n c a n be expre s s e d in dec im al fo rm (o r as a wh o le nu m be r) by divid in g th e n um be r by th e de n om in ato r.
3 = 0.3, 10 •
3 8 48 100 = 0.75, = 1, = 3, = 12.5 4 8 16 8
U n like th e e xa m ple s a bo ve , wh e n m os t f rac tio n s are co n ve rte d to de c im als , th e divis io n doe s no t te rm in ate , af te r 2 o r 3 o r 4 de c im al plac e s ; rath e r it go es o n f o re ve r w ith so me s e t of digits re pe atin g it.
2 3 5 17 = 0.66666..., = 0.272727..., = 0.416666..., = 1.133333... 3 11 12 15
Student Guide
29
•
To c om pa re tw o de c im a ls , fo llo w th e s e ru le s : W h ic h e ve r n um be r h as th e gre ate r n um be r to th e le f t o f th e dec im al po in t is gre a te r: s in c e 11 > 9, 11. 0001 > 9. 8965 an d s in c e 1 > 0, 1. 234 > . 8. ( Re c a ll th at if a de c im al is w ritte n w ith o u t a n um be r on le f t of de c im a l po in t, yo u m ay as s u me th at a 0 is th e re , so , . 8 = 0. 8) . I f th e n um be rs to th e le f t of th e de c im al po in t are equ al, pro ce e d as f o llo w s :
o
o
• • •
•
I f th e n um be rs do n o t h ave th e s ame n um be r o f digits to th e righ t o f th e dec im a l po in t, add ze ro e s to th e e n d o f th e sh o rte r o ne to m a ke th e m equ a l in le n gth . No w co m pa re th e n um be rs ign o rin g th e de c im al po in t. F o r e xam ple , to co m pare 1. 83 an d 1. 823, add a 0 to th e e n d of 1. 83 f o rm in g 1. 830. Now co m pare th em , th in k in g o f th em as wh o le n u m be rs w ith o u t de c im al po in t: s in c e 1830 > 1823, th e n 1. 830 > 1. 823.
Th e re a re two w a ys to c om pare f rac tio n s : o C o n ve rt th em to de c im als by divid in g, an d u se th e m e th o d alre ady de s c ribe d to co m pare th e s e de c im als . F o r e xam ple to c om pare and
1 , 4
> 0. 25,
o
co n ve rt th e m to de c im als .
2 5
2 1 = 0.4 an d = 0.25 . 5 4
Now , as 0. 4
1 . 4
>
2 5
C ro s s m u ltipl y th e f rac tio n s . Fo r e xam ple to co m pare c ro s s
2 5 •
1 4
S in ce
2 × 4 > 1× 5 ,
th e n
• •
1 , 4
mu ltip ly:
W h ile co m pa rin g th e f ra c tio n s , if th e y h ave s am e th e den o m in ato rs , th e
3 2 > . 5 5
If t he f r a c ti o ns ha ve t he same nume r at o r, t he fr ac t i o n wi t h t he sma l l e r de no mi na t o r i s gr e at e r. Fo r e xamp le
•
an d
2 1 > 5 4.
f ra c tio n w ith th e la rge r n u me rato r is gre ate r. F o r e xam ple
•
2 5
3 3 > . 5 10
Tw o f ra c tio n s a re c a lle d eq ui val e nt fr ac t io ns if bo th o f th e m h ave s am e de c im a l va lu e .
1 5 = 2 10
Fo r e xa m ple ,
a s bo th o f th e s e are e qu al to 0. 5.
A no th e r w a y to c he c k th e equ ivale n c e o f tw o f rac tio n s is to c ro s s - mu ltip ly. I f bo th o f th e pro du c ts a re s am e, th e f rac tio n s are equ ivale n t. Fo r E xam ple , to c om pa re
2 5
w ith
6 , 15
c ro s s - mu ltip ly. S in c e
2 × 15 = 6 × 5 ,
bo th o f th e
f ra c tio n s a re e qu iva le n t.
Student Guide
30
•
E ve ry f ra c tio n c a n be re du ce d to low e s t te rm s by dividin g th e n u me rato r a n d de no m in a to r by th e ir gre ate s t c om m on divis o r ( G C D) . I f th e G C D is 1,
10 , 15
th e f ra c tio n is a lre a dy in lo we s t te rm s . Fo r exam ple to re du ce
divide
bo th nu me ra to r a n d den o m in ato r by 5 (w h ic h is G C D o f 10 an d 15) . Th is w ill re du c e th e f ra c tio n to
•
To mu ltip ly two f ra c tio n s , m u ltipl y th e ir n u me rato rs an d mu ltip ly th e ir de no m in a to rs . F o r e xam ple
•
2 . 3 3 4 3 × 4 12 × = = . 5 7 5 × 7 35
To m u ltipl y a n u m be r to a f rac tio n , w rite th at n u m be r as a f rac tio n w ho s e de no m in a to r is 1. Fo r e xam ple
•
3 3 7 3 × 7 21 ×7 = × = = . 5 5 1 5 ×1 5
W h e n a pro ble m re qu ire s yo u to f in d th e f rac tio n o f a n um be r, m u ltip ly th at f ra c tio n w ith th e nu m be r. F o r e xam ple , to f in d two f if th (
2 ) 5
o f 200,
80
• •
2 2 200 400 × 200 = × = = 80 5 1 5/ m u ltipl y: 5 . a Th e re c ipro c a l of a f ra c tio n is ano th e r b
f rac tio n
b a
s in c e
a b × =1 b a
To divide on e f ra c tio n by th e o the r f rac tio n , m u ltip ly th e re c ipro c al of 2
divis o r w ith th e divide n d. Fo r e xam ple ,
•
22 11 22 7 2 ÷ = × = = 2. 7 7 7 11 1
To a dd o r s u btra c t th e f rac tio n s w ith s ame de n om in ato r, add o r s u btrac t n u me ra to rs and ke e p th e de n om in ato r. For e xam ple
4 1 5 + = 9 9 9
and
4 1 3 − = . 9 9 9
Per c ent s
•
Th e wo rd p e r ce nt me a n s hu n dre dth . W e us e th e s ym bo l % to e xpre s s th e w o rd pe r c e nt. F o r exa m ple “15 pe rc e n t” m e ans “15 hu n dre dth s ” an d c an be w ritte n w ith a % s ym bo l, a s a f rac tio n , o r as a de c im al.
20% =
20 = 0.20 . 100
•
To c on ve rt a de c im a l to a pe rc e n t, mo ve th e de c im al po in t tw o plac e s to th e righ t, a ddin g 0s is ne c e s s a ry, an d add th e pe rc e n t s ym bo l ( % ) . F o r e xam ple , 0. 375 = 37. 5% 0. 3 = 30% 1. 25 = 125% 10= 1000%
•
To c on ve rt a f ra c tio n to a pe rc e n t, f irs t co n ve rt th at f rac tio n to de c im al, th a n u s e th e m e tho d s ta te d abo ve to c o n ve rt it to a pe rc e n t.
•
To c on ve rt a pe rc e n t to a de c im al, mo ve th e de c im al po in t tw o plac e s to th e le f t a n d re mo ve th e % s ym bo l. A dd 0s if n e ce s s ary. F o r e xam ple , 25% = 0. 25 1% = 0. 01 100% = 1
•
Yo u s ho u ld be f am ilia r w ith th e fo llo w in g bas ic c o n ve rs io n s :
Student Guide
31
1 5 = = 0.50 = 50% 2 10 1 = 0.25 = 25% 4
1 2 = = 0.20 = 20% 5 10 3 = 0.75 = 75% 4 a : a % of
•
F o r a n y po s iti ve in te ge r
•
F o r a n y po s iti ve n u m be rs
•
Th e pe rc en t ch a n ge in th e qu an tity is
100 is
a.
a an d b : a % of b = b% of a actual change ×100% . original amount
Fo r e xam ple :
I f th e pric e o f a la m p goe s f ro m Rs . 80 to Rs . 100, th e ac tu al in c re as e is
20 1 × 100% = × 100% = 25% . 80 4 a < b a If , th e pe rc e n t in c re a s e in go in g f ro m to b is alw ays gre ate r pe rc e n t de c re a se in go in g f rom b to a . R s . 20, a n d th e pe rce n t in c re as e is
•
th an
•
To in c re a s e a n u m be r by k % , m u ltipl y it by 1 + k % , an d to de c re as e a n u m be r by k % , mu ltip ly it by 1 − k % . Fo r e xam ple , th e valu e of an in ve s tm e n t o f R s. 20, 000 af te r 25% in c re as e is 20, 000 × (1 + 25%) = 20, 000 × (1.25) = 25, 000 .
•
I f a n u m be r is th e re s u lt of in c re as in g an o th e r n um be r by o rigin a l n um be r divide it by 1 + k % , de c re a s in g a n o th e r n um be r by k % , 1− k% .
k% ,
to f in d th e
an d if a n um be r is th e re s u lt of to f in d th e o rigin al n um be r, divide it by
F o r e xam ple , Th e go ve rn me n t an n o u n ce d an 20% in c re as e in s alarie s . I f a f te r th e in c re me n t, Th e s alary of a partic u la r em plo ye e is R s . 18, 000, w h a t w a s th e o rigin a l s a la ry? O rigin a l s a la ry ( in R s. ) =
current salary 18, 000 18, 000 = = = 15, 000 1 + percent increase 1 + 20% 1.20
Ra t io s a nd Pr o p or t io ns
•
A ra t io is a f ra c tio n th a t c om pare s tw o qu an tit ie s th at are m eas u re d in th e s a me un its . Th e f irs t qu a n tity is th e n um e rato r an d th e s e co n d qu an tit y is de no m in a to r. F o r e xam ple , if th e re are 16 bo ys an d 4 girls , we s ay th at th e ra tio o f th e n um be r of bo ys to th e nu m be r of girls on th e te am is 16 to 4, or
16 . 4
Th is is of te n w rit te n as 16: 4. S in c e a ratio is ju s t a f rac tio n , it c an
be re du ce d o r co n ve rte d to a de c im al o r a pe rc en t. Th e F o llo w in g are dif f e re n t w a ys to e xpre s s th e s ame ratio :
16 to 4 ,
Student Guide
16 : 4 ,
16 4 4 , 1,
0.25 ,
25%
32
•
I f a s e t o f obj e c ts is divide d in to tw o gro u ps in th e ratio n f irs t gro u p co n ta in s c o n ta in s
b of a+b
a of a+b
a :b ,
th e to tal o bjec ts an d s im ilar ly th e s e co n d gro u p
th e to ta l n um be r o f obje c ts . Th is ru le applie s to e xte n de d
ra tio s , a s w e ll. I f a s e t is divide d in to th re e gro u ps in th e ratio th e f irs t gro u p c o n ta in s
•
th e n th e
a a+b+c
a :b:c ,
th e n
o f th e to tal o bje c ts , an d so on .
A pro po rtio n is a n equ a tio n th at s tate s th at tw o ratio s are e qu ivale n t. S inc e ra tio s a re j u s t f ra c tio n s , a n y e qu atio n su c h as
4 10 = 6 15
in wh ic h eac h s ide is
a s in gle f ra c tio n is pro po rtio n . Th is pro po rtio n s tate s th at 4 re late s to 6 in s a me ra tio a s 10 re la te s to 15.
•
F o r e a c h pro po rtio n of th e fo rm
a c = b d
,
ad = bc .
Th is pro pe rty c an be u se d
to so lve pro po rtio n s f o r u n kn o wn s ( variable s ) . Fo r e xam ple : “I f 3 o ran ges c o s t R s . 5, ho w m a n y o ra n ge s c an yo u bu y f o r R s. 100”. To so lve th is pro ble m we h a ve to se t u p a pro po rtio n . I f th e n um be r of o ran ge s fo r R s . 100 is x , th e n:
3 x 3 ×100 = ⇒ 3 ×100 = x × 5 ⇒ x = ⇒ x = 60 5 100 5 A v er a g es
•
Th e a ve r a g e o f a s e t of n n u m be rs is th e s um o f th o s e n u m be rs divide d by n.
average =
sum of n numbers n
o r s im ply
A=
Sum n
th e te c h n ic a l n am e f o r th e se kin d o f ave rage s is A rith m e tic Me an . •
I f yo u kn ow th e a ve ra ge o f n n um be rs , mu ltip ly th at ave rage w ith n to ge t th e s um of n um be rs .
•
I f a ll th e n um be rs in a se t are th e s ame , th en th at n um be r is th e ave rage .
•
A s s um e th a t th e a ve ra ge o f a s e t of nu m be rs is A. I f a ne w n u m be r x is a dde d to th a t s e t, th e n e w ave rage w ill be ; o o o
G r e a t er i f x i s g r e at er t han t he e xi st i ng ave r ag e S ma l l e r i f x i s smal l er t han t he e xi st i ng ave r ag e Unc ha ng e d i f x i s e q ual to t he e xi st i ng ave r ag e
•
A rith m e tic se qu e n ce is a n o rde re d s e t o f n um be rs , s uc h th at, th e dif f e re n ce be tw ee n tw o c o n se c u tive nu m be rs is th e s am e.
•
I f th e re is a n a rith m e tic se qu e n ce o f n te rm s , th e n th e ave rage c alc u lat io n c a n be m a de s im ple by u s in g th e s e ru le s .
Student Guide
33
o o
2.1.2
Th e a ve ra ge of th e te rm s in th at s e que n c e w ill be th e m iddle te rm , if n is o dd. I f n is e ve n, th e a ve rage w ill be th e ave rage o f tw o m iddle te rm s.
Algebra
Po lyno m ia ls
•
A mo n om ia l is a n y nu m be r o r variab le o r pro du c t of n u m be rs an d variab le s . F o r e xam ple
•
3, − 4, x, y, 3 x, − 2 xyz , 5 x 3 , 1.5 xy 2 , a 3b 2 are
all mo n om ials .
Th e n um be r th a t a ppe a rs in f ro n t of a variab le in a m on o m ial is c alle d th e c oe f f ic ie n t. Th e co e ff ic ie n t of is e ith e r 1 o r –1, be c a u se
x
5x 3
is 5. I f th e re is no n u m be r, th e co e ff ic ie n t
m e ans
1x
an d
− x m ean s −1x .
•
A po lyn o m ia l is a mo no m ial o r th e s um o f tw o o r m o re mo no m ials . E ac h m on om ia l th a t m a ke s u p th e po lyn o m ial is c alle d a te rm of th at po lyn o m ial.
•
I f a po lyn o m ia l h a s o n ly o ne te rm it is a s im ple m on om ial, if it h as tw o te rm s , it is kno w n a s bin o m ial an d if it h as th re e te rm s , it is c alle d trin o m ia l.
•
Tw o te rm s a re c a lle d like te rm s if th e y dif fe r o n ly in th e ir c oe f f ic ie n ts . and
•
−2x 3
a re like te rm s , wh e re as ,
5x 3
an d
5x 2 are
5x 3
no t.
I f like te rm s a re in vo lve d in a po lyn om ial, th e y c an be co m bin e d, by addin g th e ir co e ff ic ie n ts , to ma ke th at po lyn o m ial s im ple r. Th e po lyn o m ial
3x 2 + 4 x + 5 x − 2 x 2 − 7
is e qu ivale n t to th e po lyn o m ial
x2 + 9 x − 7 .
•
A ll la w s of a rith m e tic a re a ls o applic ab le to po lyn o m ials . th e m is PE M DA S .
•
Po lyn o m ia ls c a n be a dde d, s u btrac te d, m u ltip lie d o r divide d.
•
To a dd tw o po lyn o m ia ls , pu t a plu s s ign be tw e e n th e m , e ras e th e pa re n th e s e s , a n d co m bin e like te rm s .
M os t im po rtan t o f
Exa mp l e : W h a t is th e s u m o f
5 x 2 + 10 x − 7
an d
3x 2 − 4 x + 2 ?
S o l ut io n:
(5 x 2 + 10 x − 7) + (3 x 2 − 4 x + 2) = 5 x 2 + 10 x − 7 + 3 x 2 − 4 x + 2 = 8x2 + 6 x − 5
Student Guide
34
•
To s u btra c t tw o po lyn o m ia ls , re ve rs e th e s ign s of su btrah e n d, an d add tw o po lyn o m ia ls a s do ne bef o re . Exa mp l e : S u btra c t
3x 2 − 4 x + 2
f ro m
5 x 2 + 10 x − 7
S o l ut io n:
(5 x 2 + 10 x − 7) − (3 x 2 − 4 x + 2) = (5 x 2 + 10 x − 7) + (−3 x 2 + 4 x − 2) = 5 x 2 + 10 x − 7 − 3 x 2 + 4 x − 2 = 2 x 2 + 14 x − 9 •
To m u ltipl y mo no m ia ls , f irs t m u ltipl y th e ir c o ef f ic ie n ts , an d th e n mu ltip ly th e ir va ria ble s by a ddin g th e e xpo ne n ts . Exa mp l e : W h a t is th e pro du c t o f
3x 2 yz
f rom
−2x 2 y 2 ?
S o l ut io n:
(3x 2 yz )(−2 x 2 y 2 ) = (3 × −2)( x 2 × x 2 )( y × y 2 )( z ) = −6 x 4 y 3 z •
To m u ltipl y a m on o m ia l by a po lyn o m ial, ju s t m u ltip ly e ac h te rm of th e po lyn o m ia l by th e m on om ia l.
Exa mp l e : W h a t is th e pro du c t o f
3x
f rom
3 x 2 − 6 xy 2 + 2 ?
S o l ut io n:
(3x )(3 x 2 − 6 xy 2 + 2) = (3 x × 3 x 2 ) − (3 x × 6 xy 2 ) + (3 x × 2) = 9 x 3 − 18 x 2 y 2 + 6 x •
To m u ltipl y two bin o m ia ls , m u ltip ly e ac h te rm of f irs t bin om ial by e ac h te rm o f s e co n d bin o m ia l, th e n a dd th e re s u lts . Exa mp l e : W h a t is th e pro du c t o f
Student Guide
3x + y
f rom
3 x 2 − 6 xy 2 ?
35
S o l ut io n:
(3x + y )(3x 2 − 6 xy 2 ) = (3 x × 3 x 2 ) + (3 x × (−6 xy 2 )) + ( y × 3 x 2 ) + ( y × (−6 xy 2 )) = (9 x 2 ) + (−18 x 2 y 2 ) + (3 x 2 y ) + (−6 xy 3 ) = 9 x 2 − 18 x 2 y 2 + 3 x 2 y − 6 xy 3 •
Th e th re e mo s t im po rta n t bin om ial pro du c ts are : o
( x − y )( x + y ) = x 2 + xy − xy + y 2 = x 2 + y 2
o
( x + y )( x + y ) = x 2 + xy + xy + y 2 = x 2 + 2 xy + y 2
o
( x − y )( x − y ) = x 2 − xy − xy + y 2 = x 2 − 2 xy + y 2 M em o rizin g th e s e c an s ave a lo t of c alc u latio n tim e du rin g th e te s t.
•
To divide a po lyn o m ia l by a mo no m ial, divide e ac h te rm o f th e po lyn o m ial by th e mo n om ia l. Exa mp l e : W h a t is th e qu o tie n t if
32 x 2 y + 12 xy 3 z
is divide d by
8xy ?
S o l ut io n:
32 x 2 y + 12 xy 3 z 32 x 2 y 12 xy 3 z 3 = + = 4 x + y 2 z (by reducing the terms) 8 xy 8 xy 8 xy 2
Student Guide
36
Solving Equations and Inequalities
•
Th e ba s ic prin c ip le in so lvin g e qu atio n s an d in e qu alit ie s is th at yo u c an m a n ipu la te th e m in a n y w ay as lo n g as yo u do t he same t hi ng to bo t h si d e s . Fo r e xa m ple yo u m ay add a n u m be r to bo th s ide s , o r yo u m ay divide o r mu ltip ly bo th s ide s w ith s ame n um be r e tc .
•
B y u s in g th e fo llo w in g s ix- s te p me th o d, yo u c an s o lve m os t o f th e equ atio n s a n d in e qu a litie s . Th e me th o d is explain e d w ith th e h e lp of an e xam ple . Exa mp l e : if
1 x + 3( x − 2) = 2( x + 1) + 1 , 2
wh at is th e valu e o f
x?
S o l ut io n: Step
Wha t t o do …
Examp l e
1
Ge t rid o f f ra c tio n s an d de c im a ls by mu ltip ly in g bo th s ide s by th e L C D. Ge t rid o f a ll pa re n th e se s by so lvin g th e m . Co m bin e like te rm s on ea c h s ide . B y a ddin g a n d s u btra c tin g ge t a ll th e va ria ble s o n on e s ide ( mo s tly le f t) . B y a ddin g o r s u btra c tin g ge t a ll pla in n um be rs o n th e o th e r s ide . Divide bo th s ide s by th e co e ff ic ie n t of th e va ria ble . (I f yo u a re de a lin g w ith an in e qu a li ty and yo u divide w ith a ne ga tive n um be r, rem em be r to re ve rs e th e in e qu a lity. )
M u ltipl y
2 3 4 5 6
•
eac h
s ide
by
x + 6( x − 2) = 4( x + 1) + 2
2
to
ge t:
to
ge t:
x + 6 x − 12 = 4 x + 4 + 2 7 x − 12 = 4 x + 6 Su btrac t
3 x − 12 = 6
Add
3 x = 18
Divide
x=6
4x f ro m
12
to
bo th
e ac h
e ac h
s ide
s ide
s ide s
by
to 3
to
ge t: ge t:
W h e n yo u h a ve to s o lve on e variab le an d th e e qu atio n / in e qu ali ty in vo lve m o re th a n o ne va ria ble , tre at all o the r variab le s as plain n um be rs an d apply th e s ix- s te p m e tho d. Exa mp l e : if
a = 3b − c ,
wh a t is th e va lu e o f
b
in te rm s of
a
an d
c?
S o l ut io n: S te p
W ha t t o d o …
1
Th e re a re no f rac tio n s an d de c im a ls . Th e re a re no pare n th e se s . Th e re a re no like te rms . B y a ddin g a n d su btrac t in g ge t a ll th e va ria ble s o n o ne s ide .
2 3 4
5
Student Guide
B y a ddin g o r su btrac t in g ge t a ll pla in n um be rs on th e o th e r s ide .
Examp l e
Re me m be r th e re is o n ly o ne variable b , wh ic h is on o ne s ide on ly. Re me m be r we are a an d c as co n s ide rin g
37
plain eac h
n um be r. A dd c s ide to ge t:
to
a + c = 3b
6
•
Div ide bo th s ide s by th e c oe f f ic ie n t o f th e variab le .
Divide ge t:
bo th
s ide s
by
3
to
a+c =b 3
I t is n o t n e ce s s a ry to f o llo w th e s e s te ps in th e o rde r s pe c if ie d. S om e tim e s it m a ke s th e pro ble m m u ch e as ie r, if yo u c h an ge th e o rde r of th es e s te ps. Exa mp l e : If
x − 4 = 11 ,
wh a t is th e va lu e o f
x - 8?
S o l ut io n: G o in g imm e dia te ly to s te p 5, add 4 to e ac h s ide to ge t: s u btra c t 8 f rom bo th s ide s to ge t:
•
x −8 = 7 .
x = 15 .
Now
Do in g th e s a me th in g on eac h s ide of an e qu atio n doe s no t me an do in g th e s a me th in g to e a c h te rm o f th e e qu atio n . Th is is ve ry im po rtan t if yo u are do in g divis io n s , o r de a lin g w ith expo n e n ts an d ro o ts . Exa mp l e : If
a>0
and
a 2 + b2 = c2 ,
w h at is th e valu e of
a
in te rm s o f
b
an d
c.
S o l ut io n:
a 2 + b 2 = c 2 ⇒ a 2 = c 2 − b 2 . Now yo u c an ’t to ge t a = c − b . Yo u mu s t take th e s qu are a 2 = c 2 − b2 •
⇒
take a s qu are ro o t of eac h te rm roo t o f e ac h s ide :
a = c 2 − b2
A no th e r type o f e qu a tio n is th at in w h ic h th e variable appe ars in e xpon e n t. Th e s e e qu a tio n s a re ba s ic a ll y so lve d by in c e ptio n . E xa m ple :
= 32 , wh a t is th e va lu e o f If 2 S o lu tio n : x+ 3
2 x +3 = 32 ⇒ 2 x +3 = 25 No w a s
x = 2,
3x+ 2 ?
⇒ x+3= 5 ⇒ x = 2.
you c a n ge t
x = 2 ⇒ x + 2 = 4 ⇒ 3x + 2 = 34 = 81
•
A s ys te m of equ a tio n s is a s e t o f tw o o r m o re e qu atio n s h avin g tw o o r m o re va ria b le s . To so lve s u c h equ atio n s , yo u mu s t f in d th e valu e of eac h va ria b le th a t w ill m a ke e a c h equ atio n tru e .
•
To s o lve a s ys te m of equ a tio n s , add o r s u btrac t th em to ge t a th ird e qu a tio n . I f th e re a re m o re th an tw o e qu atio n s yo u c an ju s t add th e m. Exa mp l e : If
x + y = 10
Student Guide
and
x − y = 10
w h at is th e valu e o f
y?
38
S o l ut io n: A dd two e qu a tio n s :
x + y = 10 x− y = 2 2x
No w re pla c in g
•
x
= 12 ⇒ x = 6
w ith 6 in th e f irs t equ atio n :
6 + y = 10 ⇒
y=4
I f yo u kn ow th e va lu e o f on e variable in a s ys tem o f tw o equ atio n s , yo u c an u s e th is va lu e to ge t th e valu e o f th e o th e r variable . As it is do n e in th e pre vio u s qu e s tio n .
Word problems • To s o lve wo rd pro ble m s , f irs t tran s late th e pro ble m f ro m E n glis h to A lge bra. W h ile tra n s la t in g, us e va riable s to re pre se n t u n kn o w ns . O n ce tran s late d, it is e a s y to so lve th e m u s in g th e te c h n iqu e s yo u h ave le arn e d in pre vio u s s e c tio n s . • F o llo w in g E n glis h to A lge bra dic tio n ary w ill be h e lpf u l in tran s la tin g w o rd pro ble m s to a lge bra ic expre s s io n s . Eng l i sh wo r d s I s , w a s, w ill be , h a d, h a s, w ill h a ve, is e qu a l to , is th e s a m e as Plu s , mo re th a n , s u m , in c re as e d by, a dde d to , e xce e ds , re ce ive d, go t, o lde r th a n , f a rth e r th an , gre a te r th a n M in u s , fe we r, le s s th an , dif fe re n c e , de c re a se d by, s u btra c te d f rom , yo u n ge r th an , ga ve , lo s t Tim e s , o f, pro du c t, mu lti pl ie d by
Mat he mat i c al me ani ng E qu als
S y mb ol
=
A dditio n
+
S u btrac tio n
−
M u ltip lic a tio n
×
Divide d by, quo tie n t, pe r, f o r
Div is io n
÷ or
Mo re th a n , gre a te r th a n A t le as t Fe we r th a n , le s s th a n A t m os t W h a t, ho w ma n y, e tc.
I ne qu ality I ne qu ality I ne qu ality I ne qu ality U n kn ow n qu an tity
> ≥ < ≤ x
a b
( So me variable ) Examples: o The sum of 5 and some number is 13.
o
Javed was two years younger than Saleem.
o o
Bilal has at most Rs.10,000. The product of 2 and a number exceeds that number by 5 (is 5 more than that number).
•
5 + x = 13 J = S −2 B ≤ 10000
2N = N + 5
I n wo rd pro ble m s , yo u mu s t be su re abo u t wh at you are an sw e rin g. Do n o t a n s we r th e w ro n g que s tio n .
Student Guide
39
•
I n pro ble m s in vo lvin g a ge s, rem em be r th at “ye ars ago ” me an s yo u ne e d to s u btra c t, a n d “ye a rs f rom no w ” m ean s you n ee d to add.
•
Dis ta n c e pro ble m s a ll de pe n d o n th re e variat io n s of th e s ame fo rm u la:
distance = speed × time
o
distance time distance time = speed speed =
o
o
Exa mp l e : H ow m u c h lo n ge r, in se c on ds , is re qu ire d to drive 1 m ile at 40 m ile s pe r hour th a n at 60 m ile s pe r ho u r? S o l ut io n: Th e tim e to drive a t 40 m ile s pe r h o u r c an be c alc u late d as
time1
=
1 h o u rs 40
=
1 × 60 3 m in u te s 40 2
30 3 × 60 se c o n ds 2
=
=
90
s e co n ds Th e tim e to drive a t 60 m ile s pe r h o u r c an be c alc u late d as
time2
=
1 h o u rs 60
=
1 × 60 60
m in u te s
difference = time1 − time2 = 90 − 60 = 30 2.1.3
=
1× 60 se c o n ds
=
60 s e co n ds
se c o n ds .
Geometry
L ines a nd Ang les
•
A n a ng l e is fo rme d a t th e in te rs e c tio n of two lin e s e gm e n ts , rays o r lin e s . Th e po in t o f in te rs e c tio n is c alle d th e ve r t e x. A n gle s are m e as u re d in de gre e s.
•
A n gle s a re c la s s if ie d a c co rdin g to th e ir de gre e me as u res .
•
A n a c ut e a n gle me a s u re s le s s th an
•
A r i g ht a n gle m e as u re s
• •
A n o b t use a n gle me a s u re s m o re th an
•
I f tw o o r m o re a n gle s co m bin e to ge th e r to fo rm a s traigh t an gle , th e su m o f
90°
A s tra i gh t a n gle m ea s u re s
th e ir me a s u re s is
Student Guide
90°
90°
bu t le s s th an
180°
180°
180° .
40
a° + b° + c° + d ° = 180°
•
Th e s u m of a ll th e me a s u re s o f all th e an gle s aro u n d a po in t is
360°
a° + b° + c° + d ° + e° = 360° •
W h e n tw o lin e s in te rs e c t, f o u r an gle s are f o rm e d, tw o an gle s in e ac h pair of o ppo s ite a n gle s a re c a lle d ve r t ic al ang l e s. V e rtic al an gle s , fo rm e d by th e in te rs e c tio n of tw o lin e s , h ave equ al me as u re s.
a=c •
and
b=d
I f o n e o f th e a n gle s fo rme d by th e in te rs e c tio n o f tw o lin e s is a righ t an gle , th e n a ll fo u r a n gle s a re righ t an gle s . S uc h lin e s are c alle d pe r p e nd i c ul ar lin e s
a = b = c = 90 •
I n th e f igu re be lo w a lin e l divide s th e an gle in tw o equ al parts . Th is lin e is s a id to bi se c t th e a n gle . Th e o the r lin e k bis e c ts ano th e r lin e in to tw o e qu a l pa rts . Th is lin e is s a id to bis e c t a lin e .
•
Tw o lin e s a re s a id to be p ar al le l , if th e y ne ve r in te rs e c t eac h o the r. H ow e ve r, if a th ird lin e , c alle d a t r ansve r sal , in te rs e c ts a pair o f paral le l lin e s , e igh t a n gle s a re f o rm e d. A n d th e re latio n s h ip am on g th e s e s an gle s is s h ow n in th e fo llo w in g dia gram .
Student Guide
41
•
•
-
A ll
f ou r
ac u te
an gle s
are
equ al
•
-
A ll
f ou r
o btu s e
an gle s
are
e qu al
•
-
Th e
sum
of
pair
ac u te
a=c=e= g
b=d = f =h
an y
of
180° , a + d = 180°, d + e = 180°, b + g = 180°
o btu s e
an gle
is
an d e. g.
e tc .
Triangles
•
I n a n y tria n gle , th e s u m of th e me as u res of th e th re e an gle s is
180°
.
x + y + z = 180 •
I n a n y tria n gle : o Th e lo n ge s t s ide of trian gle is o ppo s ite th e large s t an gle . o Th e s ho rte s t s ide is o ppo s ite th e s m alle s t an gle . o S ide s w ith th e s a me le n gth are o ppo s ite th e an gle s w ith th e s am e m ea s u re .
•
Tria n g le s a re c la s s if ie d in to th re e dif f e re n t kin ds w ith re s pe c t to th e le n gth s o f s ide s . o S c a l e ne : in w h ic h all th re e s ide s are o f dif f e re n t le n gth s .
o o •
Iso sc e l e s : in w h ic h two of th e s ide s o f trian gle are e qu al in le n gth , th e th ird is dif f e re n t. Eq ui l a t e r a l : in w h ic h all th re e s ide s are e qu al in le n gth .
Tria n g le s a re a ls o c la s s if ie d w ith re s pe c t to th e an gle s . o A c ut e tr i a ng l e : in w h ic h all th re e an gle s are ac u te .
o o
O b t use tr i a ng l e : in w h ic h o ne an gle is o btu s e an d tw o are ac u te . Ri g ht t r i a ng le : Th is h as on e righ t an d two ac u te an gle s .
•
I n a righ t tria n g le , th e o ppo s ite to th e righ t an gle is kn o w n as hy p o t e nuse a n d is th e lo n ge s t s ide . Th e o the r tw o s ide s are c alle d le g s .
•
I n a n y righ t tria n g le , th e s um of th e m eas u re s o f th e tw o ac u te an gle s is
•
B y Pyth a go re a n Th e o rem , th e s u m of s qu are s o f th e le n gth s of le gs o f a righ t tri a n gle is a lw a ys e qu al to th e s qu are o f le n gth o f h ypo te n u s e.
90° .
Student Guide
42
•
a 2 + b2 = c2 I n a n y tria n gle , th e s u m o f an y tw o s ide s is alw ays gre ate r th an th e th ird o ne . A n d th e dif f e re n ce of an y tw o s ide s is alw ays le s s th an th e th ird on e .
a +b > c
•
an d
a −b < c
Th e pe r i me t er of a tria n gle is c alc u late d by addin g th e le n gth s o f all th e s ide s o f th a t tria n gle .
perimeter = a + b + c •
Th e a re a of a tri a n gle is c a lc u late d by th e fo rm u la:
area =
1 bh 2
w h e re
b
is
h
th e ba s e o f th e tria n gle a n d is th e hei g ht of th e trian gle . o A n y s ide o f tria n g le c an be take n as th e bas e. o H e igh t is th e a lti tu de ( pe rpe n dic u lar) draw n to th e bas e f ro m its o ppo s ite ve rte x. o I n a righ t tria n g le an y le g co u ld be take n as th e base , th e o the r w ill be th e a lt itu de .
Qua d r ila t er a l a nd o t her Po lyg o ns
•
A po l y go n is a c lo se d ge om e tric f igu re , made u p o f lin e se gme n ts . Th e lin e s e gm e n ts a re c a lle d si d e s an d th e en d po in ts o f lin e s are c alle d ve r t i c e s
Student Guide
43
( plu ra l o f ve r t e x). L in e s , in s ide th e po lygo n , draw n f ro m o ne ve rte x to th e o th e r, a re c a lle d di a g o na l s .
•
Th e s um of th e me a s u res o f th e a lw a ys
(n − 2) ×180° .
n
an gle s in a po lygo n w ith
n
s ide s is
360° .
•
I n a n y qu a drila te r a l, th e s um of th e m eas u re s of th e f o u r an gle s is
•
A re g ul a r p o ly g o n is a po lygo n in wh ic h all o f th e s ide s are o f th e s ame le n gth . I n a n y re gu la r po lygo n , th e me as u re of e ac h in te rio r an gle is
•
(n − 2) ×180° n
o o
AB = CD an d AD = BC o ppo s ite an gle s are e qu al. a = c an d b = d a n gle s add u p to 180° . a + b = 180° , b + c = 180°
L e n gth s of o ppo s ite s ide s are e qu al. M e a s u re s o f C o n se c u tive
e tc .
Th e tw o dia go n a ls bis e c t e ac h o th e r. AE = EC an d BE = ED A dia go n a l divide s th e paralle lo gram in to tw o trian g le s th at are c o n gru e n t.
A r e c t a ng le is a pa ra lle lo gr am in w h ic h all fo u r an gle s are righ t an gle s . I t h a s a ll th e pro pe rtie s of a paralle lo gram . I n additio n it h as th e f o llo w in g pro pe rtie s :
o o
•
360° . n
A p a r a l le l o g r a m is a s pe c ial qu adrila te ral, in w h ic h bo th pairs of o ppo s ite s ide s a re pa ra lle l. Th e Fo llo w in g are so me pro pe rtie s o f paral le lo gram .
o o o
•
a n d th e m e as u re o f e ach e xte rio r an gle is
Th e me a s u re of ea c h an gle in a rec tan gle is 90° . Th e dia go n a ls of a re c tan gle are e qu al in le n gth .
A sq ua r e is a re c ta n gle th at h as th e f o llo w in g additio n a l pro pe rtie s : o A s qu a re h a s a ll its s ide s e qu al in le n gth . o I n a s qu a re , dia go n als are pe rpe n dic u lar to e ac h o th e r.
Student Guide
44
•
•
To c a lc u la te th e a re a, th e fo llo w in g fo rm u las are re qu ire d:
o
F o r a pa ra l le lo gra m , h e igh t.
o
F o r a re c ta n gle , w idth .
o
F o r a s qu a re ,
Area = bh ,
Area = lw ,
Area = s 2 ,
wh e re
wh e re
wh e re
s
l
b
h
is th e
w
is th e
is th e base an d
is th e le n gth an d
is th e s ide o f
th e s qu are .
Pe rim e te r f o r a n y po lygo n is th e s u m o f le n gth s , o f all its s ide s.
Student Guide
45
Circles •
A ci r c l e co n s is ts o f a ll th e po in ts th at are th e s am e dis tan c e f ro m o ne f ixe d po in t c a lle d th e c e nt e r . Th at dis tan c e is c alle d th e r ad i us o f a c irc le . Th e w o rd ra diu s is a ls o u s e d to re pre s e n t an y of th e lin e s e gm e n ts jo in in g th e c e n te r a n d a po in t on th e c irc le . Th e plu ral of radiu s is r ad i i .
•
A n y tria n g le , s u ch a s VCED in th e f igu re , f o rme d by co n n e c tin g th e e n d po in ts of tw o ra dii, is a n is o s ce le s .
•
A lin e se gme n t, s u c h a s ED in th e diagram abo ve , bo th o f w ho s e e n d po in ts a re o n a c irc le is c a lle d a c ho r d .
•
A c ho rd th a t pa s s e s th ro u gh th e ce n te r of th e c irc le is c alle d th e di ame t e r o f th e c irc le . Th e le n gth o f th e diam e te r is alw ays do u ble th e radiu s o f th e c irc le . Th e dia m e te r is th e lo n ge s t co rd th at c an be draw n in a c irc le .
•
Th e to ta l le n gth a ro u n d a c irc le is kn ow n as th e ci r c umfe r e nce o f th e c irc le .
•
Th e ra tio of th e c irc u m f e re n ce to th e diam e te r is alw ays th e s am e f o r an y c irc le .
•
Th is ra tio is de no te d by th e s ym bo l
C π = ⇒ C = π d ⇒ C = 2π r d
π
( pro no u n c e d as pi) .
w he re C is th e c irc u m f e re nc e , d is th e diam e te r
a n d r is th e ra diu s of th e c irc le .
π
3.14
•
V a lu e of
•
A n a rc c o n s is ts o f tw o po in ts in a c irc le an d all th e po in ts be tw ee n th em . E . g. PQ is a n a rc in th e diagram .
•
A n a n gle w ho s e ve rte x is a t th e ce n te r of th e c irc le is c alle d th e c e nt r al a ng l e .
•
is a ppro xim a te ly
∠PCQ
in th e dia gram abo ve is a c e nt r al ang l e .
Th e de gree me a s u re of a c om ple te c irc le is
Student Guide
360° .
46
•
Th e de gree me a s u re of a n arc is th e m eas u re of th e c e n tral an gle th at in te rc e pts it. E . g. th e de gre e m eas u re of
∠PCQ •
If
x
» PQ
is equ al to th e me as u re of
in th e dia gra m a bo ve .
is th e de gre e me a s u re o f an arc , its le n gth c an be c alc u late d as
x C, 360
w he re C is th e c irc u m f e re n ce .
• •
π r2 . The area of a sector formed by the arc and two radii can be Th e a re a of a c irc le c a n be c alc u late d as
calculated as
2.2
x A , where A is the area of a circle. 360
Discrete Quantitative Questions
These are standard multiple-choice questions. Most of such questions require you to do some computations and you have to choose exactly one of the available choices based upon those computations. This section will teach you the basic tactics to attempt such questions.
2.2.1
Question format
Each question will consist of a question statement and the choices labeled from A to E. The number of choices may vary from 2 to 5, but exactly one choice will be correct for each question.
2.2.2
How to attempt?
Following are some tactics, which will lead you to the correct answer.
•
W h e ne ve r yo u kno w ho w to an s we r a qu e s tio n dire c tly, ju s t do it. Th e ta c tic s s h o u ld be u s e d on ly wh e n yo u do n o t kno w th e e xac t s o lu tio n , an d yo u j u s t wa n t to e lim in a te th e ch o ic e s .
•
R em em be r th a t n o pro blem re qu ire s le n gth y o r dif f ic u lt co m pu tatio n s . I f yo u f in d yo u rs e lf do in g a lo t o f co m ple x arith m e tic , th in k again . Yo u m ay be go in g in th e w ro n g dire c tio n .
•
W h e ne ve r th e re is a que s tio n w ith so me u n kn ow n s ( variable s ) , re plac e th e m w ith th e a ppro pria te n u me ric valu e s fo r e ase o f c alc u lat io n .
•
W h e n yo u ne e d to re pla c e variab le s w ith valu e s , ch o o se eas y- to - u s e n u m be rs , e. g. th e n um be r 100 is appro pria te in mo s t pe rc e n t- re late d pro ble m s a n d th e L C D ( le as t co mm o n den o m in ato r) is be s t su ite d in qu e s tio n s th a t in vo lve f ra c tio n s .
•
A pply “ba c k- s o lvin g” wh e n e ve r yo u kn ow w h at to do to an s we r th e qu e s tio n bu t yo u w a n t to a vo id do in g alge bra. To u n de rs tan d th is tac tic re ad th e f o llo w in g e xam ple : O n Mo n da y, a s to reo w ne r re c e ive d a s h ipme n t of bo o ks . O n Tu e s day, s h e s o ld h a lf o f th e m . O n W e dne s day af te r tw o mo re w e re so ld, s he h ad e xa c tly 2/ 5 o f th e bo o ks le f t. Ho w m an y we re in th e s h ipm e n t? ( A) 10
Student Guide
( B ) 20
( C ) 30
( D) 40
( E ) 50
47
n ow by th is ta c tic : A s s um e th a t (A ) is th e c o rre c t an sw e r, if so ; s he mu s t h ave 3 boo ks on W e dne s da y. B u t 2/ 5 of 10 are 4, s o , ( A ) is in c o rre c t; A s s um e th a t (B ) is th e c o rre c t an sw e r, if so ; s h e mu s t h ave 8 boo ks on W e dne s da y. 2/ 5 o f 20 a re 8, so , ( B) is th e c o rre c t c ho ic e , an d as th e re m ay be o n ly on e co rre c t c h o ic e , th e re is no n ee d to c he c k fo r re m ain in g c h o ic e s.
•
Th is ta c tic is ve ry h e lpf u l wh e n a n o rm al alge braic s o lu tio n fo r th e pro ble m in vo lve s co m ple x o r le n gth y c alc u lat io n s . I f yo u a re n o t s u re h ow to an sw e r th e que s tio n , do no t le ave it u n an s we re d. Try to e lim in a te a bs u rd ch o ic e s an d gu e s s f rom th e rem ain in g o ne s . M o s t o f th e tim e s fo u r o f th e c ho ic e s are abs u rd an d yo u r an s we r is no lo n ge r a gu e s s. M a n y th in gs ma y h e lp yo u to re alize th at a partic u lar ch o ic e is abs u rd. S om e o f th e m a re lis te d be low .
o o o
o
o
Th e a n s w e r m u s t be po s itive bu t so m e of th e c h o ic e s are n e gative s o e lim in a te a ll th e ne gative on e s . Th e a n s w e r m u s t be e ve n bu t s om e of th e ch o ic e s are o dd s o e lim in a te a ll th e o dd c ho ic e s . Th e a n s w e r m u s t be le s s th e n 100, bu t so me o f th e c ho ic e s are gre a te r th a n 100 (o r an y o th e r valu e ) so e lim in ate all c ho ic e s th at a re o u t of ra n ge. Th e a n s w e r m u s t be a w ho le n um be r, bu t so me of th e c h o ic e s are f ra c tio n s so e lim in ate all f rac tio n s . Th e s e a re s om e e xam ple s . Th e re may be nu m e rou s s itu at io n s w he re yo u c an a pply th is tac tic an d f in d th e c o rre c t an s we r e ve n if yo u do n o t kno w th e righ t way to s o lve th e pro ble m .
Example questions with solutions Th e f o llo w in g a re s om e e xam ple s , w h ic h w ill h e lp yo u to mas te r th e se type s of qu e s tio n s .
Example
I f 25% o f 220 equ a ls 5. 5% o f X , w h at is X ? ( A) 10 ( B ) 55 ( C ) 100
( D) 110
( E ) 1000
Solution:
S in c e 5. 5% o f X e qu a ls 25% o f 220, X is mu c h gre ate r th an 220. So , ch o ic e s A , B , C , a n d D a re im me dia te ly e lim in ate d be c au se th e se are no t large r th an 220. A n d th e co rre c t a n s we r is c h o ic e E.
(Note: An important point here is that, even if you know how to solve a problem, if you immediately see that four of the five choices are absurd, just pick the remaining choice and move on.)
Example
S c ie n ce s tu de n ts c ho o se e xa c tly on e of th re e f ie lds ( i. e . me dic al sc ie n c e s , e n gin e e rin g s c ie n ce s a n d c om pu te r s c ie n c es ) . I f, in a co lle ge , th re e- f if th s of th e s tu de n ts c ho o se m edic a l s c ie n c es , on e - fo rth of th e re m ain in g s tu de n ts take c om pu te r s c ie n c e s , w h a t p e r ce nt of th e s tu den ts take en gin e e rin g sc ie n c e s ? ( A) 10
Student Guide
( B ) 15
( C ) 20
( D) 25
( E ) 30
48
Solution:
Th e le a s t c om mo n de no m in a to r o f 3/ 5 an d 1/ 4 is 20, s o as s u me th at th e re are 20 s tu de n ts in th a t c o lle ge . Th e n th e nu m be r of s tu den ts ch o os in g me dic al s c ie n c e s is 12 ( 3/ 4 o f 20) . Of th e rem ain in g 8 s tu de n ts , 2 ( 1/ 4 o f 8) c ho o s e c om pu te r s c ie n ce s . Th e rem a in in g 6 c ho o se e n gin e e rin g s c ie n ce s . A s 6 is 30% o f 20, th e a n sw e r is E .
Example
I f a s c h oo l c a fe te ria n e e ds C c an s of s o u p eac h w ee k fo r eac h s tu de n t an d th e re are S s tu de n ts , fo r ho w man y w ee ks w ill X c an s of so u p las t? ( A) C X/ S
( B ) X S/ C
( C ) S / CX
( D) X/ C S
( E ) CS X
Solution:
R e pla c e C , S a n d X w ith th re e e as y to u s e n u m be rs . Le t C = 2, S= 5 an d X = 20. No w ea c h s tu de n t w ill ne e d 2 c ans pe r we e k an d th e re are 5 s tu de n ts , s o 10 c a n s a re ne e de d pe r we e k a n d 20 c an s w ill las t fo r 2 w ee ks . No w pu t th es e va lu e s in c h o ic e s to f in d th e co rre c t on e . Th e c h o ic e s A , B , C , D a n d E be c om e 8, 50, 1/ 8, 2 an d 200 re s pe c tive ly. So th e c ho ic e D re pre s e n ts th e c o rre c t an s w e r.
2.3
Quantitative Comparison Questions
S om e of th e qu e s tio n s in th e Q u an tita tive se c tio n of th e te s t m ay be qu a n tita ti ve co m pa ris o n que s tio n s . Th e Fo llo w in g te xt w ill e xplain yo u th e f o rm a t a n d te c h n iqu e s u ne e d to atte m pt th e qu e s tio n s of th is f o rm at.
2.3.1Question format S u c h qu e s tio n s co n s is t of tw o qu an tit ie s , o ne in c o lu m n A an d th e o the r in c o lu m n B. You h a ve to co m pare th e tw o qu an tit ie s . Th e in f o rm atio n c o n ce rn in g o ne o r bo th qu a n tit ie s is pre s e n te d be fo re th e m . O n ly th e fo llo w in g f ou r ch o ic e s w ill be give n : A. B. C. D.
Th e Th e Th e Th e
qu a n tity in co lu m n A is gre ate r qu a n tity in co lu m n B is gre ate r tw o qu a n tit ie s in bo th co lu m n s are e qu al re la tio n s h ip c a n n o t be de te rm in e d f ro m th e in f o rm atio n give n
And as it is clear from the choices, only one will be correct at one time. Your job is to choose one of them after careful comparison. The following text explains some simple tactics to attempt such questions.
2.3.2How to attempt W h e ne ve r yo u en c o un te r a qu an tit at ive co m paris o n que s tio n , th e f o llo w in g gu ide lin e s w ill he lp you to f in d th e c o rre c t an s w e r qu ic kly. •
I f th e qu e s tio n in vo lve s s om e variable s , re plac e th em w ith appro pria te n u m be rs . He re a re s om e gu ide lin e s in c h oo s in g an appro pria te n u m be r: o Th e ve ry be s t n um be rs to us e are –1, 0 an d 1. o O f te n f ra c tio n s be tw e e n 0 an d 1 are us e f u l (e . g. 1/ 2, 3/ 4 e tc . ) . o O c c a s io n a lly, “la rge ” n um be rs s u c h as 10 o r 100 c an be u s e d. o I f th e re is mo re th an on e variable , it is pe rm is s ible to re plac e e ac h w ith th e s a me n um be r. o Do n o t im po s e a n y u n - s pe c if ie d c o n ditio n s on nu m be rs . C ho o se th e m ra n do m ly.
Student Guide
49
•
E lim in a te th e c ho ic e s a n d c ho o se f rom th e re m ain in g on e s. Fo r e xam ple I f yo u f ou n d th e qu a n titie s eve r equ al, th e co rre c t c h o ic e c ou ld n e ve r be A o r B , s o , e lim in a te A a n d B.
•
A qu a n ti ta t ive co m pa ris o n qu es tio n c an be tre ate d as an e qu atio n o r in e qu a li ty. E ith e r: Column A < Column B, or Column A = Column B, or Column A > Column B S o, yo u c a n pe rf o rm s im ila r o pe ratio n o n bo th co lu m n s to s im plif y th e pro ble m j u s t a s in equ a tio n s ( o r in e qu alit ie s ) .
Example: m > 0 and m ≠ 1
m2 •
m3
I n th is e xa m ple divide bo th th e qu an titie s by m 2. Th is w ill c h an ge c o lu m n A to 1 a n d co lu m n B to m . Now th e co m paris o n is ve ry s im ple , a s w e kn ow th a t m is gre ate r th an 0 an d c an no t be 1. S o th e re la t io n s h ip is no t de te rm in able u s in g th e c u rre n t in f o rm atio n . m c an be bo th gre a te r th a n 1 o r be twe e n 0 an d le s s th an 1.
2.3.3 Example Explanations
questions
with
Answers
and
Example 1: A s tu de n t ea rn e d a 75 o n e ach of h e r f irs t th re e m a th te s ts a n d an 80 on he r f o u rth an d f if th te s ts . A B A ve ra ge a f te r 4 te s ts A. B. C. D.
Th e Th e Th e Th e
A ve rage af te r 5 te s ts
qu a n tity in co lu m n A is gre ate r qu a n tity in co lu m n B is gre ate r tw o qu a n tit ie s in bo th co lu m n s are e qu al re la tio n s h ip c a n n o t be de te rm in e d f ro m th e in f o rm atio n give n
R em em be r yo u w a n t to kn ow wh ic h ave rage is h igh e r, n o t w h at th e ave rage s a re . A f te r 4 te s ts , th e a ve ra ge is c le arly le s s th an 80, so an 80 on th e f if th te s t h a d to ra is e th e a ve ra ge . S o th e an s w e r is c ho ic e ( B) .
Example 2: A
A. B. C. D.
Th e Th e Th e Th e
B
Th e tim e it take s to Th e tim e it take s to drive 40 m ile s at 35 drive 35 m ile s at 40 m ph m ph qu a n tity in co lu m n A is gre ate r qu a n tity in co lu m n B is gre ate r tw o qu a n tit ie s in bo th co lu m n s are e qu al re la tio n s h ip c a n n o t be de te rm in e d f ro m th e in f o rm atio n give n
Student Guide
50
O n c e a ga in th e re is n o ne e d f o r c alc u latio n , as th e s pee d in c o lu m n B is h igh e r th a n th a t in co lu m n A . I t is o bvio u s th at it w ill take le s s tim e to trave l s ho rte r dis ta n c e a t a gre a te r s pe e d. S o th e valu e in co lu m n A is large r. Th e an s we r is o ptio n ( A) .
Example 3: A
B
5 5
20 2 A. B. C. D.
Th e Th e Th e Th e
qu a n tity in co lu m n A is gre ate r qu a n tity in co lu m n B is gre ate r tw o qu a n tit ie s in bo th co lu m n s are e qu al re la tio n s h ip c a n n o t be de te rm in e d f ro m th e in f o rm atio n give n 2
20 20 =5 = 4 2
S qu a re ea c h co lu m n : e qu a l a n d th e a n sw e r is c ho ic e ( C ).
2
an d
25 5 = 5 =5 5 .
So bo th c o lu m n s are
Example 4: A
B
13y
15y
To so lve th is que s tio n , s u btra c t
13y
15 y − 13 y = 2 y
13 y − 13 y = 0 fo r 2 y c an re s tric tio n s ,
f ro m bo th c o lu mn s to ge t
c o lu m n A a n d f o r c o lu m n B. As th e re are no be gre a te r th a n , le s s th a n o r e qu al to 0. S o th e co rre c t ch o ic e is ( D) .
2.4
Data Interpretation Questions
Th e s e qu e s tio n s a re ba s e d o n th e in f o rm atio n th at is pre s en te d in th e f o rm of a gra ph , c h a rt o r ta ble . Mo s t of th e data is pre s e n te d graph ic al ly. Th e mo s t c om mo n type s of gra ph s a re lin e graph s , bar graph s an d c irc le graph s . Th e o bj ec tive of s u c h que s tio n s is to te s t yo u r abili ty to u n de rs tan d an d an alyze s ta tis tic a l da ta .
2.4.1
Question Format
Da ta in te rpre ta t io n que s tio n s alw ays appe ar in se ts , yo u are pre s en te d w ith s om e da ta in a n y f o rm a t ( c h art, graph o r table ) , an d yo u w ill th e n be as ke d w ith so me que s tio n s a bo u t th a t data. Th e fo llo w in g e xam ple e xpla in s th e fo rm at of s u c h qu e s tio n s .
Example: Question 1:
W h a t is th e a ve ra ge s a le , in m illio n Rs . , f o r th e pe rio d 1994- 2000? ( A) 5. 5 ( B ) 6. 0 ( C ) 7. 0 ( D) 8. 0 ( E ) 8. 5
Question 2:
Student Guide
51
For which year, the percentage increase in sales from the previous year is the greatest. (A) 1995 (B) 1996 (C) 1999 (D) 2000 (E) 2001
2.4.2 How to attempt Do no t try to a n s we r s u c h que s tio n s im m e diate ly, f irs t o f all re ad th e pre s e n te d da ta c a re f u lly. Yo u m us t be ve ry c le ar abo u t th e data an d its m ea n in gs eve n be fo re re adin g th e f irs t qu es tio n .
•
Do n o t co n f us e n u m be rs w ith pe rc e n ts . Th is c o n fu s io n is m os t like ly to o c c u r wh e n da ta is pre s e n te d in pie graph s . F o r e xam ple in th e f o llo w in g gra ph
Sales in million Rs.
•
12 10 8 6 4 2 0 1994
1995
1996
1997
1998
1999
2000
2001
Years
No w it w ou ld be a gre a t m is take he re to th in k th at s ale s o f “TV s & VC R s ” is 15% mo re th a n th e s a le s o f C om pu te rs in 2001 by X YZ C o rpo ratio n . To kn o w th is yo u h a ve to c a lc u late it as
•
15 ×100 = 60% 25 .
Try to a vo id u n - ne c e s s ary c alc u lat io n s . Mo s t o f th e que s tio n s c o u ld e a s ily be s o lve d by o bse rvatio n an d es tim at io n . Us e e s tim atio n to e lim in a te th e ch o ic e s , if yo u are n o t able to f in d th e co rre c t an s w e r w ith o u t c a lc u la tio n . F o r e xam ple to so lve “Q u e s tio n 1” pre s e n te d in th e
Student Guide
52
e xa m ple a t th e s ta rt of th is s e c tio n , if yo u are no t s u re of th e co rre c t a n s we r, yo u c a n th e n try to c u t dow n th e nu m be r o f po s s ible c ho ic e s by o bse rva t io n . Yo u a re be in g as ke d to te ll th e pe rce n tage in c re as e . W he re a s , in ye a r 2000, th e s ale is de c re as in g in s te ad o f in c re as in g, s o , yo u c a n imm e dia te ly e lim in ate ch o ic e ( D) in th at qu e s tio n . •
•
•
•
Yo u r a n s we rs m u s t be bas e d u po n th e in f o rm atio n pre s e n te d in th e give n c h a rts a n d gra ph s . I f yo u r kno w le dge c o n tradic ts an y o f th e data pre s e n te d, ign o re w h a t yo u kn o w an d s tic k to th e pre s e n te d data. Th e pre s e n te d da ta s ho u ld be th e on ly base f o r yo u r c alc u lat io n s an d e s tim a tio n s . A lw a ys u s e th e pro pe r un its , th e re m ay be s om e qu e s tio n s th at as k yo u to c om pa re dif fe re n t data ite m s po s s ibly f ro m dif f e re n t data s e ts . B e c a re f u l a bo u t th e un its u s e d to re pre s e n t th e data. B ec a u s e gra ph s a n d c h arts pre s en t data in a fo rm th at e n able s yo u to re a dily se e th e re la tio n s h ips amo n g valu e s an d to make qu ic k c om pa ris o n s , you sh o u ld alw ays try to vis u al ize yo u an s we r in th e s am e f o rm a t a s th e o rigin a l data w as pre s e n te d. B e s u re th a t yo u r a n s we r is re aso n able . Fo r e xam ple , th e prof it c o u ld n e ve r in c re a s e th e a c tu al s ale s , o r th e expe n s es c o u ld ne ve r be ne gative e tc . W h ile a n sw e rin g th e qu e s tio n , f irs t o f all e lim in ate s u c h u n re a s o n a ble c ho ic e s , a n d th e n c ho o se f rom th e rem ain in g on e s .
Practice exercise
2.5 1
W h a t is th e a ve ra ge o f po s itive in te ge rs f rom 1 to 100 in c lu s ive ? ( A) 49 ( B ) 49. 5 ( C ) 50 ( D) 50. 5 ( E ) 51
2
If
x+ y = 6, y + z = 7,
11 ( A) 3 3
In
th e
and
x+ z =9,
11 (B ) 2 dia gra m
be lo w ,
w h at is th e ave rage of
(C)
lin e s
22 3
x, y
( D) 11
l
an d
m
z?
an d (E)
are
not
22
paralle l.
I f A re pre se n ts th e a ve ra ge m eas u re o f all th e e igh t an gle s , w h at is th e valu e of A?
A = 45 ( B ) 45 < A < 90 ( C ) A = 90 ( D) 90 < A < 180 ( E ) A = 180 ( A)
Student Guide
53
4
A s la m h a s 4 tim e s a s m an y boo ks as Salm an an d 5 tim e s as man y as J ave d. If J a ve d h as mo re th a n 40 boo ks , w h at is th e le as t n u m be r o f bo o ks th at A s la m co u ld h a ve ? ( A) 200
5
( B ) 205
( C ) 210
( D) 220
A s la m is no w 3 tim e s a s o ld as J ave d, bu t 5 ye ars ago, h e w as J a ve d w a s. Ho w o ld is A s la m no w ? ( A) 10
x% of y 10 (A) x 100 (B) x 1000 (C) x x (D) 100
6
If
(E)
( B ) 12
( C ) 24
( D) 30
( E ) 24 5 tim e s as ( E ) 36
is 10, wh a t is y?
x 10
Answer Key 1 2 3 4 5 6
D A A D D C
Student Guide
54
Analytical Ability
3
3 . 1. 1 Q ue st i o n f o r ma t E a c h a n a lytic a l re a s o n in g que s tio n is a lo gic al pu zzle , base d o n a give n s e t of c o n ditio n s . L ike m a th em a tic al que s tio n s , th e s e qu e s tio n s h ave e xac tly o ne c o rre c t a n s we r, w h ic h is w h a t yo u n ee d to se le c t. A n a lytic a l re a s on in g que s tio n s are pre s e n te d in gro u ps o f f ou r o r f ive qu e s tio n s . E a c h gro u p is bas e d o n a s h o rt pas s age fo llo w e d by a se t of c o n ditio n s . O c c a s io n a lly, th e re are graph s an d table s in s te ad o f a pas s age. To u n de rs ta n d th e ge ne ra l fo rm a t o f th e qu es tio n , c o n s ide r th e fo llo w in g e xam ple . Q ue st i o n 1 - 4 : A s pa rt o f th e ir s po rts ph ys ic a l, se ve n co lle ge ath le te s F, G, H , I , J, K an d L a re be in g we igh e d. I n a n no u n c in g th e re s u lts o f th e ph ys ic al e xam s , th e c o a c h h a s give n th e fo llo w in g in fo rm atio n . i. No n e o f th e a th le te s is e xac tly th e s am e we igh t as an o th e r ath le te . ii. K is h e a vie r th a n L, bu t ligh te r th an H. iii. I is he a vie r th a n J iv. B o th F a n d G a re he a vie r th an H . 1
E a c h of th e f o llo w in g c o u ld be tru e E X C E PT A. F is th e he a vie s t. B. G is th e he a vie s t. C. I is th e he a vie s t. D. M o re th a n th re e a th le te s are h e avie r th an K. E. M o re th a n th re e a th le te s are ligh te r th an K.
2
W h ic h o f th e fo llo w in g, if tru e , w ou ld be s u ff ic ie n t to de te rm in e w h ic h a th le te is th e ligh te s t? A. I is th e he a vie s t B. I is ligh te r th a n K C. K is h e a vie r th a n J D. J is h e a vie r th a n K E. E xa c tly f ive s tu de n ts a re ligh te r th an F .
3 I f J is h e a vie r th a n F , ho w m an y dif fe re n t ran kin gs by w e igh t, o f th e ath le te s a re po s s ible ? A. 1 B. 2 C. 3 D. 4 E. 5 4
I f H is he a vie r th a n I , w h ic h A. I ’s we igh t is e qu a l to th e B. I ’s we igh t is e qu a l to th e C. J ’s we igh t is e qu a l to th e D. J is th e se c o n d ligh te s t.
o f th e fo llo w in g CA NNO T be tru e ? ave rage o f F ’s we igh t an d G ’s we igh t. ave rage o f K’s w e igh t an d L’s we igh t ave rage o f K’s w e igh t an d L’s we igh t
Answers:
1. E
2. D
3. C
4. A
3.1.2 How to attempt
•
S im plif y th e in f o rm a tio n by u s in g abbre via tio n s an d s ym bo ls . Th e f irs t s te p is to s trip a w a y a ll of th e e xc e s s ve rbiage f ro m th e give n pas s age a n d th en to a bbre via te th e re m ain in g ke y wo rds w ith s in gle le tte rs . F o r e xa m ple , in th e que s tio n s tate m e n t “f ive mu s ic ian s a bas s is t, a dru m me r, a gu ita ris t, a pian is t, an d a tru m pe te r are pe rf o rm in g in a ta le n t sh o w ”, yo u s ho u ld im me diate ly abbre viate th e m B , D, G, P an d T.
Yo u c a n u s e a bbre via te d le tte rs to re pre s en t a w h o le se n te n c e als o . Yo u s h o u ld u s e s ym bo ls to re pre s e n t c o n ditio n s . Yo u m ay de ve lo p yo u r o w n s ym bo lic c o n ve n tio n s fo r th is . Th e obje c tive is to c o n ve rt th e pro ble m in to n o ta tio n s , so th a t, it is e as ily u n de rs tan dable . Th e f o llo w in g is a ba s ic se t o f s ym bo ls , w h ic h are mo s t co mm o n ly u s e d. ‘A ’ re pre se n ts th e s ta te m e n t “A kbar is go in g”. ‘B ’ re pre s en ts th e s ta te m e n t “B abu r is go in g”. S y mb o l ~
No t
~A
∧
An d
A
∨
Or
→
I f , th e n
Me a ni ng
Examp l e s
∧ B A ∧ ~B A∨ B A ∨ ~B A
→B
(A
↔ •
•
I f a n d on ly if
∧ B)
→S A ↔B
A kbar is no t go in g. O r yo u c an s ay, “it is n o t th e c as e th at A kbar is go in g”. A kbar an d Babu r are go in g. A kbar is go in g an d Babu r go in g. A kbar o r B abu r is go in g.
is
no t
A kbar is go in g o r Babu r is no t go in g. I f A kbar is go in g th e n Babu r is go in g. I f A kbar an d Babu r are go in g, th e n Sale e m is go in g. B abu r is go in g, if an d o n ly if A kbar is go in g.
B ef o re le a rn in g th e ta c tic s to atte m pt an an alytic a l re as o n in g que s tio n , yo u mu s t be fa m ilia r w ith s om e bas ic lo gic f ac ts , w h ic h are e xplain e d in th e fo llo w in g te xt. Co n s ide r A an d B are tw o s tate me n ts . o A is tru e me a n s ~ A is f als e . o ~ A is tru e m e an s A is f als e .
∧ B ) is tru e me an s bo th A an d B are tru e . ( A ∧ B ) is tru e me an s e ith e r A o r B o r bo th are f als e . ( A ∨ B ) is tru e me an s e ith e r A o r B o r bo th are tru e . ( A ∨ B ) is fa ls e m ean s bo th A an d B are fals e . ~ (A ∧ B) is e qu ivale n t to (~ A ∨ ~ B) . ~ (A ∨ B) is e qu ivale n t to (~ A ∧ ~ B) .
o o o o o o o
(A
o o o
If (A
o
(A
↔ B)
o
(A
↔ B)
→
If (A B ) is tru e th e n I f A is tru e B is als o tru e . I f A is f a ls e B may be tru e o r f als e .
→ B ) is fa ls e th e n A is tru e an d ( A → B ) is equ iva le n t to ( ~B → ~A ) ( A ↔ B) is tru e m ean s :
B is f als e .
I f A is tru e B is tru e . I f A is f a ls e B is f als e. is f a ls e me an s: I f A is tru e B is f als e . I f A is f a ls e B is tru e . is e qu ivale n t to [( A
→ B) ∧
(B
→ A )] .
Yo u mu s t be fa m ilia r w ith th e mo s t co mm o n type s of an alytic a l re a s o n in g qu e s tio n s . Th e f o llo w in g f ou r type s o c c u r mo re f re qu e n tly
th a n th e o th e rs , a n d w he n yo u s ee th e m, yo u s h o u ld im me diate ly kno w w h a t yo u ne e d to do to an s we r th e m . o W hi c h o f t he fo l l o wi ng c o ul d b e t r ue ? I f o n ly o ne of th e a n s we r ch o ic e s co u ld be tru e , th en e ac h o f th e o the r fo u r c ho ic e s m u s t be f a ls e ; th at is , e ac h o ne mu s t vio la te at le as t on e of th e give n c o n ditio n s .
o
W hi c h o f t he f o ll o wi ng must b e t r ue? S in ce o n ly on e o f th e a n s we r c ho ic e s mu s t be tru e , th e n fo r eac h o f th e c ho ic e s , e ith e r it is f a ls e o r it is po s s ibly ( bu t no t de f in ite ly) tru e . Yo u h ave to c h oo s e o n ly th a t c h o ic e w h ic h is def in i te ly tru e .
o
W hi c h o f t he f o ll o wi ng c anno t b e t r ue? S in c e o n ly on e of th e a n s we r ch o ic e s c ann o t be tru e , th e n e ach o f th e o the r c h o ic e s c o u ld be tru e . Th e c o rre c t ans w e r is th e o n ly ch o ic e , w h ic h vio la te s a t le a s t on e o f th e give n c on dit io n s o r is o th e rw is e in c o n s is te n t w ith w h at yo u kn o w m u s t be tru e . Ho w ma ny p o ssi b i li t i e s ar e t he r e? Th is que s tio n as ks , “Ho w m a n y dif fe re n t w ays are th e re to s atis f y all of th e give n c o n ditio n s ?” He re , yo u mu s t s ys te m atic al ly c o un t o r lis t all o f th e po s s ibil it ie s th a t do n o t vio late an y of th e c o n ditio n s .
o
•
I de n tif y th e ke y w o rds th at s e rve to lim i t th e s itu atio n . C e rtain w o rds a re c ritic a l to yo u r u n de rs tan din g o f th e s itu atio n . B e su re to in c o rpo ra te yo u r s ym bo ls . S om e f re que n tly u s e d ke y w o rds are lis te d be lo w :
A f te r B ef o re Dif f e re n t O n ly E xc e pt I mm edia te ly M u s t be U n le s s
A ll But Dire c t ly Po s s ible F ew e r I mpos s ible S am e S ma lle s t
A lw ays C an be E ac h E n tire F irs t Las t S om e G re ate s t
A t le as t C an n o t be No fe we r th an E ve ry If Le as t Th e Le as t No n e
A t mo s t C o n se c u tive No mo re th an E xac tly I f an d o n ly if Most Th e Mo s t
No te th a t ce rta in ke y w o rds h ave on ly o ne fu n c tio n , to ru le o u t a po te n tia l a m bigu ity. •
E lim in a t in g th e c ho ic e s is alw ays a goo d s trate gy. W h ile e lim in atin g th e c h o ic e s, f irs t of a ll, e lim in ate th os e w h ic h are ru le d o u t by in div idu al c o n ditio n s : Th e n wo rk th ro u gh th e rem ain in g c h o ic e s.
•
S tu dy c o n ditio n s , n o t me re ly f o r wh at th e y s tate bu t als o fo r w h at th e y im ply. C e rta in a n a lytic a l re as o n in g qu es tio n s re se m ble th e in f e re n ce qu e s tio n s yo u f in d in th e re adin g co m pre he n s io n se c tio n . To ans w e r th e m co rre c tl y, yo u mu s t u n de rs tan d no t on ly w h at th e co n ditio n s s tate e xplic i tl y, bu t a ls o wh a t th e y im ply.
•
O f te n th e ke y to a n sw e rin g an alytic a l re aso n in g qu es tio n s is to o rgan ize th e give n in f o rm a tio n in a lis t o r table . O n so me a n a lytic a l re a s o n in g qu es tio n s , an e xce lle n t w ay to de al w ith th e in f o rm a tio n is to draw a s im ple diagram , pic tu re , o r map. Th is is pa rtic u la r ly he lpf u l w h en yo u are de alin g w ith th e ph ys ic al o r tem po ral o rde r of th in gs . I t is m uc h eas ie r to te ll wh e th e r pe rs o n A c an be s e a te d o ppos ite pe rs o n B if yo u h ave s ke tc h e d a diagram o f th e table ; it is e a s ie r to kno w w he th e r pe rso n C is o lde r o r yo un ge r th an pe rs o n D if yo u h a ve e n te re d a ll o f th e give n in fo rm atio n o n a tim e lin e ; an d it is
•
e a s ie r to de te rm in e wh e th e r tow n E is e as t o f to wn W if yo u h ave draw n a s im ple m a p.
3.1.3 Example Explanations
questions
with
Answers
and
Questions 1-5:
S ix a c to rs - - - - B o b, C a ro l, Da ve E d, F ran k, an d G rac e au dit io n f o r a part in an o ff - B ro a dw a y pla y. Th e a u dit io n s w ill take plac e o ve r f ou r co n s e c u tive days , s ta rt in g o n a Th u rs da y. E ac h ac to r w ill h ave on e au ditio n ; th e days on wh ic h th e dif f e ren t a c to rs w ill a u ditio n mu s t c o nf o rm to th e fo llo w in g co n ditio n s . i. ii. iii. iv. v.
vi. vii.
A t le a s t o ne a u ditio n w ill take plac e e ac h day. No mo re th a n two au ditio n s w ill take plac e o n an y day. No mo re th a n th re e au dit io n s w ill take plac e o n an y tw o c o n se c u tive da ys . B o b’s a u dit io n m u s t take plac e on S atu rday. C a ro l’s a u ditio n m u s t take plac e on th e s am e day as an o th e r a u dit io n . F ra n k’s a u ditio n s m u s t take plac e o n th e day be f o re G rac e ’s a u dit io n . Da ve ’s a u dit io n m u s t take plac e on a day af te r E d’s au dit io n .
1
I f on ly o n e a u ditio n ta ke s plac e o n Th u rs day w h ic h ac to r co u ld h ave th at a u dit io n ? ( A) B o b ( B ) C a ro l ( C ) Dave ( D) F ran k ( E ) G rac e
2
I f B o b’s a n d F ra n k’s a u dit io n s are o n th e s am e day, w h ic h o f th e fo llo w in g m u s t be tru e ( A) Da ve ’s a u dit io n w ill ta ke plac e o n Th u rs day ( B ) Da ve ’s a u dit io n w ill ta ke plac e o n F riday ( C ) G ra c e ’s a u ditio n w ill ta ke plac e on Th u rs day ( D) C a ro l’s a u ditio n w ill ta ke plac e on Su n day ( E ) E d’s a u ditio n w ill ta ke plac e o n S u n day
3
I f th e dire c to r de c ide s to ho ld tw o au ditio n s o n Th u rs day an d tw o o n S u n da y, h o w m a n y a c to rs wo u ld be e ligible to au ditio n on F riday? ( A) 1 (B) 2 (C) 3 ( D) 4 (E) 5
4
I f E d a n d G ra c e h a ve th e ir au dit io n s on th e s am e day w h ic h of th e f o llo w in g m u s t be tru e ? ( A) E d’s a u ditio n w ill ta ke plac e o n Th u rs day. ( B ) F ra n k’s a u dit io n w ill ta ke plac e o n F riday. ( C ) C a ro l’s a u ditio n w ill ta ke plac e on Satu rday. ( D) G ra c e ’s a u ditio n w ill ta ke plac e on S atu rday. ( E ) C a ro l’s a u ditio n w ill ta ke plac e on Su n day.
5
I f E d’s a u ditio n is o n S atu rday, wh ic h o f a u dit io n o n th e s a me da y a s an y o th e r ac to r? ( A) B o b ( B ) C a ro l (C) Ed
th e
fo llo w in g
( D) F ran k
ac to rs
c an no t
( E ) G rac e
Questions 6-10: Du rin g th e f irs t h a lf of th e ye ar, f rom J an u ary th ro u gh J u ne , th e c h airpe rs o n o f th e m a th em a tic s de pa rtm e n t w ill be o n s abbatic a l. Th e de an o f th e co lle ge h as a s ke d e ac h o f th e s ix pro fe s s o rs in th e de partm e n t -- - A rke s , Bo ro f s ky, Ch an g, De n tu re , H o bbe s , a n d Le e - -- to se rve as ac tin g c h airpe rs o n du rin g on e o f th o s e
m on th s . Th e ma th e m a tic ia n s c an de c ide th e o rde r in wh ic h th e y w ill s e rve , s u bj e c t on ly to th e f o llo w in g c rite r ia es tabl is h e d by th e de an . i. C h a n g w ill se rve a s c h airpe rs o n in F e bru ary. ii. A rke s w ill se rve a s c h airpe rs o n bef o re H o bbe s doe s . iii. B o rof s ky a n d De xte r w ill s e rve as ch airpe rs o n s in co n s e cu tive m on th s . 6
W h ic h o f th e fo llo w in g pro fe s s o rs co u ld s e rve as c h airpe rs o n in J anu ary?
(A) B o ro df s ky
(B) Chang
( C ) De xte r
( D) H o bbe s
( E ) Le e
7
I n ho w ma n y w a ys c an th e s c he du le be m ade u p if Le e h as to s e rve as c h a irpe rs o n in Ma y? ( A) 1 (B) 2 (C) 3 ( D) 4 (E) 6
8
I f L e e s e rve s in Apri l, a ll o f th e fo llo w in g co u ld be tru e E XC E PT ( A) A rke s se rve s in J a n u a ry ( B ) H o bbe s se rve s in m a rc h ( C ) B o rof s ky s e rve s in ma y ( D) B o rof s ky s e rve s in J u ne ( E ) H o bbe s se rve s in J u n e
9
I f B o rof s ky s e rve s in M a y, wh at is th e late s t m on th in w h ic h A rke s c o u ld s e rve ? ( A) J a n u a ry ( B ) F e bru a ry ( C ) M a rc h ( D) A pril (E) June
1 0 W h ic h o f th e fo llo w in g CA NNO T be tru e ? ( A) A rke s a n d L e e s e rve in co n s e c u tive m on th s . ( B ) L e e a n d Ho bbe s se rve in c o ns e c u tive m on th s . ( C ) H o bbe s a n d De xte r se rve in co n se c u tive mo n th s . ( D) A rke s a n d C h a n g se rve in c o n se c u tive mo n th s . ( E ) B o rof s ky a n d C h a n g se rve in c o ns e c u tive m on th s .
Solutions 1-5: F irs t e xpre s s ea c h of th e c o n ditio n s s ym bo lic al ly: B , C , D, E , F, a n d G: 1 a u ditio n eac h Da ys : Th u , F ri, S a t, Su n E a c h da y: 1 o r 2 a u ditio n s 2 c o n se c u tive da ys : 2 o r 3 au ditio n s B =S a t Cx F
2
Th e c o n ditio n th a t B o b’s a n d F ran k’s au ditio n s are on th e s ame day c om ple te ly de te rm in e s th e s c h e du le . Th e y mu s t take plac e o n S atu rday (B = S at) . To a vo id h a vin g m o re th a n th re e au ditio n s o n two co n s e c u tive days , th e re c an be o n ly o ne a u ditio n on F rida y an d on e o n Su n day, wh ic h m e ans th e re w ill be tw o o n Th u rs da y. S in ce F ra n k mu s t h ave to pre ce de G race ( F< G ) , G rac e ’s au ditio n w ill ta ke pla c e on Su n da y. S in c e E d m u s t pre c e de Dave , E d’s au ditio n w ill take pla c e o n Th u rs da y a n d Da ve ’s au ditio n on F riday. F in ally, C aro l’s au ditio n w ill be th e s e co n d a u dit io n on Th u rs day. Th e f in al s c he du le is “C an d E on Th u rs da y, D on F rida y, B a n d F o n S atu rday an d G on S un day”. O n ly c h o ic e B is c o n s is te n t w ith th is s c h e du le , s o “B ” is th e c o rre c t c h o ic e .
3
S in c e o n ly o n e a u ditio n c a n take plac e on F riday, it c an n o t be C aro l’s ( C x) ; a n d, of co u rs e , it c a n n o t be B ob’s ( B = Sat) . An y o f th e o the r f ou r ac to rs c o u ld a u ditio n on F rida y a s in dic ate d in th e f o llo w in g s c h e du le s : E / F o n Th u , D o n F ri, B o n S at, C/ G on Su n C / F o n Th u , E on F ri, B on Sat, D/ G on Su n C / E on Th u , E o n F ri, B on Sat, D/ G on S un E / F o n Th u , G on F ri, B o n Sat, C / D on Su n S o th e co rre c t c ho ic e is D.
4
Th e on ly s c he du le th a t fu lf ils th e c on dit io n s is “F o n Th u , E / G o n F ri, B on S at, a n d C / D on Su n ”. On ly c ho ic e E is co n s is te n t w ith th is s ch e du le .
5
S in c e E d a n d B o b’s a u ditio n s are bo th takin g plac e on S atu rday, e lim in ate c h o ic e s A a n d C . S in c e C aro le m us t au ditio n on th e s ame day as ano th e r a c to r, e lim in a te B. F in a lly, s in c e Dave ’s au ditio n m u s t take plac e o n Su n day ( E < D) , F ra n k’s a u ditio n m u s t take plac e o n Th u rs day an d G rac e ’s au dit io n on F rida y ( F < G) . E lim in a te c h o ic e D. Th e co m ple te s c he du le is : “C / F o n Th u , G o n F ri, B/ F on Sa t, a n d D on S un . ”
Solutions 6-10:
L e t A , B , C , D, H , L re pre s en ts prof e s so r n ame s . C = Fe bru a ry, A
6
O n ly ch o ic e E is th e re , wh ic h do e s n o t vio late an y of th e c o n ditio n s , s o is th e c o rre c t c h o ic e .
7
W ith C s e rvin g in F ebru a ry a n d L in M ay, th e o n ly co n s ec u tive m on th s availab le f o r B a n d D a re M a rc h a n d April. Th e n s in c e A mu s t se rve is be fo re H in J u ne . Th e re a re two po s s ible s c he du le s , de pe n din g on th e o rde r of B an d D, s o th e c o rre c t c h o ic e is B.
8
I f L s e rve s in April, th e co n s e c u tive m on th s availa ble fo r B an d D are M ay an d J u n e; s o c h o ic e s C a n d D co u ld be tru e . S in c e A mu s t s e rve be fo re H , c h o ic e s A a n d B mu s t be tru e , o n ly c h o ic e E c an no t be tru e .
9
S in c e A pril? w ou ld occur
10
Th e on ly pro fe s s o rs th a t c a n se rve in J an u ary are A an d L, so , on e of th em m u s t se rve in J a n u a ry, a n d n e ith e r s e rve s in Fe bru ary. S o c h o ic e A c an n o t be tru e .
.a
A mu s t se rve be fo re H do e s, A c an n o t s e rve in J u ne . C an A se rve in No, be c a u s e th e n, D w ou ld s e rve in J un e ( B< < D o r D<< B ) , an d again A n o t pre c e de H. Th e late s t th at A co u ld s e rve in M arc h , wh ic h c ou ld in th e f in a l o rde r: L, C , A , D, B an d H .
Logical Reasoning
E a c h lo gic a l re a so n in g que s tio n re qu ire s yo u to an alyze an argu me n t pre s e n te d in a s ho rt pa s s a ge . Of te n yo u a re as ke d e ith e r to f in d a c o n c lu s io n th at is a lo gic al c o n se qu e n ce of th e pa s s a ge , o r to c ho o s e a s tate m e n t th at, if tru e , s tre n gth e n o r w e a ke n s th e a rgu me n t.
3.2.1Question format L o gic a l re a so n in g que s tio n s a re bas e d u po n a pas s age c alle d argu m e n t. Yo u h ave to a n a lyze th e a rgu me n t pre se n te d in th e pas s age . Th e pas s age is f o llo we d by a qu e s tio n . O c c a s io n a lly, th e re is m o re th an o ne que s tio n re late d be th e s am e pa s s a ge . No ma tte r w h a t th e n u m be r is , th e qu e s tio n s alw ays aim at yo u r abili ty to u n de rs ta n d th e co n c lu s io n re ac h e d by th e au th o r o f th e pas s age, an d to give a rgu m e n t a n d co n tra a rgu m e n ts . Lo gic al re as o n in g qu e s tio n s are a lo t like re adin g c om pre h e n s io n qu e s tio n s in a ve rbal se c tio n . F o r ea c h lo gic a l re a s on in g que s tio n , th e argu me n t is fo llo w e d by a m u lti c h o ic e qu e s tio n . Th e c h o ic e s a re s im ple s tate m en ts . Mo s tly th e qu es tio n s tate me n t be gin s w ith th e ph ra s e “w h ic h of th e f o llo w in g s tate m e n ts ”. He re are a f ew e xa m ple s : • W h ic h o f th e fo llo w in g s tate me n ts is an as s u m ptio n on w h ic h th e c o n c lu s io n o f th is a rgu me n t is ba se d?
•
W h ic h o f th e fo llo w in g s tate me n ts ide n tif ie s a f law in th e re as o n in g o f th is a rgu m e n t?
•
W h ic h o f th e fo llo w in g s tate me n ts c an be m os t re aso n ably in fe rre d, f ro m th e s ta te m e n ts in th e give n pas s age ?
•
W h ic h o f th e fo llo w in g s tate me n ts , if tru e , wo u ld m os t se rio u s ly, we ake n th e a rgu m en t of fe re d?
•
W h ic h of th e f o llo w in g s tate me n ts , if tru e , w o u ld s tre n gth e n th e c o nc lu s io n in th e pre c e din g a rgu m e n t?
•
W h ic h of th e f o llo w in g s tate me n ts wo u ld be th e mo s t im po rtan t to kn o w to e va lu a te th e a rgu m e n t give n in th e pre ce din g paragraph ? E ve ry lo gic al re a s o n in g qu e s tio n do e s no t f it th is m o ld, bu t yo u s ho u ld try.
3.2.2 How to attempt •
•
W h ile a tte m ptin g lo gic a l re as o n in g qu e s tio n s , yo u s h o u ld re ad th e qu es tio n s ta te m e n t be fo re re a din g th e argu me n t. Th e n yo u s ho u ld an alyze th e a rgu m e n t pre s en te d in th e pas s age . Yo u m u s t kn ow w h at as pec t of th e a rgu m e n t yo u a re to co n c e n trate o n , an d f oc u s on it. B y th is , yo u w ill no t be un n e ce s s a ril y w a s tin g yo u r tim e . Yo u mu s t be a ble to s po t th e que s tio n type by re adin g th e que s tio n s ta te m e n t. I f yo u do th is , you w ill be be tte r able to appro ac h th e argu m e n t in h a n d. Th e f o llo w in g s ix c ate go rie s are th o s e w h ic h m os t c om mo n ly o c c u r:
1
Assumption:
2
Inference:
3
Conclusion:
4
Central Point:
5
Support:
6
Argument Evaluation: an argument.
Q ue s tio n s th at te s t yo u r abili ty to re co gn ize th e pre m is e s on w h ic h a n a rgu me n t is ba s e d, of te n take th e f o llo w in g f o rm s : o Th e c o n c lu s io n abo ve de pen ds on w h ic h o f th e f o llo w in g a s s u m ptio n s ? o Th e a u th o r o f th e pas s age abo ve m ake s w h ic h of th e fo llo w in g a s s u m ptio n s ? o I n th e pa s s a ge abo ve , th e au th o r ass u me s wh ic h of th e f o llo w in g s ta te m e n t to be tru e ? Q u e s tio n s , w h ic h te s t yo u r abil ity to go be yo n d th e au th o r’s e xplic i t s ta te me n ts a n d se e w h at th es e s tate m e n ts im ply, m ay be w o rde d like th e s e . o I t c a n be in fe rre d f rom th e pas s age abo ve th at th e au th o r be lie ve s th a t … o W h ic h o f th e fo llo w in g is im plie d by th e pas s age abo ve ? o F ro m th e in f o rm atio n abo ve , wh ic h of th e f o llo w in g is th e mo s t re a s o n a ble in f e ren c e ? Q u e s tio n s th at te s t yo u r abil it y to de te rm in e w h at c laim c an lo gic a l ly be ma de o n th e ba s is of e vide n c e in th e pas s age abo ve ? o I f th e s ta te m e n ts abo ve are tru e , wh ic h o f th e fo llo w in g in a c o n c lu s io n th a t c an be pro pe rly draw n ? o Th e s ta te m e n ts in th e pas s age , if tru e , be s t s u ppo rts w h ic h of th e f o llo w in g c o n c lu s io n s ? Q u e s tio n s th at te s t yo u r abil it y to u n de rs tan d th e th ru s t o f a n a rgu me n t. o Th e s ta te m e n t s ite d abo ve c o n ve ys w h ic h o f th e fo llo w in g pro po s itio n s ? o Th e a u th o r o f th e pas s age abo ve argu e s th at… o W h ic h o f th e fo llo w in g e xpre s se s th e po in t th e au th o r o f th e pa s s a ge a bo ve m ake s ? Q ue s tio n s th at te s t yo u r abili ty to re co gn ize wh e th e r an a s s e rtio n s u ppo rts o r u n de rm in e s an argu m en t. o W h ic h of th e f o llo w in g, if tru e , be s t su ppo rts th e au th o r’s c o n c lu s io n ? o W h ic h o f th e fo llo w in g, if tru e , m os t w e ake ns th e au th o r’s c o n c lu s io n ?
Questions that test your ability to judge
o
o
W h ic h o f th e fo llo w in g ide n tif ie s a f law in th e s pe ake r’s re a s o n in g? W h ic h o f th e fo llo w in g wo u ld be mo s t im po rtan t to kn o w w h e n e va lu a tin g th e ac c u rac y o f th e argu m en t abo ve ?
•
Do no t try to s kim th e pas s age , re ad eac h argu me n t c aref u lly. I t is no t e no u gh to h a ve a ge ne ral ide a abo u t th e argu m e n t; yo u m u s t be able to a n a lyze it ve ry c a ref u lly.
•
Yo u m u s t f in d th e co n c lu s io n of th e argu m e n t, w h ic h th e au th o r c laim s to h a ve re a c he d. Th a t m os t c om mo n s itu atio n s are as fo llo w s : o Th e co n c lu s io n is th e las t s en te n c e of th e pas s age , o f te n s tart in g by w o rds su c h as so , th e ref o re , th u s , he n c e , c o n se qu e n tly e tc. o Th e co n c lu s io n is th e f irs t s en te n c e of th e pas s age fo llo w e d by th e s u ppo rtin g e vide n ce . o O c c a s io n a lly, th e co n c lu s io n is n o t pre s e n t in th e pas s age ; in th is c a s e , th e que s tio n as ks yo u to ide n tif y th e c o nc lu s io n .
•
Pa y pa rtic u la r a tte n tio n to s ign al w o rds su c h as acc o rdin gly, f o r th is re a s o n , h e n ce , a lth o u gh , bu t, e xc e pt, in co n tras t, n e ve rth e le s s , u n like e tc .
•
E lim in a t in g th e c ho ic e s is alw ays th e be s t s trate gy if yo u do no t kn o w wh at th e c o rre c t a n s we r is . Th is pro c e s s w ill e lim in ate so me o bvio u s w ro n g c h o ic e s. An d yo u w ill be able to make an e du c ate d gu e s s f ro m th e re m a in in g on e s.
•
E ve ry a rgu me n t is ba se d u po n c e rtain as s u m ptio n s made by th e au th o r. I f a n a rgu m en t’s ba s ic pre m is e s are so u n d, th e argu m e n t is s tre n gth e n e d. I f a n a rgu m e n t’s ba s ic pre m is e s are f law e d, th e argu m e n t is w eake n e d. I n s u ppo rt qu es tio n s , wh e re yo u h ave to de c ide abo u t we ake n in g o r s tre n gth e n in g th e que s tio n , pin po in t w h at th e argu m e n t as s um e s . Th e n c om pa re th a t a s s um ptio n w ith th e an s w e r c ho ic e s . I f th e qu e s tio n as ks yo u to f in d th e ch o ic e , wh ic h m os t s tre n gth e n s th e argu m en t, lo o k f o r th e c h o ic e th a t is m os t in ke e pin g w ith th e argu m e n t’s bas ic as s u m ptio n . I f th e qu e s tio n a s ks yo u to c ho o s e th e c ho ic e th at mo s t w e aken s th e argu me n t, lo o k fo r th e a n s we r th a t c as ts th e mo s t do u bt on th at as s u m ptio n .
•
S om e lo gic a l re a s o n in g qu es tio n s are e s se n tia lly m in i an alytic a l re as o n in g qu e s tio n s , so , be f am ili a r w ith all o f th e im po rtan t lo gic al f ac ts an d apply w he n e ve r ne e de d. E xa m ple qu e s tio n s w ith A n sw e rs an d E xplan atio n s
3.2.3Example Questions with Answers and Explanations Questions 1-2:
Th e m ic ro w a ve o ve n h a s be c om e a s tan dard applian c e in m an y kitc h e n s , m ain ly be c a u se it of fe rs a f a s t w a y of c o o kin g f oo d. Ye t, so me h om eo w ne rs be lie ve th at th e o ve n s a re s till n o t c om ple te ly s afe . M ic ro w aves , th e re fo re , sh o u ld n o t be a s ta n da rd a pplia n c e un ti l th e y h a ve bee n c are f u lly re se arc h e d an d te s te d. 1
W h ic h o f th e fo llo w in g, if tru e , w ou ld mo s t we ake n th e c o n c lu s io n of th e pa s s a ge a bo ve ? ( A) H om eo w ne rs , o f te n pu rc h as e ite m s de s pite kn o w in g th e y may be u ns af e . ( B ) Th o s e ho m eo w ne rs in do u bt abou t m ic ro w ave s afe ty o u gh t n o t to pu rc h ase m ic ro w a ve s . ( C ) R es e a rc h a n d te s tin g o f h om e applian c e s s e ldom re ve als s afe ty h azards . ( D) M ic ro w a ve s a re no t a s dan ge ro us as s te am iro n s , wh ic h are u s e d in almo s t e ve ry h om e.
( E ) H om eo w ne rs o f te n pu rc h as e ite m s th at th e y do n o t n ee d. 2
W h ic h o ne o f th e fo llo w in g, if tru e , w ou ld mo s t s tre n gth e n th e c o n c lu s io n of th e pa s s a ge a bo ve ? ( A) H om eo w ne rs o f te n do u bt th e adve rtis e d s af e ty o f all n ew applian c e s . ( B ) S pe e d of fo o d pre pa ra t io n is n o t th e on ly co n c e rn of to day’s ho me o w ne r. ( C ) M o de rn h om e ow n e rs h a ve m o re f ree tim e th an e ve r be fo re . ( D) F oo d pre pa ra t io n h a s be co me alm o s t a s c ie n ce , w ith m o re c om plic a te d an d in vo lve d re c ipe s . ( E ) M a n y m ic ro w a ve o ve n s h ave be e n fo u n d to le ak radio ac t ive e le me n ts .
3
Ye a rs a go , a po ll co n c lu de d th at th e re are m o re te le vis io n s th an th e re are ba th tu bs in A me ric a n h om e s . No do u bt th at f ac t rem ain s to day, e s pec ial ly in ligh t of th e gro w in g po pu la ri ty of ho me c om pu te rs . Now , in additio n to ow n in g te le vis io n s f o r e n te rta in m e n t, mo re an d m o re fam ilie s are pu rc h as in g TV m on ito rs fo r u s e w ith a pe rs o n al c om pu te r. W e c an s afe ly gue s s th at th e re are s til l m a n y mo re pe o ple s ta rin g at a pic tu re tu be th an s in gin g in th e s ho we r. W h ic h o f th e fo llo w in g s ta te me n ts c an be in f e rre d f rom th is pas s age ? ( )A Pe rs o n a l c om pu te rs pro bably c o s t le s s th an in s tall in g a s ho we r o r bath tu b. ( ) B Pe o ple c a n w a s h th em s e lve s w ith o u t a tu b o r s h ow e r, bu t th e y c an n o t w a tc h te le vis io n u n le s s th e y o wn a te le vis io n se t. ( ) C TV mo n ito rs w ill wo rk w ith pe rs o n al c om pu te rs in plac e of re gu lar c om pu te r m on ito rs . ( ) D A s m a n y co m pu te rs a re so ld to day as te le vis io n s e ts a f ew ye ars ago. ( ) E M o re te le vis io n m on ito rs are no w u s e d w ith pe rso n al co m pu te rs th an are u s e d to w a tc h co mm e rc ia l te le vis io n bro adc as ts .
4
S om e sc ie n tis ts h a ve pro po se d th at, ove r two h u n dre d m illio n ye ars ago , o ne gia n t la n d m a s s , ra th e r th a n vario u s c o n tin e n ts an d is lan ds , co ve rs on e th ird o f th e e a rth . L o n g be fo re th e re was an y h um an lif e , an d o ve r vas t pe rio ds o f tim e , is la n ds a n d co n tin e n ts drif te d apart. Au s tral ia w as th e f irs t to se parate , w h ile S ou th A me ric a a n d A f ric a w e re late in s plitt in g apart. S om e is lan ds , of c o u rs e, we re fo rm e d by vo lc an o e s an d w e re ne ve r part of th e gre at lan d m as s. A ll th e f o llo w in g w ou ld s u ppo rt th e au th o r’s c laim E XC E PT
()A M a n y
of th e pla n ts o f th e So u th Am e ric an rain f o re s ts are m arke dly s im ilar to th o s e o f A f ric a n ra in fo re s ts . ()B A u s tra lia h a s m o re a n im als th at are no t fo u n d in an y o th e r c o n tin e n t th an h a ve se ve ra l of th e m u c h large r c o n tin e n ts . ( ) C V o lc a n ic is la n ds like H aw aii h ave ec o s ys te ms ve ry dif f e re n t f ro m th o se o f c o n tin e n ta l la n ds w ith th e s ame ave rage tem pe ratu re . ( ) D Th e pla n ts of s im ila r co n dit io n s in S ou th A me ric a h ave le s s in c om mo n w ith th o s e o f A u s tra lia th a n w ith th o s e o f A s ia, Af ric a o r E u ro pe. ( ) E Th e prim i tive la n gu a ge s o f Au s trali a are un like th os e o f Af ric a, wh ic h re s em ble s th o s e o f S ou th A me ric a. 5
E ve ry Sa tu rda y, Am ir h a s pizza f o r lu n c h an d th e n goe s to th e mo vie s . I f th e s ta te m e n t a bo ve is tru e , w h ic h o f th e fo llo w in g s tate m e n ts m u s t als o be tru e ? 1 I f it is no t S a tu rda y, th an A m ir is n o t h avin g pizza fo r lu n c h an d is no t go in g to th e mo vie s . 2 I f A m ir h a s pizza fo r lu n c h an d th e n goe s to th e m o vie s , it is S atu rday. 3 I f A m ir h a s pizza fo r lu n c h , bu t do e s no t go to th e m ovie s , it is no t a S a tu rda y. ( )A 1 o n ly ( ) B 2 o n ly ( ) C 3 o n ly
( ) D 1 a n d 2 on ly ( ) E 2 a n d 3 on ly
6
A n tif re e ze low e rs th e me ltin g po in t o f an y liqu i d to w h ic h it is adde d so th at th e liqu id w ill no t f ree ze in c o ld we ath e r. I t is co mm o n ly u s e d to m ain tain th e c oo lin g s ys te m in a u tom o bile radia to rs . O f c o u rs e, th e we ath e r m ay be c om e s o co ld th a t e ve n a n tif re e ze is no t e ff e c tive , bu t s u c h a s e ve re c lim atic c o n ditio n ra re ly oc c u rs in w e ll- trave le d plac e s .
W h ic h o f th e fo llo w in g c a n be de du c e d f ro m th e pas s age ? ( )A W e ll- tra ve le d pla c e s h a ve me an s of tran s po rtat io n o th e r th an au to mo bile s . ( ) B A n tif re e ze doe s n o t low e r th e me ltin g po in t o f ce rtain liqu ids in extre m e c o n ditio n s . ( ) C S e ve re c lim a tic c o n ditio n s rare ly o c c u r. ( ) D I t is n o t of te n th a t m a n y trave le rs wh o u se an tif re e ze h ave th e ir c oo lin g s ys te m f re e ze. ( ) E A n tif re e ze ra is e s th e m e ltin g po in t o f s om e liqu ids .
Solutions:
1
Th e c o n c lu s io n o f th e pa s s age is th at, be c au s e of s afe ty c o n ce rn s , m o re re s e a rc h a n d te s tin g ou gh t to be do ne be fo re m ic ro w ave s be co me s tan dard h o u se h o ld a pplia n c e s . I f , ho w e ve r, re s e arc h an d te s tin g are in e ff e c tive me an s o f dis c e rn in g s a fe ty pro ble m s ( as c ho ic e C s ays ), th en re se arc h an d te s tin g w ou ld be irre le va n t. Th is c rit ic is m s e rio u s ly w e ake n s th e co n c lu s io n . So c h o ic e C is th e co rre c t a n sw e r.
2
I f m a n y m ic ro w a ve o ven s h ave be e n f o un d to le ak radio ac ti ve e le me n ts ( as c h o ic e E s a ys ) , th e n th e c o n c lu s io n th at m ic ro w ave s s ho u ld no t be s tan dard a pplia n c e s u n til th e y a re mo re c are f u lly re s e arc he d an d te s te d is f u rth e r s tre n gth e n e d be c a u s e mo re s afe ty c o nc e rn s n e e d to be addre s s e d. So , c ho ic e E is th e co rre c t a n sw e r.
3
Th o u gh C ho ic e s A a n d B m ay we ll be tru e , th e y c an no t be in fe rre d f ro m th e in f o rm a tio n in th e pa s s a ge . B u t c ho ic e C c an be in f e rre d s in c e, “m o re an d m o re f am il ie s a re pu rc h a s in g TV m on ito rs fo r u s e w ith a pe rs o n al c om pu te r. ” TV m on ito rs mu s t wo rk w ith th es e c om pu te rs , o the rw is e , peo ple wo u ld no t bu y th e m fo r th a t pu rpo s e. Ch o ic e s D an d E m ay o r m ay n o t tru e , bu t th e y are no t in f e re n ce s f ro m th e pa s s a ge , s im ply additio n al in f o rm atio n . S o, th e co rre c t c h o ic e is C.
4
I f A u s tra li a wa s th e f irs t c o n tin e n t to s e parate , it wo u ld f o llo w th at its f lo ra a n d fa u n a w o u ld de ve lo p in is o latio n o ve r a lo n ge r pe rio d of tim e . S im ilarl y, w e m a y e xpe c t th e pla n ts an d an im al of So u th Am e ric a an d Af ric a th at s e pa ra te d la te r, to be mo re alike . C ho ic e s A, B, an d D su ppo rt th e se ide as . Th e se pa ra te l y de ve lo pe d is lan ds are dif f e re n t at is als o in ac c o rd w ith th e pa s s a ge . H ow e ve r th e la n gu age s of all th e co n tin e n ts w ou ld h ave de ve lo pe d in is o la t io n , s in ce ma n did n o t e vo lve u n til af te r th e bre ak- u p o f th e lan dm as s, a n d it is s u rpris in g th a t A f ric an an d So u th Am e ric an lan gu age s are s im ilar. H um a n like n e s s o r dif f e re n ce s are irre le van t to th e c laim s of th e pas s age . S o c h o ic e E is th e co rre c t a n sw e r.
5
Th is lo gic a l re a s on in g qu e s tio n is ve ry eas y as so o n as yo u e xpre s s th e give n s ta te m e n t s ym bo lic a l ly. “I f it is S atu rday, th e n A m ir h as Pizza an d go e s to M o vie s ” tra n s la te s a s
S → (P ∧ M ) .
Th is is equ ivale n t to
~ ( P ∧ M ) →~ S ,
w h ic h is e qu iva le n t to (~ P ∨ ~ M ) →~ S . S o if e ith e r P o r M is fals e , th e n S is f a ls e . Th e re fo re , 3 is tru e , ne ith e r 1 no r 2 are tru e . So , th e c o rre c t c h o ic e is C.
6
C h o ic e D is th e c o rre c t a n s we r. S in ce s e ve re c lim atic c o n ditio n s rare ly oc c u r in w e ll- tra ve le d pla c e s , it is no t ne c e ss ari ly tru e th at “I t is n o t of te n th at man y tra ve le rs w ho u s e a n tif re e ze h ave th e ir c oo lin g s ys te m s f re e ze . ” C ho ic e A m en tio n s o th e r m ea n s of tran s po rtat io n , w h ic h is n o t addre s se d in th e pa s s a ge . C ho ic e B ref e rs to “ce rtain ” liqu ids .
Verbal Ability
4
Th e pu rpo s e o f th e Ve rba l Te s t is to e valu ate an d an alyze you r E n glis h c om pre h e n s io n a n d u n de rs ta n din g to w ards th e lan gu age . Th e que s tio n s w ill be ba s ic a l ly a s ke d to j u dge th e se n te n c e co m ple tio n , an alo gy an d c ritic a l re adin g s kil ls . Th e qu e s tio n s of dif f e ren t type s i. e. abo u t se n te n c e co m ple tio n an d a n a lo gy te s tin g w ill be a s ke d ran dom ly. Th e qu e s tio n s abo u t th e c rit ic al re adin g h ow e ve r w ill be a s ke d se pa ra te l y.
.a About the Verbal Questions
A s a lre a dy dis c u s s e d, th is s ec tio n w ill co n s is t of th e f o llo w in g type s o f qu e s tio n s i. e . s e n te nc e c om ple tio n , a n a lo gy an d th e c rit ic al re adin g. Th e de tail abo u t eac h s e c tio n is a s be lo w ;
4.1.1
Sentence Completion
Th e qu es tio n s th a t c om e un de r th is c ate go ry are pro vide d w ith vario u s ch o ic e s . Yo u a re a s ke d to co m ple te th e se n te n ce s by f ill in g in th e blan ks w ith th e m os t s u ita ble c h o ic e. Th e qu e s tio n s fo r s e n te n ce co m ple tio n c an be re late d to an y o f th e o the r are as o f s tu dy i. e. s c ie n ce , lite ra tu re , h is to ry, geo graph y e tc bu t th e s u bje c t matte r w ou ld n o t h in de r yo u r la n gu a ge a bili tie s . Yo u are as ke d to c om ple te th e se n te n c e w ith th e u se o f co rre c t gra m m a r o r vo c abu lary. Th e s e qu es tio n s try to de te rm in e yo u r abili ty to re c o gn ize th e c o rre c t se n te n c e s tru c tu re , righ t gra m m a r a n d h o w yo u make th e c o rre c t c h o ic e of vo c abu lary.
Techniques for Sentence Completion F o r th e s e n te n ce co m ple tio n a f ew c ho ic e s are give n th at c o u ld be s e le c te d fo r c om ple tin g th e se n te n c e s . O n ly on e c ho ic e is c o rre c t ou t of th e s e ve ral c ho ic e s . Yo u h a ve to c om ple te th e se n te n c e by s e le c tin g th e c o rre c t c h o ic e ac c o rdin g to th e gra m m a r o r vo c a bu la ry. Fo r m akin g th e righ t c ho ic e yo u c an be ne f it f ro m th e f o llo w in g te c h n iqu e s ;
•
A f te r yo u re a d th e in c om ple te s en te n c e do no t loo k at th e c h o ic e s. Try to th in k a bo u t th e c o rre c t an sw e r yo u rs e lf . I f yo u th in k th at yo u h ave c om ple te d th e s en te n c e an d f o un d th e co rre c t c ho ic e yo u c an c on s u lt yo u r lis t of c h o ic e s . I f th e an sw e r yo u th o u gh t matc h e s on e o f th e c ho ic e s m en tio n e d in th e lis t th a t is m os t pro bably th e righ t c ho ic e to be marke d. I f it doe s n o t ma tc h w ith th e c h o ic e yo u c an lo o k f o r a s yn o n ym re pla c e m e n t. Th is ta c tic is ve ry h e lpf u l in f in din g th e righ t an sw e r, it pre ve n ts yo u f ro m c o n fu s in g yo u rs e lf w ith th e w ro n g ch o ic e s .
•
Do n o t se le c t th e c ho ic e h as tily. E ve n if yo u are s atis f ie d w ith yo u r c h o ic e try to s u bs titu te it w ith th e o the r c ho ic e s s o th at yo u are m o re s atis f ie d w ith yo u r de c is io n . So me tim e s th e o th e r c ho ic e f its m o re appro pria te ly to th e se n te n c e .
•
W h e n yo u a re a s ke d to co m ple te a se n te n c e, w h ic h h as tw o s pace s to be f ille d in , try to pu t th e f irs t w o rd of e ve ry c h o ic e in th e f irs t blan k. No te do w n th e c ho ic e th a t you f in d be s t. No w f o r th e s e co n d blan k try eve ry s e co n d c ho ic e o f a ll c ho ic e s . No te th e c ho ic e th at yo u th in k is m os t a ppro pria te . C he c k if th e two s e le c te d c h o ic e s are m atc h in g o n e o f th e give n pa ir o f ch o ic e s . I f it doe s th e n s e le c t it as yo u r c o rre c t c ho ic e , if no t th e n co n s ide r th is pa ir a s a w ro n g c ho ic e an d try w ith th e o th e r c h o ic e s.
•
I f yo u f in d dif f ic u lt y in makin g s e n se ou t of c e rtain w o rds an d yo u are no t ve ry f am ili a r w ith th e m yo u c an try to make a gue s s w ith re fe re n c e to th e c o n te xt of th e s e n te n ce . Try to bre ak th e wo rd in to vario u s parts an d a n a lyze its m e an in g e. g. if yo u do n o t kn ow th e me an in g of th e wo rd “c ivi li za t io n ” bre a k it in to tw o i.e . ‘c ivil ize ’ an d ‘atio n ’ no w yo u may kn o w th e m e a n in g o f c ivil ize a n d th ro u gh th e te rm ‘atio n ’ yo u c an m ake o u t th at th e w o rd is a n o u n of c ivi li ze . I f yo u f in d th e wo rd u nf am ilia r w ith pre f ixe s a n d su f f ixe s divide th e wo rd in to its parts e. g. pre re c o rdin g. Th is wo rd c o n s is ts of bo th pre f ix a n d s u f f ix. Yo u c an bre ak th e w o rd like pre - re c o rdin g. He re yo u kn o w th a t pre m ean s be fo re , re c o rd m e ans to s to re an d - in g is a te rm of co n tin u o u s te n s e. So yo u c an f in d th is bre ak u p of wo rds qu ite h e lpf u l in m a kin g o u t th e righ t s en s e . I f no n e of th e te c h n iqu e wo rks try m a kin g a gu e s s w ith ref e re n ce to th e c o n te xt.
•
W h e n lo n g a n d co m ple x s e n te nc e s co n f u se yo u th e n try to bre ak th at s e n te n ce in to s m a lle r m o re s e n te n ce s by re ph ras in g it. Af te r yo u divide it c om pa re w ith th e o rigin a l se n te n c e to avo id an y m is in te rpre ta tio n . I f yo u a re s a tis f ie d re a d th e s m alle r s e n te n ce s to ge t th e ide a m o re c le arly.
Example Questions 1. M u lta n ________ ___ a ve ry h o t c lim ate . A. Has B . H a ve C . H a s be e n D. W ith 2. O n e of th e le a s t e ff e c tive ways of s o rtin g ______ ___ it. A . R epe a t B . R e pe a tin g C . To re pe a t D. h ow re pe a t
in f o rm atio n
is
le arn in g
3. S a lm a n f in is h e d________ __ tw o o f h is pu blis h e d co m pos it io n s be fo re h is tw e lf th birth d a y. A. W ritte n B. W rit in g C . To w rite D. W ro te 4. S of ia ______ ____ co lle c t s tam ps , bu t n o w s h e h as o th e r in te re s ts . A. U se d to B. W a s u se d to C . U s e d to be D. Us in g to 5. A f te r pa s s in g th ro u gh a gre at trau m a o f he r hu s ban d’s ______ ____ h a rd to a c h ie ve me n tal re laxatio n . A. S tru ggle d B. S tru gglin g C . S tru ggle D. To s tru ggle
de ath ,
s he
6. I n pa rtn e rs h ip w ith Pa kis tan , S ou th Ko re a ________ ____o n M o to r way. A. He lpe d w o rke d B. H e lpin g w o rk C . H e lpe d w o rkin g D. To h e lp w o rkin g 7. W e w ill wa it if yo u ______ ____ go .
A. W a n te d to B. W a n t C. W a n t to D. W a n tin g to 8. I f I h a d mo re tim e I ________ ____ c h e c ke d m y pape r. A. Wo u ld h a ve B. Wo u ld C . Wo u ld h a d D. W il l h a ve 9. I th o u gh t th a t he _______ ____ c om in g to day. A. H a s bee n B. I s C. Was D. H a s 10. Th a t pro fe s s o r en j o ys te ac h in g an d _________ __. A. W ritin g B. W ritte n C . To w rite D. W rite 11. J u s t _______ ___ th e f ile s o n my table . A. Let B . L e a ve s C . S ta y D. L e a ve 12. Th a n k yo u A. B. C. D.
f o r ______ ____ me yo u r boo k. B o rro w in g L e n din g Bo rro we d H a d le n t
13. ______ ____ __ dis c o ve ry dia be te s . A. Prio r B. Be fo re to th e C. Prio r to th e D. To prio r th e
of
in s u lin ,
it
was
not
14. Dis t ribu te th e h a n do u ts _________ __ th e c an didate s . A. Be tw ee n B. Am on g C. To D. I n 15. O n ly _________ w e re pre s e n t at th e se m in ar. A. a f ew peo ple B. a li tt le pe o ple C. a fe w peo ple s D. th e lit tle peo ple
Answer Key 1. 2. 3. 4.
A C B A
9. C 10. 11. 12.
A D B
po s s ible
to
tre at
5. 6. 7. 8.
A C C A
13. 14. 15.
C B A
4.1.2Analogy Questions A n a lo gy me a n s s im ila ri ty in e xa m ple s o r de s c ribin g like n e s s be tw ee n tw o o r mo re w o rds . Th e s e qu e s tio n s a s k th e re ade r to an alyze th e re latio n s h ip be tw e en tw o w o rds in a pa ir a n d lo o k fo r a n o th e r s im ilar o r equ ivale n t pair o f w o rds . Yo u are pro vide d w ith f ive o the r pa irs o f w o rds. Yo u are e xpec te d to m atc h th e o rigin a l pa ir, w h ic h is give n in th e que s tio n w ith on e of th e pairs in th e give n c h o ic e s on th e ba s e s o f s im ila r re la t io n s h ips be tw ee n th e m . Th is e xe rc is e o r s u c h qu e s tio n s try to de te rm in e yo u r ba s ic u n de rs tan din g to w ards vo c abu lary an d yo u r abil it y to re c o gn ize th e re la tio n s h ip be tw ee n wo rds . S om e que s tio n s may als o as k yo u to s e le c t a s u ita ble a n to n ym f o r a give n w o rd.
Techniques for Analogy Questions F o r th e a n a lo gy que s tio n s yo u c an f o llo w th e gu ide lin e s me n tio n e d be lo w ; •
Do n o t re a d th e c ho ic e s be f o re you h ave an alyze d th e re latio n s h ip be tw e e n th e pa ir of wo rds , yo u rse lf . Try to u n de rs tan d th e w o rds m o re a ppro pria te ly a n d th in k o n w h ic h bas is th e re latio n s h ip be twe e n th e w o rds is fo rm e d. Af te r you re a c h a co n c lu s io n re ad th e give n c ho ic e s af te rw ards to ge t a pro pe r m a tc h w ith an o th e r pair h avin g th e s ame re latio n s h ip.
•
W h e n yo u f in d you rs e lf s tu c k w ith a wo rd of dif f ic u lt vo c abu lary, do no t fe e l c o nf u s e d. Try to un de rs tan d its m ean in g ref e re n ce to th e c o n te xt o r if it is s om e wh a t f am il ia r try to re m em be r w he re an d wh e n yo u h e ard th e w o rd be fo re . I t c a n be a gre a t h e lp.
•
S om e tim e s yo u f in d th a t th e re is m o re th an on e pair th at f its w e ll to th e qu e s tio n a n d is a ppro pria te f o r th e c h o ic e, give th e o rigin a l pair a lit tle m o re th o u gh t s o th a t yo u c an f u rth e r s tu dy th e re latio n s h ip be tw ee n th e w o rds a n d n a rro w it dow n to a m o re dis tin c t on e . Af te r yo u h ave bee n s u c c es s f u l in f in din g a c lo se r re latio n s h ip you c an no w s c ru tin i ze th e tw o o th e r pa irs th a t c o nf u s e d yo u e arlie r. R e pe atin g th e s am e pro c e du re w ith th e s e w o rds wo u ld pro ve u se f u l. Do n o t ge t c a u gh t u p by th e tric ks o f th e te s t m ake rs . S om e time s th e qu e s tio n s a re pro vide d w ith ve ry tric ky an d do dgin g c ho ic e s th at m is gu ide gre a tly. Try to th in k o f e ve ry c ho ic e m o re s pe c if ic al ly an d n arro w ly.
•
•
I f yo u a re f am il ia r w ith th e parts of s pe ec h an d th e ir n atu re , it c an be be ne f ic ia l in ma kin g a mo re se n s ible c h o ic e. Re me m be r if th e w o rds in th e o rigin a l pa ir a re a n o un an d an adje c tive , th e co rre c t c h o ic e yo u make s h o u ld a ls o co n ta in th e wo rds in th e s ame gramm atic al o rde r. O th e rw is e , yo u r ch o ic e is w ro n g. So , if yo u are c o nf u s e d w ith two pairs an d c an n o t c h oo s e th e c o rre c t ch o ic e yo u c an e as ily lo o k at th e ir gramm atic al o rde r a n d give pre f e ren c e to th e o ne , wh ic h m atc h e s th e o rigin al o n e.
•
Exclude the choice from your consideration that you think is incorrect, e.g. the choices that do not have the same grammatical unit as of the original pair cannot match the original pair in anyway. Spend more time on considering the more possible choices.
•
You should know about the various kinds of analogies that are more frequently asked. Some of the common analogy types are as follows;
i.
Synonyms
Some words are linked together in a pair which means the same or has a similar dictionary definition.e.g Pretty- Beautiful ii.
Describing Qualities Some pairs have some words in which one word describes the other word. Heavy- Rain
iii.
Class and Member Some pairs have words which are based on class and member basis e.g. Electronics-Radio
iv.
Antonyms Some pairs consist of the words that are opposite to each other e.g. Love- Hate
v.
Describing Intensity Some pairs consist of the intensity of the other e.g. Smile-Laughter
words
in
which
one
describes
the
vi.
Function In some pairs a word describes the function of the other word e.g. Pen-Write
vii.
Manners Some words in a speech describe the manners and behavior e.g. Polite-Speech
viii.
Worker- Workplace Some pairs in a word describe the profession and its workplace e.g. Doctor-Clinic
Example Questions 1.
HEIGHT: MOUNTAIN
(A) (B) (C) (D) (E)
2. (A) (B) (C) (D) (F)
3.
Depth : Shade : Weight Speed : Mineral :
Trench Tree : Age Highway Mine
OBLIVIOUS : AWARENESS Comatose Serene Erudite Adroit Invigorate
: Consciousness : Composure : Knowledge : Skill : Energy
BELLWETHER : BAROMETER
(A) Proselyte : Spark plug (B) Panhandler : Kill
(C) Embezzler : Abduct (D) Cynosure : Magnet (F) Morass : Catalyst
4. (A) (B) (C) (D) (E)
5. (A) (B) (C) (D) (E)
6. (A) (B) (C) (D) (E)
7. (A) (B) (C) (D)
8. (A) (B) (C) (D)
9. (A) (B) (C) (D)
ACT : ACTION Therapy Oblivion Liturgy Image Bowl
: Thermometer : Obvious : Literature : Imagine : Bowdlerize
BIBULOUS : DRINK Rapacious : Clothing Gluttonous : Food Altruistic : Money Vegetarian : Meat Controversy : Reconcile SONG : RECITAL Author Episode Coach Dancer Poetry
: Bibliography : Series : Team : Agile : Prose
HOUSE : BIG Home School Water Clothes
ANIMAL
: Live : Daily : Cold : Socks
: MONKEY
Zebra : Giraffe Stationery: Pencil Book : Cap Tree : Wood HEAVEY
: LIGHT
Fat : Thin Stupid : Idiot Rough : Surface Beautiful : Diary
Choose the lettered word or phrase that is most nearly opposite in meaning to the word in capital letters.
10. (A) (B) (C) (D) (E)
11. (A) (B) (C) (D) (E)
12. (A) (B) (C) (D) (E)
13. (A) (B) (C) (D) (E)
14. (A) (B) (C) (D) (E)
15. (A) (B) (C) (D) (E)
DETER Twist Intimidate Encourage Straighten Supply INDIGENOUS Modern Alien Ornamental Natural Conceal THERAPEUTIC Curative Injurious Medicinal Practical Slander QUIZZICAL Amused Unequivocal Contorted Dissimilar Lax ANCILLARY Dependent Concomitant Appendix Primary Buffet VIRTUOSO Wicked Dazzling Mediocre Honorable Bawdy
Answer Key 1. A 2. A 3. A
4. D 5. B 6. B
7. C 8. B 9. A
10. C 11. B 12. B
13. B 14. D 15. E
4.1.3
Critical Reading Questions
Q u e s tio n s re la te d to c rit ic a l re a din g try to ju dge yo u r re adin g s kills an d h ow yo u u n de rs ta n d a n d in te rpre t wh a t yo u re ad. Th e pape r in c lu de s a fe w pas s age s th at a s k a n s we rin g qu e s tio n s re la te d to th e pas s age .
Techniques for Critical Reading Exercises There are a few techniques related to the Critical Reading Questions that prove to be a good guideline for solving such questions. •
Do not read the questions before reading the whole passage. Try to skim through the whole passage and then read the questions to look for a more specific answer. Read the passage quickly with understanding but do not panic. Try to analyze what the whole passage is about and what the author really intends to convey. While reading mark the lines where you think the passage carries the most important points. These strategies would definitely help you find the answers.
•
When you find yourself stuck with a question, do not waste your time on it and go ahead for the next questions. Sometimes, answering other questions guide you about the earlier question. But, if you still do not find the answer mark it for doing in the end more calmly, having enough time to think.
•
Try to familiarize yourself with the types of critical reading questions. Once you know the nature of such questions, you will be able to find the answers more quickly even when you are reading the passage. The examples of some commonly asked questions are as follows: o
Central Idea Mostly, questions are asked to explain the central idea or main theme of the whole passage, which analyzes how you skim through it. Sometimes, the opening and closing lines can give you a better clue about answering such questions properly.
o
Specific Details Sometimes to analyze your scanning abilities you are asked to answer some specific details about the passage. Such questions are about ‘when’, ‘where’, ‘which’ and ‘who’. You can get the answers of this kind of questions from the area of the passage which you marked in the first reading, where you think the most important and informational remarks of the author lies.
o
Making Inferences Most of the questions ask you to infer from the passages, making your opinion about what is said in the paragraph, implying meaning and making your own point of view. These questions try to assess your judgment; you must be clear in your mind about what the author is referring to and then make your own opinion
according to your understanding and comprehension. Read and think about all the choices and analyze each of it logically according to your comprehension rather than the author’s point of view. o
Meaning in Context Some selected words from the passage are pointed out to explain them with reference to the context to check your reading comprehension. Sometimes the word that describes something in a dictionary portrays it the other way when it appears in the context. The test tries to judge your ability to make sense of the word in the context.
o
Author’s Approach Some questions ask you to explain the mood in which the author is writing whether it is sarcastic, humorous, witty, sad etc. When you are asked questions like these you can look for certain expressions, words, phrases or exclamations, which describe the tone, mood or style of the author. The feelings of the writer are mostly exhibited through choice of words. While answering these questions read the message carefully observing particularly the use of words.
o
Title Selection Some passages ask for selecting a title that best suits the passage. Remember that the chosen title should not be narrowly or broadly selected. Try to avoid choosing those titles that describes only one or two paragraphs but the one, which is applicable to the whole passage and portrays it best.
Example Questions Passage I: We are profoundly ignorant about the origins of language and have to content ourselves with more or less plausible speculations. We do not even know for certain when language arose, but it seems likely that it goes back to the earliest history of man, perhaps half a million years. We have no direct evidence, but it seems probable that speech arose at the same time as tool making and the earliest forms of specifically human cooperation. In the great Ice Ages of the Pleistocene period, our earliest human ancestors established the Old Stone Age culture; they made flint tools and later tools of bone, ivory, and antler; they made fire and cooked their food; they hunted big game, often by methods that called for considerable cooperation and coordination. As their material culture gradually improved, they became artists and made carvings and engravings on bones and pebbles, and wonderful paintings of animals on the walls of caves. It is difficult to believe that the makers of these Paleolithic cultures lacked the power of speech. It is a long step Admittedly, from the earliest flint weapons to the splendid art of the late Old Stone Age: the first crude flints date back perhaps to 500,000 B.C., while the finest achievements of Old Stone Age man are later than 100,000 B.C.; and, in this period, we can envisage a corresponding development of language, from the most primitive and limited language of the earliest human groups to a fully developed language in the flowering time of Old Stone Age culture.
How did language arise in the first place? There are many theories about this, based on various types of indirect evidence, such as the language of children, the language of primitive societies, the kinds of changes that have taken place in languages in the course of recorded history, the behavior of higher animals like chimpanzees, and the behavior of people suffering from speech defects. These types of evidence may provide us with useful pointers, but they all suffer from limitations, and must be treated with caution. When we consider the language of children, we have to remember that their situations are quite different from that of our earliest human ancestors, because the child is growing up in an environment where there is already a fully developed language, and is surrounded by adults who use that language and are teaching it to him. For example, it has been shown that the earliest words used by children are mainly the names of things and people (“Doll,” “Spoon,” “Mummy”): but, this does not prove that the earliest words of primitive man were also the names of things and people. When the child learns the name of an object, he may then use it to express his wishes or demands: “Doll!: often means “Give me my doll!” Or “I’ve dropped my doll: pick it up for me!”; the child is using language to get things done, and it is almost an accident of adult teaching that the words used to formulate the child’s demands are mainly nouns, instead of words like “Bring!”’ “Pick up!”; and so on. 1
The main idea A. to provide B. to present C. to discuss D. to present E. to narrate
of this excerpt is evidence of the origin of language. the need for language. how early man communicated. the culture of early man. the story of English.
2
Theories of the origin of language include all of the following EXCEPT A. Changes occurring through the years. B. The need to communicate. C. Language of children. D. The first man’s extensive vocabulary. E. Communication among primitive men.
3
The purpose of the discussion of the word, “Doll,” is intended to A. Trace the evolution of a noun. B. Support the fact that naming things is most important. C. Indicate how adults teach language to children. D. Show the evolution of many meanings for one word. E. Evince man’s multiple uses of single words
4
The implication of the author regarding the early elements of language is that A. There were specific real steps followed to develop our language. B. Care must be exercised when exhuming what we consider the roots of language. C. We owe a debt of gratitude to the chimpanzee contribution. D. Adults created language in order to instruct their children. E. Language was fully developed by primitive man.
F.
5
If we accept that primitive man existed for a very long period of time without language, then we may assume that A. Language is not necessary to man’s existence. B. Language developed with the developing culture of primitives. C. Primitives existed in total isolation from one another. D. Children brought about a need for language. E. Mankind was not intended to communicate.
6
After a reading of this article, one might infer that A. Society creates problems with language. B. Language is for adults to instruct children. C. Society uses language to improve itself. D. With the evolution of language came wisdom. E. Language brings power. Answer Key 1. A
2. D
3.C
4. B
5. B
6. E
COMMON QUERIES
5
About the General Test
Q
What is the General Test generally about?
The NTS General Test is generally divided into three sections i.e. The Verbal Section, Quantitative Section and the section of Analytical Reasoning. The duration of these tests is 120 minutes which you can yourself manage for each section, as there is no specific time distribution for any. The following time table informs of the number of questions in each section as well as the marks given for that section:
Q
Test Sections
No Questions
of
Verbal
25
25
Analytical Reasoning
35
35
Quantitative
40
40
Marks
What Kind of Questions are asked?
The nature of the test is objective type, each section is based on Multiple Choice Questions (MCQs), and every question will have at least two choices or five choices at the most.
Q
What are the Contents of the Test?
The General Test is generally divided into three sections i.e. The Verbal, Quantitative and Analytical Reasoning. All the questions are based on Multiple-Choice Question format. The Verbal section of the test is based on completing sentences with the appropriate words, comprehension exercises to assess the basic knowledge about the vocabulary and grammar of the language. Questions basically about sentence completion, analogy, finding antonyms, and critical reading are asked. In the Quantitative Section the NTS tries to measure your basic mathematical skills and check your understanding of the elementary level mathematics. The MCQs in this section are based on areas like Arithmetic, Algebra and Geometry, data analysis etc. In the Analytical Reasoning Section various objective type questions are asked to analyze the capability of every student with regard to their problem solving aptitude in their daily life activities and also the academic interests. Questions asked are basically on Analytical Reasoning and Logical Reasoning.
Q
From Where Can I Get Help to Prepare for the Test?
NTS does not refer to one specific book for consultation during the test preparation. However, the candidates can go through this Student Guide, published by NTS, which is easily available in the market. It contains sample question papers as well as examples of the types of questions you may find in each segment. You can also practice by solving the sample tests and the other questions found in this guide and the NTS website. It would help you in becoming familiar with the nature of the test. Try practicing the tests by keeping the allotted time in mind. Give yourself an average of one minute to complete each question. It would help you pace yourself through out the test. Do not leave any question unsolved. For further measures you can consult materials easily available at any good bookstore for TOEFL, SAT, GRE etc.
Q
What are the General Guidelines to Attempt the Test?
This Student Guide by the NTS is the right source to be consulted. The sample question papers for any of the three areas of study are a great help for you. The test is composed on the same test pattern and the questions are selected on the same level. You may also use additional books for your preparation. If you answer 75% of the questions correctly, you will receive an excellent score.
Q
Can I Get My Registration Cancelled?
If you cannot take the test and want to cancel your registration, you should inform the NTS Office in writing by sending an application or email at least one week before the test date. Q How Can I Get My Test Schedule or Test Centre Changed? Once you have been allotted a Test Center and the time of the test, no changes can be made possible to that schedule. However, you can ask NTS by email and NTS may try to help you, if it finds it administratively feasible.
Q
Can I Appear for the Test More Than One Time?
Yes, if you want to improve your score and ranking, you can reappear in the test whenever the new schedule is announced. However you have to register again with full fee payment. You also have to wait when the next schedule of the test is announced.
Q
From Where Can I Get the Registration Forms for the General Test (NAT)?
For the paper based tests, you can get a free of charge NTS Registration Form, enclosed in its brochure, which is made available in the NTS’ allied bank branches, the Front Office or Reception of the NTS or the allied institutes of NTS. However, please ensure that you get these before the last date of registration.
Q
How Can I Register for NTS’ General Test?
After receiving the form, fill it appropriately. Submit it at the NTS Allied Institute while submitting the NTS Registration Forms NTS Test Fee is charged by the NTS Bank Branches/ Allied Institutes according to the announced specifications. Fill the form according to the instructions given at the back of it. Submit it by paying the Test Fee in any branch of NTS allied bank/institutes/organizations/NTS by email or post. You get a Test Entry Coupon from the bank/institute, which shows you your Roll Number on it. How Shall I Fill the Forms?
Q
A few things must be clear to you before you fill in the Form. Any incomplete or ambiguous information in the form may cause delay in the registration process and you may not be able to take the test. For filling in the forms correctly it is necessary to;
1. 2.
Use black ink and BLOCK LETTERS to fill in the form. Write the appropriate test title, for which you want to register i.e. General Test
3. 4.
Be careful while spelling your name. Write the mailing address correctly where you can be contacted in future. Ensure that the Test Fee is submitted in the bank/Institute through ‘Challan Form’ attached with the Registration Form. After submitting the fee, one copy of the ‘Challan’ Form must be attached to this Registration Form and you will need to keep the other for yourself. Do not forget to fill in the bank ‘Challan’ details in the appropriate columns. If the ‘Challan’ Form is not attached with your form, the Registration Form will not be accepted and no further processing will be made on your request for registration. Also indicate your choice of city, where you want your test center to be. Your group and Test Center information will be intimated to you well before the test day. Specify the institute that you want your test score to be forwarded to. You can get the list of Allied Institutes from the NTS’ website. If handed over to the same bank where you have submitted the fee. The bank will give you one part of this form as a Test Entry Coupon. You have to show this coupon at the time of test. Without this, you may not be allowed to enter the Test Center.
5.
6. 7. 8.
NOTE: These instructions are also given on the back of the Registration Form. The General Test for some allied institutes/organizations may not need NTS Registration Form.
Q
How Can Testing?
I
Pay
the
Registration
Fee
for
the
Paper-based
You can submit the Registration Fee through a Bank Voucher in an NTS Authorized Bank along with your Registration Form. However the fee and fee deposition procedure is subject to change from time to time. The exact particulars are communicated on the announcement of the test schedule.
On occasions the Test Fee can also be submitted at the institutes where the test is being conducted. How to Submit the Form for the Paper-based Testing?
Q
After you have completed the form according to the instructions, get it submitted at the same branch of the bank/institute/organization from where you collected your registration form. Do not forget to collect a stamped and photographed Test Entry Coupon from the bank, which ensures your identification on the Test Day. After receiving the forms, the NTS Head office checks the essential requirements for NTS registration i.e.
i ii iii iv v
Three copies of the recent photographs Candidate's name clearly written in the block letters Candidate's father’s clearly written name in block letters. Candidates postal address clearly written in block letters Phone number clearly written etc.
If any essential requirement is missing from the Registration Form, it is clearly marked as rejected. Note: The Registration Forms are at times differently printed for different institutes/organizations. The instructions for those forms are available at the back of the Registration Form.
Q
How does NTS Confirm My Registration for the Paper-based Testing?
After submitting the Registration Form at the bank/institute/organization, you get your Test Entry Coupon, which indicates your Roll Number and also serves as your Identification Slip. This slip confirms your registration. In case of any confusion or problems with the registration process you may contact NTS.
Q
May I Register on the Day of Examination for the General Test?
The registration of candidates on the day of the NTS Examination cannot be entertained. The candidate should have got oneset registered before the deadline, announced by NTS for the close of the registration process.
Q
How Can I Get Help Registration Process?
in
Case
of
Any
Problem
During
the
If you have any confusion about the registration process you can clarify this by calling the NTS Office or by sending an email.
Q
How Can I Get the Test Schedule for the Test?
If you have any confusion about the Test Schedule you can obtain details from the news media as well as NTS website.
Q
How Can I Get My Test Entry Coupon for the Paper-based Testing?
You are given your Test Entry Coupon when you submit your form. It serves as your Identification Slip and also informs you about the location of the center, Roll Number and other details.
Q
What do I have to do with the Test Entry Coupon?
Take the Test Entry Coupon with you on the Test Day. At the Test Center you are asked to show the Test Entry Coupon that was given to you after you submitted your form there. The staff at the Test Center identifies you with the photograph attached on the Coupon. Remember to attach a photograph, which is not more than six months old. If you fail to show your Test Entry Coupon to the administration on the test day or if your photograph does not match your appearance, you may not be allowed to enter the Test Center.
Q
What Should I Take With Me to the Test Center for the Paperbased Testing?
You are required to bring your own sharpened pencils and eraser. Besides this, the candidate is also asked to show his/her Test Entry Coupon.
Q
What Things Should I not bring with me in the Test Center for Paper-based Testing?
Calculators, cell phones, books, booklets, any kind of paper or cheating material are strictly prohibited inside of the Test Center. If any of these items are found to be in your possession during the test you will be disqualified from the examination.
Q
What are the Rules and Regulations that are applied to me inside the Test Center for the Paper-based Testing?
The test is taken on the day and at the time scheduled. You are asked to observe punctuality. 1. You are assigned a seat by the invigilation staff. 2. Testing aids are not permitted to be taken along to the Test Center. Items like calculators, pagers, cell phones, headphones, and any paper or writing material, dictionaries etc are prohibited in the test center. 3. You are not allowed to eat, drink, or use tobacco during the test. 4. If you do not show the Test Entry Coupon and your photograph does not match, you will not be permitted to take the test. 5. No discussion or communication with your fellow candidates is allowed during the test session. 6. You are not allowed to leave the test center without the permission of the supervisor. 7. Under no circumstances can the test questions or any part of a test be removed, reproduced or disclosed verbally, electronically, or physically or by any other means to any person or entity. 8. Test centers do not have large waiting areas. Friends or relatives who accompany you to the test center are not permitted to wait in
9. 10. 11. 12. 13. 14. 15.
the near vicinity of the test center or contact you while you are taking the test. If you need to leave your seat at any time during the test, raise your hand and ask the invigilator. Timing of the section does not stop. Repeated unscheduled breaks will be documented and reported to NTS. NTS reserves the right to videotape any or all of the testing sessions. Dress in such a way that you can adapt to any room temperature. You cannot communicate with anyone (other than the test center staff) while the test session is in progress or even during the breaks. You are not permitted to leave the test center vicinity during the test session or breaks. If at any time during the test you believe that you have a problem with your test, or need the Invigilation Staff for any reason, raise your hand to notify the Invigilation Staff. On What Basis Can I be disqualified from the Test?
Q
If you are found indulged in any of the following activities, you will be disqualified from the test: Arriving late to the test center. Taking the test for someone else. Failing to provide the Test Entry Coupon. Using any objectionable material during the test. Trying to create a disturbance inside the test center. Showing ill behavior towards the invigilation staff. Trying to communicate with fellow candidates while the test is in progress. 8. Trying to tear pages from the question paper. 9. Showing indiscipline i.e. eating, smoking etc. 10. Leaving the test center without permission.
1. 2. 3. 4. 5. 6. 7.
How Shall I Mark the Answer Sheet?
Q 1. 2. 3.
4. 5. 6. 7.
Fill in the particulars carefully like your Name, Father’s Name, Enrolment Number and the Test Name i.e. General Test and other particulars as mentioned on the answer sheet. Read the directions carefully before you begin your test. The invigilator announces the procedure for marking the answer sheets. Listen carefully to the instructions. When you mark the answer sheets, make sure that the space is completely filled in. You can change the answer, by erasing the earlier choice neatly. If a question is found with no answer or it has more than one marked choice, it will not be considered for marking. Completely fill in the corresponding circles on the answer sheet using a lead pencil. Do not use ink, ball-pen or any other marking material to mark the oval. Filling more than one oval will render your answer incorrect. Please fill in the oval completely and make no other marks on it.
Incorrect Correct What are the Other Test Taking Strategies for the General Test?
Q 1.
2. 3. 4. 5. 6.
7. 8. Q
The test is divided into three sections i.e. Verbal, Analytical Reasoning and Quantitative. The directions given at the beginning of every section will tell you the total number of questions and the recommended time. You are provided with a few blank pages in the test paper. You can use them for your rough work. Some formulas and helping tables are given at the end of the question paper. You can take help from those for solving the questions. Keep a very careful track of time. Do not panic while solving your paper. Give each section a specific time period and try to complete every section on time. If you find difficulty with some questions, do not waste your time by thinking about them for a long time. Try finishing the easier questions first and you can go back and finish the difficult questions later. Do not leave any question unanswered, if you are confused or have no idea about a certain question, try making a guess for the right answer. Do not make any extra marks on the answer sheet. Computer might register these and consider them as another marked choice. If I am disqualified from the Test, Can I apply for it at a Later Time?
If you are dismissed from the test session, you will be given a second chance and will be allowed to reappear in the next testing session.
Q
How can I Ask for Result Reporting?
You can ask for your result by requesting it from NTS, through a phone call, fax or by sending an e-mail. You can also visit the web site of NTS to check your results. The results will be sent to you by post on request. A proper result would also be prepared for the institutes and the candidates can check up their performances by contacting their respective institute.
Q
How is My NTS Test Scored?
The papers are marked according to the international marking standards. Each question carries one mark. Every question which is correctly answered will be given one mark unless the computer finds an error with your marking.
Q
Is There Any Negative Marking While Scoring?
If the answer is wrong you will lose one mark but there is no negative marking for an incorrect answer.
Q
If I have already appeared in the Test, How Will the First Score Affect My New Score?
If the candidate has appeared more than two times in an NTS test, his/her highest score would be considered to be valid.
Q
Is There Any Chance to Improve My Score?
If you are not satisfied with your test score and you want to improve your grade you will be allowed to apply and appear in the test again.
Q
What Should I do, if I Register and Then Can Not Take the Test?
If you do not appear to take the test you will be given another chance to take the test on the next scheduled test, but no refunds can be made.
Q
Who Shall I Contact in Case of any Confusion?
If you have any confusions about the testing service, registration, test execution process and the announcement of results etc you can call, mail or fax the NTS Head office for the details. Queries for Online General Test Q. In What Ways is NTS General Test Different from Other NTS Tests? The NTS General Tests are different from its other tests in many ways. Unlike the NTS Subject tests, the General Tests aims to assess the verbal, quantitative and analytical abilities that have been attained over a period of time and that are not necessarily related to any specific field of study. Q. How Can I Register for NTS-General Tests? For the NTS, General Test Registration, you have to fill the NTS’ Online Registration Form on the NTS’ website. Before you get registered online you have to pay the registration fee as per the specified procedure for that test. You can fill the form online at our present website and submit it. You will get e-mail from NTS after the submission of the form, which indicates that your form has been received by NTS. NTS will confirm your registration by sending you an email once the bank confirms the receipt of your fee. This form is available when the NTS has announced its online test schedule. Q. What happens when I submit my Online Registration Form? After you submit your Online Registration Form you receive an email from NTS which confirms the receipt of your registration request. NTS takes 3-5 day’s time to check up the valid Bank Challan No from the bank. When NTS confirms the deposition of your fee from the bank, it sends you the Admission Ticket which gives you your User ID, location of the Test Center, Test Time etc. Q. When do I receive confirmation of my final Registration Status?
After submitting your Online Registration Form, you receive the confirmation of your Test Registration and some other information about the test in the form of an Admission Ticket within 3-5 days, through an email by NTS. If your registration is not confirmed during the given time you can Contact Us for inquiring about the reasons. Q. How Can I Pay the Registration Fee? For the NTS General Test, the Test Fee is to be deposited in the prescribed Bank Branches or a draft to be sent to NTS or the allied institute as prescribed. The reference of your Bank Deposit Slip Number (that you received from the bank after depositing the fee) is necessary to be endorsed on your Online Registration Form for getting your registration confirmed. Q. Will NTS Confirm my Registration? Yes, after receiving a completely and properly filled NTS Online Registration form, NTS confirms your registration by sending you an email as soon as the bank confirms the receipt of your registration. Q. May I Register on the Day of Online Test? No, for the NTS Online General Test, you have to get registered by the due date, intimated on the NTS’ website or advertised through various newspapers prior to the test. Q. Where Shall I Contact if I Do Not Get my Registration Confirmed? If NTS does not confirm your registration within a week’s time after you submit your form, you may contact
[email protected] by giving the reference of your Bank Deposit Receipt Number and your other personal particulars. Q. Can I Get My Registration Cancelled? If you cannot take the test and want to cancel your registration, you should inform the NTS Office in writing by sending an application or email at least one week before the test date. Q. How Can I Get the Test Schedule? The Test Schedule that includes the Test Date, Test Time and the Venue of the test, is sent to you by NTS through an email. Q. How Can I Get My Test Schedule or Test Centre Changed? Once you have been allotted a Test Center and the time of the test, no changes might be possible to that schedule. However, you can ask NTS by email and NTS may try to help you, if it finds feasible administratively. Q. Can I Appear for the Test More Than One Time? Yes, if you want to improve your score and ranking, you can reappear in the test whenever the new schedule is announced. However you have to register again with full fee payment. You also have to wait when the next schedule of the test is announced.
Q. Is There Any Chance to Improve My Score? If you want to improve your score and ranking, you are allowed to apply and appear in the test again. However, you have to register again, once the schedule is announced. Q. What Computer Skills are Necessary for NTS Online General Tests? For the NTS computer-based online General Tests, minimal computer skills are required. The skills that are required include, using a mouse, entering and confirming a response, changing a response, accessing the help function, and moving to the next question although a help function is available throughout the test. These Test Instructions will also be given to you before the test is given. Q. How Often is the NTS Online General Test Conducted? A series of computer-based General Tests is planned. NTS announces the Schedule from time to time on its website www.nts.org.pk and through newspaper advertisements. Q. When Should I Arrive at the Test Center? Try to arrive at the testing center at least 45 minutes before your scheduled Test Time so that no delays are made during the check-in procedures and your identification. Q. What Should I Take With Me to the Test Center? Bring your ID card with you for your identification. No other items e.g. stationary, books, calculators are required nor allowed to be taken inside the Test Centre. Q. How Long Will I be at the Test Center? Although the actual test takes 3 hours, you should be prepared to spend up to 4 hours at the center. You will spend extra time on taking Test Instructions, getting seated, and other administrative arrangements, etc. Q. What are the important Things to be careful about for Online General Tests? You should be particularly careful about a few things while taking the Online General Test: • Online testing does not allow you to come back and reattempt the question that you have already marked. • If you face any difficulty in logging on to your system or face any other related problem you can ask for help from any lab assistant or invigilator.
Q. How to take NTS Online Test? You will go through the following screen shots to learn how to take NTS Online test. Step: 1
This is the first screen named as Candidate Login Screen. You will enter your Candidate ID and Password provided to you by NTS
Step: 2 You will see Test Instructions’ Screen after you successfully login. Please read the instructions carefully to avoid any confusion during the test. After reading the instructions, press Start Test button on center bottom of the page.
Step: 3 After you click on the Start Test button your test starts and a page appears which shows your first question of the test. Each question has various choices, if you know the answer you can select the correct choice for your answer and press Next Question button. You can also add this question in the Pass Box to answer it at some another stage. You will also find some additional information about your test on this page. This information includes: • • •
Total Number of Questions in the Test Total Number of Questions Answered by you Total Number of Questions in the Pass box to be attempted later
Step: 4 If you place a question in Pass Box you will notice that the Questions in Pass Box field will increase by one.
Step: 5 If you want to answer the questions in Pass Box, simply click on Questions in Pass Box link at the top. It will take you on the following screen. Now click Answer this Question button for the question you want to answer.
Step: 6 You have selected this question from Pass Box now select its answer and proceed for next question.
Step: 7 You have attempted all questions and now this last screen will show your detailed result.
Wish You Good Luck with your Test. National Testing Service
Q. How is NTS Online Test different from paper-based Test? For the Paper-based Test,
• • • •
A pencil, eraser and a sharpener is required to attempt the paper-based test. You can make the changes in the answer that you have already marked. The announcement of results is delayed than the online tests. You have to fill in a separate answer sheet to mark your answers.
Where as for the Online Test, • • • •
•
No stationery items are required to attempt online test. If you want to attempt a question at the end, you can place it in the Pass Box for attempting later. You can not reattempt a question that you have already answered. As soon as you finish the test, the result is displayed on the screen. In case of a system failure during the test, you will have to log-in again and the test will start from the same question where you had left. No information will be lost while the system was unavailable.
Q. How Can I Ask for Result Reporting? Your result is reported to you right after you finish your test. You are given the certificate fifteen days after the conduct of the test of the last batch. If you still do not get the result you can Contact Us. You can also visit the website of NTS to check your result. The final result is sent to you by email. Q. Is There Any Negative Marking While Scoring? There is no negative marking for wrong answers. However the negative marking may be activated if it is required by the allied institute or organization. Q. What are the Rules and Regulations that apply to me in the Test Center when taking the Online General Test? Rules and Regulations: • If you do not appear with the Identity Card (NIC) on the Test Center, you will not be allowed to take the test. • The test will be given on the day and at the scheduled time. You are asked to observe punctuality. Arriving late at the center may disqualify you from taking the test. • You are not allowed to bring any testing aids inside the test center. Nothing, except the original Identity Card is required to be taken along. • You are not allowed to smoke, eat or drink inside the test center. • No discussion or any form of communication with the fellow candidates is allowed during the testing session. • You will also not be allowed to leave the test center without the permission of the supervisor. • Test centers do not have large waiting areas. Friends or relatives who accompany you to the test center will not be permitted to wait in the test center or contact you while you are taking the test. • You will be required to sign the attendance sheet before and after the test session and any time you leave or enter the premises where the test is being conducted. • If you need to leave your seat at any time during the test (which shall only be allowed in case of serious illness), raise your hand and ask the invigilator. • Repeated unscheduled breaks will be documented and reported to NTS. NTS reserves the right to videotape all or any of Testing Sessions and use it to determine any misconduct, etc. • If at any time during the test you believe that you have a problem with your test, or need the Invigilation Staff for any reason, raise your hand to notify the Invigilation Staff.
NOTE: The rest of the queries regarding the test format, contents and other procedures have almost the same answers as of the paper based tests, given above.
DRILL TESTS General
Note: The sample papers do not include quantitatively the same number of questions as there would be in the actual papers. They are merely meant to provide conceptual guidance to the users or prospective candidates.
Drill Test I
I Quantitative Section
No. Of Questions
10
Choose the correct answer for each question and shade the corresponding CIRCLE on the answer sheet
1. The number of degrees through which the hour hand of a clock moves in 2 hours and
12 minutes is A. B. C. D. E. A
66 72 732 723 None of these B
C
D
E
2. A cylindrical container has a diameter of 14 inches and a height of 6 inches. Since one gallon equals 231 cubic inches, the capacity of the tank is approximately A. B. C. D. E. A
2-2/7 gallons 4 gallons 1-1/7 gallons 2-2/7 gallons None of these B
C
D
E
3. A train running between two towns arrives at its destination 10 minutes late when it goes 40 miles per hour and 16 minutes late when it goes 30 miles per hour. The distance between the two towns is A. B. C. D. E. A
720 miles 12 miles 8-6/7 miles 12-7/7 miles None of these B C D E
4. If the base of a rectangle is increased by 30% and the altitude is decreased by 20% the area is increased by A. B. C. D. E. A
25% 10% 5% 1% 4% B
C
D
E
5. If the sum of the edges of a cube is 48 inches, the volume of the cube is A. 512 inches B. 96 cubic inches C. 64 cubic inches
D. 698 cubic inches E. None of these A
B
C
D
E
6. A certain triangle has sides, which are, respectively, 6 inches, 8 inches, and 10 inches long. A rectangle equal in area to that of the triangle has a width of 3 inches. The Perimeter of the rectangle, expressed in inches, is A. B. C. D. E.
11 16 22 23 24
A
B
C
D
E
7. The cube of 1/3 is A. B. C. D. E. A
3/9 3/27 1/81 1/27 1/9 B
C
D
E
8. In general, the sum of the squares of two numbers is greater than twice the product of the numbers. The pair of numbers for which this generalization is not valid is A. B. C. D. E.
8,9 9,9 9,10 9,8 8,10
A
B
C
D
E
9. A piece of wire 132 inches long is bent successively in the shape of an equilateral triangle, a square, a regular hexagon, a circle. The plane surface of the largest area is included when the wire is bent into the shape of a A. B. C. D. E. A
Circle Square Hexagon Triangle Line B
C
D
E
10. If pencils are bought at 35 cents per dozen and sold at 3 for 10 cents the total profit on 5 1/2 dozen is
A. B. C. D. E.
25 35 27 28 31
A 0
B
cents cents 1/2 cents 1/2 cents 1/2 cents C
D
E
II No. Of Questions
ANALYTICAL Section
20
Choose the correct answer for each question and shade the corresponding CIRCLE in the answer sheet
For question 1 to 4 Three adults—R, S, and V—will be traveling in a van with five children—F, H, J, L, and M. The van has a driver's seat and one passenger seat in the front, and two benches behind the front seats, one bench behind the first. Each bench has room for exactly three people. Everyone must sit in a seat or on a bench, and seating is subject to the following restrictions: An adult must sit on each bench. Either R or S must sit in the driver's seat. J must sit immediately beside M. 1. Which of the following can sit in the front passenger seat? A: J B: L C: R D: S E: V A
B
C
D
E
2. Which of the following groups of three can sit together on a bench? A: F, J, and M B: F, J, and V C: F, S, and V D: H, L, and S E: L, M, and R A
B
C
D
E
3. If F sits immediately beside V, which of the following CANNOT be true? A: J sits immediately beside S. B: L sits immediately beside V. C: H sits in the front passenger seat. D: F sits on the same bench as H. E: H sits on the same bench as R. A
B
C
D
E
4. If S sits on a bench that is behind where J is sitting, which of the following must be true? A: H sits in a seat or on a bench that is in front of where M is sitting. B: L sits in a seat or on a bench that is in front of where F is sitting. C: F sits on the same bench as H. D: L sits on the same bench as S
E: M sits on the same bench as V. A
B
C
D
E
For question 5 to 9 The principal of a school is forming a committee. There are to be five members: three teachers, chosen from Mr. J, Ms. K, Ms. L, Mr. M, and Mr. N; and two students, chosen from O, P, Q, and R. The composition of the committee must conform to the following conditions: Ms. J will serve only if R is also on the committee. Ms. L will not serve unless Ms. K and O also serve. Neither Mr. M nor Mr. N will serve without the other. If P serves, neither Q nor R can serve. 5. Which of the following is an acceptable committee? A: J, L, M, N, O B: K, L, N, O, P C: K, M, N, O, R D: L, M, N, O, R E: M, N, O, P, Q A
B
C
D
E
6. How many different committees could include Mr. J and Q? A: 1 B: 2 C: 3 D: 4 E: 5 A
B
C
D
E
7. If Q and R are both on the committee, who else must be on the committee? A: J B: K C: L D: M E: O A
B
C
D
E
8. If M is not on the committee, each of the following must be on the committee EXCEPT A: J B: L C: O D: Q E: R A B C D E 9. In how many different ways can the principal select an acceptable committee? A: Fewer than 3 B: 3
C: 5 D: 7 E: More than 7 A
B
C
D
E
For question 10 to 13 A contractor will build five houses in a certain town on a street that currently has no houses on it. The contractor will select from seven different models of houses—T, U, V, W, X, Y, and Z. The town's planning board has placed the following restrictions on the contractor: No model can, be selected for more than one house. Either model W must be selected or model Z must be selected, but both cannot be selected. If model Y is selected, then model V must also be selected. If model U is selected, then model W cannot be selected. 10. If model U is one of the models selected for the street, then which of the following models must also be selected? A: T B: W C: X D: Y E: Z A
B
C
D
E
11. If T, U, and X are three of the models selected for the street, then which of the following must be the other two models selected? A: V and W B: V and Y C: V and Z D: W and Y E: Y and Z A
B
C
D
E
12. Which of the following is an acceptable combination of models that can be selected for the street? A: T, U, V, X, Y B: T, U, X, Y, Z C: T, V, X, Y, Z D: U, V, W. X, Y E: V, W, X, Y, Z A
B
C
D
E
13. If model Z is one model not selected for the street, then the other model NOT selected must be which of the following? A: T B: U C: V D: W E: X A
B
C
D
E
For question 14 to 16 Seven children—F, J, K, M, R, S, and T—are eligible to enter a spelling contest. From these seven, two teams must be formed, a red team and a green team, each team consisting of exactly three of the children. No child can be selected for more than one team. Team selection is subject to the following restrictions: If M is on the red team, K must be selected for the green team. If F is on the red team, R, if selected, must be on the green team. R cannot be on the same team as S. J cannot be on the same team as K. Which of the following can be the three members of the Red team?
14.
A: F, J, and K B: F, R, and T C: J, K, and T D: K, M, and R E: M, R, and T A
B
C
D
E
15. If M and F are both on the red team, the green team can consist of which of the following? A: J, K, and R B: J, S, and T C: K, R, and S D: K, R, and T E: R, S, and T A
B
C
D
E
16. If M is on the red team, which of the following, if selected, must also be on the red team? A: F B: J C: R D: S E: T A
B
C
D
E
For question 17 to 20 A mail carrier must deliver mail by making a stop at each of six buildings: K, L, M, O, P, and S. Mail to be delivered are of two types, ordinary mail and priority mail. The delivery of both types of mail is subject to the following conditions: Regardless of the type of mail to be delivered, mail to P and mail to S must be delivered before mail to M is delivered. Regardless of the type of mail to be delivered, mail to L and mail to K must be delivered before mail to S is delivered. Mail to buildings receiving some priority mail must be delivered, as far as the above conditions permit, before mail to buildings receiving only ordinary mail. 17. If K is the only building receiving priority mail, which of the following lists the buildings in an order, from first through sixth, in which they can receive their mail? A: L, K, P, S, O, M B: L, K, S, P, M, O C: K, L, P, M, S, O D: K, P, L, S, O, M E: O, K, L, P, S, M A
B
C
D
E
18. If L, M, and S are each receiving priority mail, which of the following lists the buildings in an order, from first to sixth, in which they must receive their mail? A: K, L, P, S, O, M B: L, K, O, P, S, M C: L, K, S, P, M, O D: M, L, S, P, K, O E: S, L, M, P, K, O A
B
C
D
E
19. If the sequence of buildings to which mail is delivered is O, P, L, K, S, M and if S is receiving priority mail, which of the following is a complete and accurate list of buildings that must also be receiving priority mail? A: O, L B: O, P C: P, L D: P, M E: O, P, L, K A
B
C
D
E
20. If only one building is to receive priority mail, and, as a result, O can be no earlier than fourth in the order of buildings, which of the following must be the building receiving priority mail that day? A: K B: L C: M D: P E: S A
B
C
D
E
III VERBAL Section
No. Of Questions
20
Choose the correct answer for each question and shade the corresponding CIRCLE in the answer sheet
Each sentence below has one or two blanks, each blank indicating that something has been omitted. Beneath the sentence are five lettered words or sets of words. Choose the word or set of words that, when inserted in the sentence, best fits the meaning of the sentence as a whole. 1. Florence Nightingale was ___ in the development of modern medicine, ___ such practices as sanitization of hospital wards and isolation of actively infected patients. A. B. C. D. E. A
a collaborator…rejecting a maverick…protesting an innovator…initiating a pioneer…criticizing an individualist…standardizing B
C
D
E
2. As a journalist who works to overturn erroneous convictions, Griffin Nicholson was opposed to the court ruling ___ appeals for inmates who might be ___ . A. B. C. D. E. A
barring…culpable curbing…exonerated encouraging…innocent scrutinizing…eligible shielding…esteemed B
C
D
E
3. Linda Greenhouse's articles for the New York Times are an outstanding example of ___, capsulizing prose into a necessarily limited space. A. B. C. D. E. A
Callousness Brevity Intuition Propriety Fortitude B
C
D
E
4. Roberto Clement was seen as ___ during his life because of both his selflessness on the baseball field and his humanitarian work in his native Nicaragua. A. B. C. D. E. A
An individualist a grandstander a sybarite an altruist an opportunist B
C
D
E
5. His habit of spending more than he earned left him in a state of perpetual-----but he------------hoping to see a more affluent day. A. B. C. D. A
indigence: persevered in confusion: compromised by enervation: retaliated by motion: responded B
C
D
E
6. Known for his commitment to numerous worthy causes, the philanthropist deserved------ for his-----------. A. recognition: folly B. blame: hypocrisy C. reward: modesty D. credit: altruism A
B
C
D
E
7. You should --------this paragraph in order to make your essay more-----. A. B. C. D. A
Delete, succinct Enlarge, redundant Remove, discursive Revise, abstruse B
C
D
E
8. A------glance pays-----attention to details. A. B. C. D. A
Furtive: meticulous Cursory: little Cryptic: close Keen: scanty B
C
D
E
Each question below consists of a related pair of words or phrases, followed by five lettered pairs of words or phrases. Select the lettered pair that best expresses a relationship similar to that expressed in the original pair.
9. TIRADE: ABUSIVE A. Diatribe: familial B. Satire: pungent C. Panegyric: laudatory D. Eulogy: regretful A
B
C
D
E
10. SOLDIER: REGIMENT A. Colonel: martinet B. Dancer: balletomane C. Singer: chorus D. Trooper: rifle A
B
C
D
E
11. ASYLUM: SHELTER A. Harbor: concealment B. Palisade: display C. Stronghold: defense D. Cloister: storage A
B
C
D
E
12. STATIC: MOVEMENT A. Humdrum: excitement B. Chronic: timeliness C. Ecstatic: decay D. Diligent: industry A
B
C
D
E
13. INTEREST: FASCINATE A. Vex: enrage B. Vindicate: condemn C. Regret: rue D. Appall: bother A
B
C
D
E
14. LAUREL: VICTOR A. Chevrons: army B. Oscar: movie star C. Power: glory D. blue ribbon: cooking A
B
C
D
E
15. PRECEDENT: JUSTIFICATION A. Kindness: obedience B. Authority: sanction C. Usage: submission D. Tradition: novelty A B C D E 16. IMPLICATE: COMPLICATE A. Vitality: inevitable B. Empathy: sympathy C. Importune: construct D. Imply: simplify A
B
C
D
E
17. PERMEATE: RUEFUL A. Truculent: merciful B. Sadden: pitiful C. Evaporate: mournful D. Penetrate: sorrowful A
B
C
D
E
18. ENERVATE: STRENGTHEN A. Aver: attribute B. Divert: turn C. Apprise: appraise D. Stultify: enliven A
B
C
D
E
Read the passages and answer the questions given at the end: Recent technological advances in manned undersea vehicles have overcome some of the limitations of divers and diving equipment. Without vehicles, divers often become sluggish and their mental concentration was limited. Because of undersea pressure that affected their speech organs, communication among divers was difficult or impossible. But today, most oceanographers make observations by the means of instruments that are lowered into the ocean or from samples taken from the water direct observations of the ocean floor are made not only by divers of more than seven miles and cruise at the depth of fifteen thousand feet. Radio equipment buoys can be operated by remote
control in order to transmit information back to land based laboratories, including data about water temperature, current and weather. Some of mankind’s most serous problems, especially those concerning energy and food, may be solved with the help of observations made by these undersea vehicles. 19. With what topic is the passage primarily concerned? A. Recent technological advances. B. Communication among divers. C. Direct observation of the ocean floor D. Undersea vehicles A
B
C
D
E
20. Divers have problems in communicating underwater because? A. The pressure affected their speech organs B. The vehicles they used have not been perfected. C. They did not pronounce clearly D. The water destroyed their speech organs. A
B
C
D
E
Drill Test II
I Quantitative Section
1.
A
A
A
C
D
E
225 sq. yds. 2.5 sq. yds. 250 sq. ft. 22.5 sq. yds 225 sq. ft.
B
C
D
E He was given successive discounts of
$129.60 $119.60 $118.20 $115.20 $112.00
B
C
D
E
Mr. Jones' income for a year is $15,000. He pays 15% of this in federal taxes and 10% of the remainder in state taxes. How much is left? A. B. C. D. E.
A 5.
B
1 1/2 inches 10 1/2 inches 10 1/2 inches 1 1/2 inches 8 1/2 inches
A man bought a TV set that was listed at $160. 20% and 10%. The price he paid was A. B. C. D. E.
4.
feet, feet, feet, feet, feet,
The tiles in the floor of a bathroom are 15/16 inch squares. The cement between the tiles is 1/16 inch. There are 3240 individual tiles in this floor. The area of the floor is A. B. C. D. E.
3.
10
Choose the correct answer for each question and shade the corresponding CIRCLE in the answer sheet
A piece of wood 35 feet, 6 inches long was used to make 4 shelves of equal length. The length of each shelf was A. 9 B. 8 C. 7 D. 7 E. 6
2.
No of Questions
$12,750 $9,750 $14,125 $13,500 $11,475
B
C
D
E
The radius of a circle which has a circumference equal to the perimeter of a hexagon whose sides are each 22 inches long is closest in length to which one of the following? A. B. C. D. E.
7 21 14 28 24
A
B
C
D
E
6.
If a, is a multiple of 5 and b = 5a, which of the following could be the value of a + b? I. 60 II. 100 III. 150 A. B. C. D. E.
A 7.
A
C
D
E
4×4÷4+4 4÷ 4×4+4 4×4–4×4 4÷4+4×4 2÷2+2×2
B
C
D
E
If (a + 3) / 5 is an integer, what is remainder when ‘a’ is divided by 5? A. B. C. D. E.
A 9.
B
Which of the following expressions has the greatest value?
A. B. C. D. E. 8.
I only III only I and III only II and III only None of these
1 2 3 4 5
B
C
D
E
The integral part of logarithm is called A. Characteristic B. Mantissa C. Solution D. Root E. None of these
A
B
C
D
E
10. On the y-axis, the x-coordinate is A. 1 Β. ∞ C. zero D. -∞ E. –1
A
B
C
D
E
II ANALYTICAL Section
No. Of Questions
20
Choose the correct answer for each question and shade the corresponding CIRCLE in the answer sheet
For question 1 to 3 A volunteer uses a truck to pick up donations of unsold food and clothing from stores and to deliver them to locations where they can be distributed. He drives only along a certain network of roads. In the network there are two-way roads connecting each of the following pairs of points: 1 with 2, 1 with 3, 1 with 5, 2 with 6, 3 with 7, 5 with 6, and 6 with 7. There are also one-way roads going from 2 to 4, from 3 to 2, and from 4 to 3. There are no other roads in the network, and the roads in the network do not intersect. To make a trip involving pickups and deliveries, the volunteer always takes a route that for the whole trip passes through the fewest of the points 1 through 7, counting a point twice if the volunteer passes through it twice. The volunteer's home is at point 3. Donations can be picked up at a supermarket at point 1, a clothing store at point 5, and a bakery at point 4. Deliveries can be made as needed to a tutoring center at point 2, a distribution center at point'6, and a shelter at point 7.
1. If the volunteer starts at the supermarket and next goes to the shelter, the first intermediate point his route passes through must be A: 2 B: 3 C: 5 D: 6 E: 7 A
B
C
D
E
2. If, starting from home, the volunteer is then to make pickups for the shelter at the supermarket and the bakery (in either order), the first two intermediate points on his route, beginning with the first, must be A: 1 and 2 B: 1 and 3 C: 2 and 1 D: 2 and 4 E: 4 and 2 A
B
C
D
E
3. If, starting from the clothing store, the volunteer next is to pick up bread at either the supermarket or the bakery (whichever stop makes his route go through the fewest of the points) and then is to go to the shelter, the first two points he reaches after the clothing store, beginning with the first, must be A: 1 and 2 B: 1 and 3 C: 4 and 2 D: 6 and 2 E: 6 and 4 A
B
C
D
E
For question 4 to 5 There are seven cages next to each other in a zoo. The following is known about the cages. Each cage has only one animal, which is either a monkey or a bear. There is a monkey in each of the first and last cages. The cage in the middle has a bear. No two adjacent cages have bears in them. The bear’s cage in the middle has two monkey cages on either side. Each of the two other bear cages are between and next to two monkey cages 4. How many cages have monkeys in them? A: 2 B: 3 C: 4 D: 5 E: 6 A
B
C
D
E
5. The bear cage in the middle must have A: No other bear cage to its left B: No monkey cage on its right. C: A bear cage to its left and to its right D: Other bear cages next to it. E: No monkey cage to its left. A
B
C
D
E
For question 6 to 8 A nursery class in a school has a circular table with eleven seats around it. Five girls (Kiran, Lado, Maryam, Omera and Parveen) and five boys (Farhan, Ghaus, Haris, Imdad and Jahangir) are seated around the table. None of the girls are seated in a seat adjacent to another girl. Kiran sits between Farhan and Ghaus, and next to each of them. Jahangir does not sit next to Imdad.
6. Which of the following is a possible seating order around the table? A: Empty seat, Farhan, Kiran, Ghaus, Lado, Omera, Haris, Imdad, Parveen, Jahangir, and Maryam.
B: Empty seat, Farhan, Kiran, Ghaus, Lado, Jahangir, Parveen, Omera, Imdad, Maryam, Haris. C: Empty seat, Farhan, kiran, Ghaus, Omera, Jahangir, Parveen, Imdad, Maryam, Haris, Lado. D: Empty seat, Omera, Farhan, Kiran, Ghaus, Lado, Jahangir, Imdad, Parveen, Haris, Maryam. E: Empty seat, Maryam, Farhan, Kiran, Ghaus, Lado, Jahangir, Perveen, Imdad, Omera, Haris. A
B
C
D
E
7. If Lado, Haris, Maryam, Jahangir, and Ghaus are seated in that order, which of the following is a correct completion of the seating order after Ghaus? A : Kiran, Farhan, Omera, Imdad, Parveen, empty seat. B : Kiran, Farhan, Imdad, Omera, empty seat, Parveen C : Farhan, Parveen, Kiran, Imdad, Omera, empty seat. D : Kiran, Farhan, Parveen, Imdad, empty seat, Omera. E : Kiran, Farhan, Omera, empty seats, Parveen, Imdad. A
B
C
D
E
8. If Jahangir leaves his seat and occupies the empty seat, his new seating position would be between: A : Farhan and Kiran B : Maryam and Ghaus C : Kiran and Ghaus D : Imdad and Lado E : Parveen and Lado A
B
C
D
E
For question 9 to 11 Four telephone operators (Abid, Baqir, Chauhan, and Daud) each have to perform duties at the telephone exchange on four different days, Thursday through Sunday. The following is known about their duty schedule: Chauhan has his duty day before Abid. Daud has his duty day later than Baqir.
9. Which of the following is a possible order of duty days for the four operators? A: Chauhan, Daud, Abid and Baqir. B: Daud, Chauhan, Abid, and Baqir. C: Baqir, Chauhan, Daud and Abid. D: Abid, Chauhan, Daud and Baqir. E: Abid, Baqir, Daud and Chauhan. A
B
C
D
E
10. If Chauhan has his duty day on Saturday, who must have his duty day on Thursday? A: Either Abid or Daud.
B: Daud C: Abid D: Either Baqir or Daud. E: Baqir. A
B
C
D
E
11. Each of the following is possible EXCEPT: A: Chauhan has his duty on Thursday. B: Baqir has his duty on Thursday. C: Daud has his duty on Saturday. D: Baqir has his duty on Sunday E: Abid has his duty on Sunday. A
B
C
D
E
For question 12 to 13 There are 12 seats facing the blackboard in a classroom, four seats (A1, A2, A3 & A4) in that order are in row A, the first row from the blackboard. Immediately behind row A is row B with four seats (B1, B2, B3 & B4) in that order. Immediately behind row B, is the last row C with four seats (C1, C2, C3 & C4) in that order. Six students attend the class the following is known about there seating arrangement: Ejaz sits exactly in front of Comil, Seat A2 is always unoccupied Daud does not sit next to Farhat, Gharuy sits in seat A4 Hamid does not sit in seat B4 All the seats in row C always remain empty 12. If Daud sits in seat B3, then Farhat must sit in seat: A: A3 B: A1 C: B4 D: B2 E: C2 A B
C
D
E
13. Suppose that Hamid and Ejaz are sitting in seats A1 and A3 respectively, then it CANNOT be true that seat: A: B1 is occupied by Daud. B: B2 is empty C: B1 is empty D: B3 is OCCUPIED BY Comil E: B4 is empty A
B
C
D
E
For question 14 to 17 The principal of a school is forming a committee. There are to be five members: three teachers, chosen from Mr. J, Ms. K, Ms. L, Mr. M, and Mr. N; and two students, chosen from O, P, Q, and R. The composition of the committee must conform to the following conditions: Ms. J will serve only if R is also on the committee. Ms. L will
not serve unless Ms. K and O also serve. Neither Mr. M nor Mr. N will serve without the other. If P serves, neither Q nor R can serve.
14. Which of the following is an acceptable committee? A: J, L, M, N, O B: K, L, N, O, P C: K, M, N, O, R D: L, M, N, O, R E: M, N, O, P, Q A
B
C
D
E
15. How many different committees could include Mr. J and Q? A: 1 B: 2 C: 3 D: 4 E: 5 A
B
C
D
E
16. If Q and R are both on the committee, who else must be on the committee? A: J B: K C: L D: M E: O A
B
C
D
E
17. In how many different ways can the principal select an acceptable committee? A: Fewer than 3 B: 3 C: 5 D: 7 E: More than 7 A
B
C
D
E
For question 18 to 20 Three adults—R, S, and V—will be traveling in a van with five children—F, H, J, L, and M. The van has a driver's seat and one passenger seat in the front, and two benches behind the front seats, one bench behind the other. Each bench has room for exactly three people. Everyone must at in a seat or on a bench, and seating is subject to the following restrictions: An adult must sit on each bench. Either R or S must sit in the driver's seat. J must sit immediately beside M. 18. Which of the following can sit in the front passenger seat? A: J B: L C: R D: S E: V A
B
C
D
E
19. Which of the following groups of three can sit together on a bench? A: F, J, and M B: F, J, and V C: F, S, and V D: H, L, and S E: L, M, and R A
B
C
D
E
20. If F sits immediately beside V, which of the following CANNOT be true? A: J sits immediately beside S. B: L sits immediately beside V. C: H sits in the front passenger seat. D: F sits on the same bench as H. E: H sits on the same bench as R. A
B
C
D
E
III VERBAL Section
No. Of Questions
20
Choose the correct answer for each question and shade the corresponding CIRCLE in the answer sheet
Each sentence below has one or two blanks; each blank indicates that something has been omitted. Beneath the sentence are five lettered words or sets of words. Choose the word or set of words that, when inserted in the sentence, best fits the meaning of the sentence as a whole. 1. Surprisingly enough, it is more difficult to write about the--------than about the---and strange. A. B. C. D. A
specific, foreign abstract, prosaic commonplace, exotic simple, routine B
C
D
E
2. A-----response is one that is made with----------. A. B. C. D. A
stupid, fear speedy, alacrity sure, slowness harmful, grimaces B
C
D
E
3. A----is a-------. A. B. C. D. A
norm, standard criterion, mistake discipline, school doctrine, follower B
C
D
E
4. It is widely believed that a nuclear war could ____ enough smoke and dust to block out the sun and freeze the earth. A. B. C. D. E. A
billow extinguish generate duplicate decimate B
C
D
E
5. Consumption of red meat has ____ because its fat content has become a worrisome and ____ matter. A. B. C. D. E. A
abated ... dubious skyrocketed ... stressful abounded ... divisive stabilized ... newsworthy declined ... controversial B
C
D
E
6. It takes ____ character to ____ the extremities of the arctic region. A. B. C. D. E. A
an unflappable ... sustain a dictatorial ... brook a Spartan ... negotiate an inimitable ... resist a nomadic ... espouse B
C
D
E
7. Consumers refused to buy meat products from the company because of rumors that the water supply at the meat processing plant was ______; the rumors, however, were quite ______, with no hard evidence to back them up. A. B. C. D. E. A
uninspected .. reckless contaminated .. unsubstantiated impure .. damaging misdirected .. scandalous unscrupulous .. vicious B
C
D
E
8. Many kinds of harmful viruses are unhindered when passing through different parts of the host organism; indeed, there are few organic substances which such viruses’ cannot______. A. B. C. D. E. A
undermine disseminate aerate exterminate perforate B C D E
9. Their conversation was unsettling, for the gravity of their topic contrasted so oddly with the ______ of their tone A. B. C. D. E. A
uniqueness rapidity lightness precision reverence B
C
D
E
10. Throughout the animal kingdom, ____ bigger than the elephant. A. B. C. D. E. A
whale is only the only the whale is is the whale only only whale is the whale is only B
C
D
E
Each question below consists of a related pair of words or phrases, followed by five lettered pairs of words or phrases. Select the lettered pair that best expresses a relationship similar to that expressed in the original pair. 11. YAWN: BOREDOM :: A. dream : sleep B. anger : madness C. smile : amusement D. face : expression E. impatience : rebellion A
B
C
D
E
12. OBSTRUCTION : BUOY :: A. B. C. D. E. A
construction : building boy : girl danger : red light iceberg : titanic arise : lay down B
C
D
E
13. CONCERT : MUSIC :: A. B. C. D. E. A
performance : artist exhibition : art play : actor operetta : singer rock : role B
C
D
E
14. TEAMMATE : ADVERSARY :: A. B. C. D. E. A
felon : criminal enemy : associate pacifier : agitator winner : loser friend : foe B
C
D
E
For Question 15-20 read the following passage: A popular theory explaining the evolution of the universe is known as the Big Bang Model. According to the model at some time between twenty billion years ago, all present matter and energy were compressed into a small ball only a few kilometers in diameter. It was, in effect, an atom that contained in the form of pure energy all of the components of the entire universe. Then, at a moment in time that astronomers refer to as T = 0, the ball exploded, hurling the energy into space. Expansion occurred. As the energy cooled most of it became matter in the form of protons, neutrons and electrons. These original particles combined to form hydrogen and helium and continued to expand. Matter formed into galaxies with stars and planets. 15. Which sentence best summarizes this passage?
A. The big band theory does not account for the evolution of the universe B. According to the Big Bang Model, an explosion caused the formation of the universe C. The universe is made of hydrogen and helium D. The universe is more than ten billion years old A
B
C
D
E
16. According to this passage when were the galaxies formed? A. B. C. D. A
Ten Billion Years ago Fifteen billion Years ago At T = 0 Twenty billion years ago B
C
D
E
17. The word “compressed” in the passage could best be replaced by A. B. C. D. A
Excited Balanced Reduced Controlled B
C
D
E
18. It may be inferred that A. B. C. D. A
Energy and matter are the same Protons, neutrons, and electrons are not matter Energy may be converted into matter The galaxies stopped expanding as energy cooled B
C
D
E
19. The word “it” in the passage refers to A. Energy B. Space C. Expansion
D. Matter A
B
C
D
E
20. The environment before the Big Bang is described as all the following EXCEPT A. B. C. D. A
Compressed matter Energy All the components of the universe Protons, electrons and neutrons B
C
D
E
Drill Test III
I Quantitative Section
No. Of Questions
20
Choose the correct answer for each question and shade the corresponding OVAL in the answer sheet
1. If the pattern of dots shown above is continued so that each row after Row One contains 1 dot more than the row immediately above it, which row will contain 12 dots? A. B. C. D. E. A
Seven Eight Nine Ten Twelve B
C
D
E
2. Each of Steve's buckets has a capacity of 11 gallons, while each of Mark's buckets can hold 8 gallons. How much more water in gallons can 7 of Steve's bucket's hold compared to 7 of Mark's buckets? A. B. C. D. E.
3 7 21 24 56
A
B
C
D
E
3. Two integers have a sum of 42 and a difference of 22. The greater of the two integers is A. B. C. D. E.
22 25 28 31 32
A
B
C
D
E
4. The average of five numbers is 34. If three of the numbers are 28, 30 and 32, what is the average of the other two? A. 40 B. 50 C. 60
D. 70 E. 80 A
B
C
D
E
5. In the figure above, what is the value of x? A. B. C. D. E.
30 40 50 80 100
A
B
C
D
E
6. In a certain cake, two straight cuts (made along two different radii) succeed in removing 4/15 of the total cake. piece cut? A. B. C. D. E.
26 60 85 92 96
A
B
C
D
What is the central angle in degrees of the
E
7. If an equilateral triangle and a square have the same perimeter, what is the ratio of the length of the sides of the equilateral triangle to the lengths of the sides of the square? A. B. C. D. E.
3:4 4:3 1:4 1:3 3:1
A
B
C
D
E
8. If 2 and 4 each divide q without remainder, which of the following must q divide without remainder. A. B. C. D. E. A
1 2 4 8 It cannot be determined from the information given. B
C
D
E
9. The ratio of boys to girls in a certain classroom was 2 : 3. If boys represented five more than one third of the class, how many people were there in the classroom? A. B. C. D. E.
15 25 30 45 75
A
B
C
D
E
10. Let xy = z, where x,y,z and nonzero numbers. If x is multiplied by 3 and z is divided by 3, this is equivalent to multiplying y by A. B. C. D. E.
1/9 1/3 1 3 9
A
B
C
D
E
11. If 5x = 3, then (5x + 3)² = A. B. C. D. E.
0 9 18 36 81
A
B
C
D
E
12. If the postal charges for a package are 62 cents for the first five ounces and 8 cents for each additional ounce, what is the weight of a package for which the charges are $1.66? (Assume there are 16 ounces in one pound) A. B. C. D. E. A
1.05 pounds 1.1 pounds 1.125 pounds 1.25 pounds 1.5 pounds B
C
D
E
13. If m/n = .75, then what is 3m + 2n? A. B. C. D. E.
0 8 14 17 24
A
B
C
D
E
14. Which is greater?
A. B. C. D. E. A
if if if if if
Column A
Column B
(10/4) / (3/2) * (3/7)
(3/4) * (10/7) / (3/2)
the quantity in Column A is greater the quantity in Column B is greater the two quantities are equal there is no relationship between these two quantities the relationship cannot be determined from the information given
B
C
D
E
15. Which of the following has a graph that is symmetric to the x-axis A. y = x B. y = x2 + 3 C. y2 = x D. y = x3 – x E. y != x A
B
C
D
E
16. The prime factors of 96 are: A. B. C. D. E. A
2 and 3 6 and 8 2, 3 and 4 8 and 12 3 and 9 B
C
D
E
17. 8 are what percent of the 6? A. B. C. D. E. A
1.25 75 125 133.333 150 B
C
D
E
C
D
E
18. 2- 3 = A. B. C. D. E.
-8 8 -6 -1/8 1/8
A
B
19. If x + 1 < 3x + 5, then A. B. C. D. E. A
X > -2 x < -2 x = 0√√√√ x<2 x>2 B
C
D
E
20. Which of the numbers cannot be represented by a repeating decimal? A. B. C. D. E. A
11/9 23/7 √3 4 1/3 2 B
C
D
E
II Analytical Reasoning
No. of Questions
15
Choose the correct answer for each question and shade the corresponding CIRCLE in the answer sheet
The office staff of the XYZ Corporation presently consists of three bookkeepers (L, M and N ) and five secretaries (O, P, Q, R and S). Management is planning to open a new office in another city sending three secretaries and two bookkeepers from the present staff. To do so they plan to separate certain individuals who do not function well together. The following guidelines were established to set up the new office: (a) Bookkeepers L and N are constantly finding faults with one another therefore should not be sent together to the new office. (b) N and P function well alone but not as a team. They should be separated. (c) O and R have not been on speaking terms for many months. They should not go together. (d) Since O and Q have been competing for a promotion, they should not be in one team. Based on the information given above find the correct answers to the following Questions: 1.
If M insists on staying back then how many combinations are possible? A. B. C. D.
1 2 3 None
A 2.
B
A
A
B
C
D
E
O M Q R
B
C
D
E
If O is sent to the new office then which of the following is a possible team? A. B. C. D.
A 5.
LMOPS LMPQS LMORS LMPRS
If N is sent to the new Office which member of the staff CANNOT be sent? A. B. C. D.
4.
E
If L is to be moved as one of the bookkeepers, which of the following CANNOT be a possible working unit? A. B. C. D.
3.
D
C
LMOPR MNOQS MNOPS LMOPS
B
C
D
E
If both N and Q are moved to the new office, how many combinations are possible? A. 2 B. 3
C. 4 D. 1
A
6.
B
C
D
E
A map representing countries R, S, W, X, Y and Z is to be drawn. cannot have the same color in the map.
Adjacent countries
The countries adjacent to each other are as follows: Each of R, S, X and Y is adjacent to W. X is adjacent to Y. Each of R and S is adjacent to Z. If X is the same color as Z then it must be true that A. B. C. D.
A
W is a different color from any other country. S is a different color from any other country. X is the same color as Y. S is the same color as X.
B
C
D
E
Two statements, labeled I. & II, follow each of the following questions. The statements contain certain information. In the questions you do not actually have to compute an answer, rather you have to decide whether the information given in the statements I. and II. is sufficient to find a correct answer by using basic mathematics and every day facts?
7.
A long distance runner has just completed running 28 miles. How long did it take him to finish the journey? I. His record speed is 8.25 miles per hour. II. His average speed through the journey was 8 miles per hour.
A.
Statement I. ALONE is sufficient but II. ALONE is not sufficient to answer question. B. Statement II. ALONE is sufficient but I. ALONE is not sufficient to answer question. C. Statements I. and II. TOGETHER are sufficient to answer the question NEITHER of them is sufficient ALONE. D. Statements I. and II. COMBINED are NOT sufficient to answer the question additional information is needed to find the correct answer.
A
8.
B
C
D
this this but and
E
Captain of the national cricket team has to be the most popular member of the team. Who is the captain of Pakistan’s national cricket team? I. Waqar is the best player on the team. II. Waseem is the senior-most member. A. Statement I. ALONE is sufficient but II. ALONE is not sufficient to answer question. B. Statement II. ALONE is sufficient but I. ALONE is not sufficient to answer question. C. Statements I. and II. TOGETHER are sufficient to answer the question NEITHER of them is sufficient ALONE. D. Statements I. and II. COMBINED are NOT sufficient to answer the question additional information is needed to find the correct
this this but and
answer.
A
9.
B
C
D
E
In a BCE class at CIIT, 30 boys and 10 girls registered Calculus II. passed the course?
How many boys
I. 5 students could not pass. II. There were 2 girls who obtained A grade. A. Statement I. ALONE is sufficient but II. ALONE is not sufficient to answer question. B. Statement II. ALONE is sufficient but I. ALONE is not sufficient to answer question. C. Statements I. and II. TOGETHER are sufficient to answer the question NEITHER of them is sufficient ALONE. D. Statements I. and II. COMBINED are NOT sufficient to answer the question additional information is needed to find the correct answer.
A
B
C
D
this this but and
E
10. A horse ran 100 miles without stopping.
What was its average speed in miles per hour? I. The journey started at 8 PM and ended at 4 AM the following day. II. The horse ran 20 miles per hour for the first 50 miles. A. Statement I. ALONE is sufficient but II. ALONE is not sufficient to answer question. B. Statement II. ALONE is sufficient but I. ALONE is not sufficient to answer question. C. Statements I. and II. TOGETHER are sufficient to answer the question NEITHER of them is sufficient ALONE. D. Statements I. and II. COMBINED are NOT sufficient to answer the question additional information is needed to find the correct answer.
A
B
C
D
E
this this but and
11. How much time will computer a need to solve 150 problems? I. The computer needs 50 seconds to solve one problem. II. Computer never takes more than 60 seconds to solve a problem. A. Statement I. ALONE is sufficient but II. ALONE is not sufficient to answer question. B. Statement II. ALONE is sufficient but I. ALONE is not sufficient to answer question. C. Statements I. and II. TOGETHER are sufficient to answer the question NEITHER of them is sufficient ALONE. D. Statements I. and II. COMBINED are NOT sufficient to answer the question additional information is needed to find the correct answer.
A
B
C
D
this this but and
E
12. How many pencils does Raheel have? I. He bought two boxes each containing 10 pencils. II. He lent two pencils to Khaleel A. Statement I. ALONE is sufficient but II. ALONE is not sufficient to answer question. B. Statement II. ALONE is sufficient but I. ALONE is not sufficient to answer question. C. Statements I. and II. TOGETHER are sufficient to answer the question NEITHER of them is sufficient ALONE. D. Statements I. and II. COMBINED are NOT sufficient to answer the question additional information is needed to find the correct answer.
A
B
C
D
this this but and
E
13. In a certain farm there are 47 goats.
How many large brown goats are there?
I. 16 of the goats are large. II. There are 18 brown goats in the farm. A. Statement I. ALONE is sufficient but II. ALONE is not sufficient to answer question. B. Statement II. ALONE is sufficient but I. ALONE is not sufficient to answer question. C. Statements I. and II. TOGETHER are sufficient to answer the question NEITHER of them is sufficient ALONE. D. Statements I. and II. COMBINED are NOT sufficient to answer the question additional information is needed to find the correct answer.
A
B
C
D
this this but and
E
14. Can there be more than 200 pictures in a 60-page book? I. There is at least one picture in each page. II. There are no more than 3 pictures in any page. A. Statement I. ALONE is sufficient but II. ALONE is not sufficient to answer question. B. Statement II. ALONE is sufficient but I. ALONE is not sufficient to answer question. C. Statements I. and II. TOGETHER are sufficient to answer the question NEITHER of them is sufficient ALONE. D. Statements I. and II. COMBINED are NOT sufficient to answer the question additional information is needed to find the correct answer.
A
B
C
D
E
this this but and
15. If P > Q and R > S, then, P + R > Q + S. Is X > Y? I. X + A > Y + B II. A > B A. Statement I. ALONE is sufficient but II. ALONE is not sufficient to answer question. B. Statement II. ALONE is sufficient but I. ALONE is not sufficient to answer question. C. Statements I. and II. TOGETHER are sufficient to answer the question NEITHER of them is sufficient ALONE. D. Statements I. and II. COMBINED are NOT sufficient to answer the question additional information is needed to find the correct answer.
A
B
C
D
E
this this but and
III VERBAL Section
No of Questions
Choose the correct answer for each question and shade the corresponding CIRCLE in the answer sheet 10
Each sentence below has one or two blanks, each blank indicates that something has been omitted. Beneath the sentence are five lettered words or sets of words. Choose the word or set of words that, when inserted in the sentence, best fits the meaning of the sentence as a whole.
1.
Although its publicity has been ___, the film itself is intelligent, well-acted, handsomely produced and altogether ___ A. tasteless … respectable B. extensive … moderate C. sophisticated … moderate D. risqué … crude E. perfect … spectacular A
2.
C
D
E
The Inuit natives of Alaska's North Slope worry that ___ oil exploration might ___their sensitive natural environment. A. B. C. D. E. A
3.
B
additional…assist current…bolster curtailed…shatter unregulated…damage controlled…reassess B
C
D
E
Ants live in colonies based on ___; each member contributes to the good of all by actively working with others in performing necessary tasks. A. B. C. D. E. A
Heredity Individualism Cooperation Reasoning Instinct B
C
D
E
Each question below consists of a related pair of words or phrases, followed by five lettered pairs of words or phrases. Select the lettered pair that best expresses a relationship similar to that expressed in the original pair. 4.
STUDYING: LEARNING:: A. running : jumping B. investigating : discovering C. reading : writing
D. dancing : swimming E. talking : listening A 5.
B
C
D
E
AFTERNOON : DUSK :: A. breakfast : dinner B. yesterday : tomorrow C. Sunday : Saturday D. night : dawn E. arise : lay down A
6.
C
D
E
VIBRATION: SOUND : A. B. C. D. E. A
7.
B
gravity : pull watercolor : paint accident : death worm : reptile arrive : home B
C
D
E
RUN : RACE :: A. B. C. D. E. A
walk : pogo stick swim : boat fly : kite sink : bottle repair : automobile B
C
D
E
Read the passages and answer the questions asked at its end. Almost a century ago Alfred Binet, a gifted psychologist, was asked by the French Ministry of Education to help determine who would experience difficulty in school. Given the influx of provincials to the capital, along with immigrants of uncertain stock, Parisian officials believed they needed to know who might not advance smoothly through the system. Proceeding in an empirical manner, Binet posed many questions to youngsters of different ages. He ascertained which questions when answered correctly predicted success in school, and which questions when answered incorrectly foretold school difficulties. The items that discriminated most clearly between the two groups became, in effect, the first test of intelligence. Binet is a hero to many psychologists. He was a keen observer, a careful scholar, an inventive technologist. Perhaps even more important for his followers, he devised the instrument that is often considered psychology's greatest success story. Millions of people who have never heard Binet's name have had aspects of their fate influenced by instrumentation that the French psychologist inspired. And thousands of psychometricians — specialists in the measurement of psychological variables — earn their living courtesy of Binet's invention.
Although it has prevailed over the long run, the psychologist's version of intelligence is now facing its biggest threat. Many scholars and observers — and even some iconoclastic psychologists — feel that intelligence is too important to be left to the psychometricians. Experts are extending the breadth of the concept — proposing much intelligence, including emotional intelligence and moral intelligence. They are experimenting with new methods of ascertaining intelligence, including some that avoid tests altogether in favor of direct measures of brain activity. They are forcing citizens everywhere to confront a number of questions: What is intelligence? How ought it to be assessed? And how do our notions of intelligence fit with what we value about human beings? In short, experts are competing for the "ownership" of intelligence in the next century. 8.
According to the passage, which of the following is most similar to the "barometer" developed by Binet? A. B. C. D. E. A
9.
The S.A.T. or other standardized college admission test. The written portion of a driver's license test. Open tryouts for a varsity athletic team An electronic scan of brain-wave activity. The trivia questions of a game show. B
C
D
E
The author suggests which of the following about "citizens everywhere"? A. They do not have a sufficiently accurate definition of intelligence to evaluate recent scientific developments. B. They stand to benefit from recent progress in the scientific assessment of intelligence. C. The experiments they are performing with new methods of intelligence measurement are valuable and interesting. D. They are at odds with the experts over who should have the right to define "intelligence." E. Traditionally they have not given careful consideration to some important issues concerning intelligence.
A B C D E 10. As used in line # 8, "discriminated" most nearly means A. B. C. D. E. A
equalized predetermined showed favoritism displayed intolerance distinguished B
C
D
E
Drill Test IV
I Quantitative Section
No. Questions
Of
20
Choose the correct answer for each question and shade the corresponding CIRCLE in the answer sheet
1
1. If the length of BC is twice the length of AC, what are the coordinates of B where A=(x,y)? A. B. C. D. E. A
(x,2y) (-x,2y) (2x,y) (-2x,y) (-2x,2y) B
C
D
E
2. The average of five numbers is 34. If three of the numbers are 28, 30 and 32, what is the average of the other two? A. 40 B. 50 C. 60 D. 70 E. 80 A
B
C
D
E
G
3. In the figure above, rectangle AEJL has been divided into 8 congruent squares with each of the 8 squares having an area of 16. What is the length of AE + MF + LG+ AL + BK + CJ + DH + EG? A. B. C. D. E.
32 44 88 128 176
A
B
C
D
E
4. For any positive integer x, #x = x²/3 and &x = 9 /x.
which of the following is an
expression for the product of #x and &x? A. 3x B. x C. 1 D. x3/64 E. 27 x3 A B C
D
E
5. In a certain town, p gallons of gasoline are needed per month for each car. How long will q gallons last at this rate given that there are r cars in town? A. B. C. D. E.
pr/q qr/p r/pq q/pr pqr
A
B
C
D
E
6. Let xy = z, where x,y,z are nonzero numbers. If x is multiplied by 3 and z is divided by 3, this is equivalent to multiplying y by A. B. C. D. E.
1/9 1/3 1 3 9
A
B
C
D
E
7. If x, y, and z are different positive odd integers and x + y + z = 11, what is the greatest possible value of z? A. B. C. D. E.
10 9 8 7 6
A
B
C
D
E
8. If the postal charges for a package are 62 cents for the first five ounces and 8 cents for each additional ounce, what is the weight of a package for which the charges are $1.66? (Assume there are 16 ounces in one pound) A. B. C. D. E. A
1.05 pounds 1.1 pounds 1.125 pounds 1.25 pounds 1.5 pounds B
C
D
E
9. What fraction of two weeks is 24 minutes? A. B. C. D. E. A
1/120 1/336 1/840 1/2880 1/20160 B
C
D
E
10. If the vertices of a triangle are at (0,0), (-3, 4) and (3, 4), what is the area of the triangle? A. B. C. D. E.
4 6 12 14 18
A
B
C
D
E
11. A water-tank has a base with dimensions 2 feet by 6 feet. If a cube with each side 1 foot is totally immersed in the water, how many inches will the water rise? (12inches = 1 foot) A. B. C. D. E. A
1 2 4 8 It cannot be determined from the information given B
C
D
E
12. In the figure above, the quadrilateral ABCD is a trapezoid with x = 2. The diameter of each semicircle is a side of the trapezoid. What is the sum of the lengths of the four drawn semicircles? (Round to the nearest whole number.) A. B. C. D. E.
13 16 19 22 31
A
B
C
D
E
13. If n + 3 = n x 3, then n = A. B. C. D. E.
0.5 1.5 2 2.5 3
A
B
C
D
E
14. If an equilateral triangle and a square have the same perimeter, what is the ratio of the length of the sides of the equilateral triangle to the lengths of the sides of the square? A. B. C. D. E.
3:4 4:3 1:4 1:3 3:1
A
B
C
D
E
15. A restaurant has a special whereby both parents can eat for $20 and each child can eat for $5. Assuming a family group consists of both parents and at least one child, what is the maximum number of family groups that could have attended given that the restaurant took $115? A. B. C. D. E. A
6 5 4 3 2 B
C
D
E
16. Which of the following points lays in the interior of the circle whose radius is 10 and whose center is at the origin? A. B. C. D. E. A
(-9, 4) (5, -19) (0, -10) (10, -1) (0,15) B
C
D
E
II
Choose the correct answer for each question and shade the corresponding CIRCLE in the answer Analytical No. Of 15 sheet Reasoning Questions 17. If the perimeter of the rectangle ABCD is 14, what is the perimeter of ∆BCD? 7 12 7 + √29 86 It cannot be determined from the information given. A
B
C
D
A
B
D
C
E
18. The roots of ax2 + bx + c = 0 are real only if A. B. C. D. E. A
b2 – 4ac ≥ 0 b2 – 4ac = 0 b2 + 4ac = 0 b2 – 4ac < 0 b2 – 4bc < 0 B
C
D
E
19. The two numbers, whose sum is -13 and product -30, are A. B. C. D. E. A
2, 15 2, -15 -3, 10 3, 10 -3, -13 B
C
D
E
20. Let A = total area of five circles of radius r and let B = total area of three circles of radius s. If A = B, then r / s = A. 3/5 B. √3 / √5 C. 3π / 5 D. √(3π) / √5 E. 3π A
B
C
D
E
Two statements labeled I & II, follow each of the following questions. The statements contain certain information. In the questions you do not actually have to compute an answer, rather you have to decide whether the information given in the statements I. and II. is sufficient to find a correct answer by using basic mathematics and every day facts? 1.
What day of the week is today? I. Today is March 25. II. Akram left Pakistan on Wednesday. A. Statement I. ALONE is sufficient but II. ALONE is not sufficient to answer question. B. Statement II. ALONE is sufficient but I. ALONE is not sufficient to answer question. C. Statements I. and II. TOGETHER are sufficient to answer the question NEITHER of them is sufficient ALONE. D. Statements I. and II. COMBINED are NOT sufficient to answer the question additional information is needed to find the correct answer.
A 2.
B
C
D
this this but and
E
Can any of the four rivers be more than 300 meters wide? I. The narrowest of the four rivers is 240 meters wide. II. Average width of the four rivers is 300 meters. A. Statement I. ALONE is sufficient but II. ALONE is not sufficient to answer question. B. Statement II. ALONE is sufficient but I. ALONE is not sufficient to answer question. C. Statements I. and II. TOGETHER are sufficient to answer the question NEITHER of them is sufficient ALONE. D. Statements I. and II. COMBINED are NOT sufficient to answer the question additional information is needed to find the correct answer
A
3.
B
C
D
this this but and
E
If it is raining then there must be clouds. Are there clouds? I. It is not raining. II. It rained yesterday. A. Statement I. ALONE is sufficient but II. ALONE is not sufficient to answer question. B. Statement II. ALONE is sufficient but I. ALONE is not sufficient to answer question. C. Statements I. and II. TOGETHER are sufficient to answer the question NEITHER of them is sufficient ALONE. D. Statements I. and II. COMBINED are NOT sufficient to answer the question additional information is needed to find the correct answer.
A
B
C
D
this this but and
E
Read the passage to answer the question 4-5 A map representing countries R, S, W, X, Y and Z is to be drawn. Adjacent countries cannot have the same color in the map. The countries adjacent to each other are as follows:
Each of R, S, X and Y is adjacent to W. X is adjacent to Y. Each of R and S is adjacent to Z. 4. Which of the following countries can be the same color as W? A. B. C. D. A 5.
S X Y Z B
C
D
E
Which of the following is a pair of countries that can be the same color? A. B. C. D.
A
R and S S and W W and X X and Y
B
C
D
E
Questions 6 to 11 depends on the following passage A college president wishes to select four members of a faculty-student committee as special representatives to meet with the college's board of trustees. The faculty-student committee consists of eight members four of which (F, G, H and I) are faculty members whereas the other four (R, S, T and U) are students. The president can select any four of the eight committee members as long as the following rules are observed: The four representatives must consist of exactly two faculty members and two students. Either F or G must be one of the representatives but F and G both cannot be the representatives. If R is a representative then H must also be a representative. If T is a representative then G cannot be a representative. 6.
If T is a representative but H is not a representative then the whole group can be determined if it were also true that: A. B. C. D.
A 7.
B
C
D
E
If R is a representative then which of the following CANNOT be a representative? A. B. C. D.
A 8.
F is a representative. I is a representative. R is not a representative. U is not a representative.
H I S T
B
C
D
E
If G is a representative then which of the following can be the other three representatives? A. F, S and U B. H, I and R
C. H, R and S D. I, R and U 9.
A
B
C
D
E
D
E
If neither S nor U is a representative then which of the following is the pair of facultymember representatives? A. B. C. D.
A
F and G F and H F and I G and H
B
C
10. If G, I and S are representatives then which of the following must also be a representative? A. B. C. D.
A
H R T U
B
C
D
E
11. If F and I are representatives then which of the following is not a representative? A. B. C. D.
A
I S U R
B
C
D
E
Questions 12 to 14 depends on the following passage
At a congress of the Ruling Party, the seven top party leaders, who are all cabinet ministers, are seated on a platform in order of rank the Prime Minister being in the center. The closer a person is to the Prime Minister; the higher is his/her rank. Moreover, a person sitting on the right of the PM outranks the one sitting equidistant on the left of the PM. The seven leaders are T, U, V, W, X, Y, and Z. Y is four places to the left of the Minister of Agriculture, who is two places to the right of V. U’s neighbors are T and the Minister of Agriculture. Z is two places to the left of W. The Ministers of Education, Mining and Culture are seated together, in order, from left to right. The remaining Ministers are those of Social Welfare and Defense. 12. The fifth A. B. C. D. A
ranking person in the party hierarchy is: Z, the Minister of Mining Y, the Minister of Culture W, the Prime Minister. X, the minister of Defense. B
C
D
E
13. How many of the seven party leaders outrank the Minister of Education? A. 3 B. 4 C. 5 D. 6 A
B
C
D
E
14. The lowest ranking Minister is A. Minister of Social Welfare. B. Minister of Defense. C. Minister of Education. D. Minister of Mining. A
B
C
D
E
15. “A meadow in springtime is beautiful, even if no one is there to appreciate it.”
This statement would be a logical opposite to which of the following claims? A. People will see only what they want to see. B. Beauty exits only in the eyes of the beholder. C. Beauty does not depend on seasons. D. The greatest pleasure available to mankind is the contemplation of beauty. A
B
C
D
E
III VERBAL Section
No. Of Questions
10
Choose the correct answer for each question and shade the corresponding CIRCLE in the answer sheet
Each sentence below has one or two blanks, each blank indicates that something has been omitted. Beneath the sentence are five lettered words or sets of words. Choose the word or set of words that, when inserted in the sentence, best fits the meaning of the sentence as a whole. 1.
Some illnesses such as smallpox, which have been almost eliminated in the United States are still ____ in many places abroad. A. discussed B. prevalent C. scarce D. unknown E. hospitalized A
2.
B
C
D
E
A recent study indicates that the crime rate in the United States remains ____ and that one in three households ____ some form of major crime in any year A. incredible ... witnesses B. astronomical ... experiences C. simultaneous ... perpetrates D. unsuccessful ... initiates E. defeated ... prosecutes A
B
C
D
E
Each question below consists of a related pair of words or phrases, followed by five lettered pairs of words or phrases. Select the lettered pair that best expresses a relationship similar to that expressed in the original pair. 3.
SALVAGE : TREASURE A. settle : argument B. incorporate : company C. send : correspondence D. rescue : victim E. recycle : newspaper A
4.
B
C
D
E
CONTROVERSY : ARBITRATOR A. peacemaker : conflict B. artifact : anthropologist C. game : referee D. dispute : mediator E. disease : pathologist A
B
C
D
E
Read the passages and answer the questions given at its end:
We are profoundly ignorant about the origins of language and have to content ourselves with more or less plausible speculations. We do not even know for certain when language arose, but it seems likely that it goes back to the earliest history of man, perhaps half a million years. We have no direct evidence, but it seems probable that speech arose at the same time as tool making and the earliest forms of specifically human cooperation. In the great Ice Ages of the Pleistocene period, our earliest human ancestors established the Old Stone Age culture; they made flint tools and later tools of bone, ivory, and antler; they made fire and cooked their food; they hunted big game, often by methods that called for considerable cooperation and coordination. As their material culture gradually improved, they became artists and made carvings and engravings on bones and pebbles, and wonderful paintings of animals on the walls of caves. It is difficult to believe that the makers of these Paleolithic cultures lacked the power of speech. It is a long step Admittedly, from the earliest flint weapons to the splendid art of the late Old Stone Age: the first crude flints date back perhaps to 500,000 B.C., while the finest achievements of Old Stone Age man are later than 100,000 B.C.; and, in this period, we can envisage a corresponding development of language, from the most primitive and limited language of the earliest human groups to a fully developed language in the flowering time of Old Stone Age culture. How did language arise in the first place? There are many theories about this, based on various types of indirect evidence, such as the language of children, the language of primitive societies, the kinds of changes that have taken place in languages in the course of recorded history, the behavior of higher animals like chimpanzees, and the behavior of people suffering from speech defects. These types of evidence may provide us with useful pointers, but they all suffer from limitations, and must be treated with caution. When we consider the language of children, we have to remember that their situations are quite different from that of our earliest human ancestors, because the child is growing up in an environment where there is already a fully developed language, and is surrounded by adults who use that language and are teaching it to him. For example, it has been shown that the earliest words used by children are mainly the names of things and people (“Doll,” “Spoon,” “Mummy”): but, this does not prove that the earliest words of primitive man were also the names of things and people. When the child learns the name of an object, he may then use it to express his wishes or demands: “Doll!: often means “Give me my doll!” Or “I’ve dropped my doll: pick it up for me!”; the child is using language to get things done, and it is almost an accident of adult teaching that the words used to formulate the child’s demands are mainly nouns, instead of words like “Bring!”’ “Pick up!”; and so on. 5.
The main idea of this excerpt is (A) to provide evidence of the origin of language. (B) to present the need for language. (C) to discuss how early man communicated. (D) to present the culture of early man. (E) to narrate the story of English. A
6.
B
C
D
E
Theories of the origin of language include all of the following EXCEPT (A) changes occurring through the years. (B) the need to communicate. (C) language of children. (D) the first man’s extensive vocabulary. (E) communication among primitive men.
A 7.
D
E
B
C
D
E
The implication of the author regarding the early elements of language is that (A) There were specific real steps followed to develop our language. (B) Care must be exercised when exhuming what we consider the roots of language. (C) We owe a debt of gratitude to the chimpanzee contribution. (D) Adults created language in order to instruct their children. (E) Language was fully developed by primitive man. A
9.
C
The purpose of the discussion of the word, “Doll,” is intended to (A) Trace the evolution of a noun. (B) Support the fact that naming things is most important. (C) Indicate how adults teach language to children. (D) Show the evolution of many meanings for one word. (E) Evince man’s multiple uses of single words A
8.
B
B
C
D
E
If we accept that primitive man existed for a very long period of time without language, then we may assume that (A) language is not necessary to man’s existence. (B) language developed with the developing culture of primitives. (C) primitives existed in total isolation from one another. (D) children brought about a need for language. (E) mankind was not intended to communicate. A
B
C
D
E
10. After a reading of this article, one might infer that (A) society creates problems with language. (B) language is for adults to instruct children. (C) society uses language to improve itself. (D) with the evolution of language came wisdom. (E) language brings power. A
B
C
D
E
Answer Keys to Drill Tests
A A A BB B
C
D DD EE EEE
DRILL TEST I - ANSWER KEY Section-I Quantitative 1.
B
C
D
E
B
C
D
E
C
D
E
C
D
2.
A
3.
A
4.
A
B
5.
A
B
D
E
6.
A
B
D
E
7.
A
B
8.
A
9.
B
10.
A
C
E
C
D
E
C
D
E
D
E
B
Section-II Analytical Reasoning 1. A
C
D
2. A
B
C
3.
A
B
C
D
4. A
B
C
D
5. A
B
6.
B
7. A
E E
D
E
C
D
E
C
D
E
8. A 9. A
B
C
E
B
E
10. A
B
C C
11. A
B
12. A
B
13. A 14. A
B
D D D
E
C
D
E
C
D
E
15.
A
16.
A
17.
A
B
18.
A
B
19.
A
20.
A
B
C
E
C
B
Section-III
D
C
E E
D
E
C
D
E
C
D
Verbal
1.
A
B
D
E
2.
A
B
D
E
3.
A
C
D
E
4.
A
C
D
E
B
C
D
E
B B
C C
D
E E
C
D
E
5. 6.
A
7. 8.
A
9.
A
B
10.
A
B
D
E
11.
A
B
D
E
C
E
12.
B
C
D
E
13.
B
C
D
E
14.
A
C
D
E
15.
A
C
D
E
16.
A
C
D
E
17.
A
18.
A
19.
A
20.
B
C
E
B
C
E
B
C
E
B
C
D
E
DRILL TEST II - ANSWER KEY Section-I Quantitative 1.
A
C
D
E
2.
A
C
D
E
3.
A
B
C
4.
A
B
C
D
5.
A
C
D
E
6.
A
B
D
E
7.
A
B
8.
A
9.
A
B
10.
A
B
E
C C
E D
E
D
E E
C
Section-II Analytical Reasoning 1.
A
2.
B
3.
A
4.
A
5. 6.
C
D
E
C
D
E
C
D
E
B
D
E
A
B
D
E
A
B
C
D
B
C
D
C
D
7. 8.
A
B
9.
A
B
10.
A
B
C
11.
A
B
C
B
C
D
C
D
12. 13.
A
B
14.
A
B
D
E E
D E
D
E E
15.
B
C
16.
A
B
17.
A
B
18.
A
19.
A
B
C
20.
A
B
C
D
E
D
E
C C
E D
E E
D
Section-III
Verbal
1.
A
D
E
2.
A
C
D
E
C
D
E
D
E
3.
B B
4.
A
B
5.
A
B
6.
A
B
7.
A
8.
A
B
9.
A
B
10.
A
11.
A
B
12.
A
B
13.
A
14.
A
15.
A
16.
A
17.
A
18.
A
19. 20.
A
C
D D
C
D
C
E E E
D
E
C
D
E
C
D
E
D
E
C
D
E
C
D
C
D
E
B
D
E
B
D
E
D
E
D
E
B
B B
C
B
C
E
DRILL TEST III - ANSWER KEY Section-I Quantitative 1.
A
B
C
D
E
2.
A
B
C
D
E
3.
A
B
C
D
E
4.
A
B
C
D
E
5.
A
B
C
D
E
6.
A
B
C
D
E
7.
A
B
C
D
E
8.
A
B
C
D
E
9.
A
B
C
D
E
10.
A
B
C
D
E
11.
A
B
C
D
E
12.
A
B
C
D
E
13.
A
B
C
D
E
14.
A
B
C
D
E
15.
A
B
C
D
16.
A
B
C
17.
A
B
18.
A
19. 20.
11.
A
B
C
D
E
12.
A
B
C
D
E
13.
A
B
C
D
E
14.
A
B
C
D
E
15.
A
B
C
D
E
Section-III Verbal 1.
A
B
C
D
E
2.
A
B
C
D
E
3.
A
B
C
D
E
4.
A
B
C
D
E
5.
A
B
C
D
E
6.
A
B
C
D
E
7.
A
B
C
D
E
E
8.
A
B
C
D
E
D
E
9.
A
B
C
D
E
C
D
E
10.
A
B
C
D
E
B
C
D
E
A
B
C
D
E
A
B
C
D
E
Section-II Analytical Reasoning 1.
A
B
C
D
E
2.
A
B
C
D
E
3.
A
B
C
D
E
4.
A
B
C
D
E
5.
A
B
C
D
E
6.
A
B
C
D
E
7.
A
B
C
D
E
8.
A
B
C
D
E
9.
A
B
C
D
E
10.
A
B
C
D
E
DRILL TEST IV - ANSWER KEY Section-I Quantitative 1.
A
B
C
D
E
2.
A
B
C
D
E
3.
A
B
C
D
E
4.
A
B
C
D
E
5.
A
B
C
D
E
6.
A
B
C
D
E
7.
A
B
C
D
E
8.
A
B
C
D
E
9.
A
B
C
D
E
10.
A
B
C
D
E
11.
A
B
C
D
E
12.
A
B
C
D
E
13.
A
B
C
D
E
14.
A
B
C
D
E
15.
A
B
C
D
16.
A
B
C
17.
A
B
18.
A
19. 20.
11.
A
B
C
D
E
12.
A
B
C
D
E
13.
A
B
C
D
E
14.
A
B
C
D
E
15.
A
B
C
D
E
Section-III Verbal 1.
A
B
C
D
E
2.
A
B
C
D
E
3.
A
B
C
D
E
4.
A
B
C
D
E
5.
A
B
C
D
E
6.
A
B
C
D
E
7.
A
B
C
D
E
E
8.
A
B
C
D
E
D
E
9.
A
B
C
D
E
C
D
E
10.
A
B
C
D
E
B
C
D
E
A
B
C
D
E
A
B
C
D
E
Section-II Analytical Reasoning 1.
A
B
C
D
E
2.
A
B
C
D
E
3.
A
B
C
D
E
4.
A
B
C
D
E
5.
A
B
C
D
E
6.
A
B
C
D
E
7.
A
B
C
D
E
8.
A
B
C
D
E
9.
A
B
C
D
E
10.
A
B
C
D
E
SAMPLE TEST General
Note: The Sample Test does not include quantitatively the same number of questions as there would be in the actual papers. They are merely meant to provide conceptual guidance to the users or prospective candidates.
I VERBAL Section
No. Of Questions
15
Choose the correct answer for each question and shade the corresponding CIRCLE in the answer sheet
Each sentence below has one or two blanks, each blank indicates that something has been omitted. Beneath the sentence are five lettered words or sets of words. Choose the word or set of words that, when inserted in the sentence, best fits the meaning of the sentence as a whole. 1. Despite the millions of dollars spent on improvements, the telephone system in India remains ________ and continues to ___________ the citizens who depend upon it.
A. B. C. D. E.
Primitive…inconvenience Bombastic...upset Suspicious...connect Outdated...elate Impartial...vex
2. Unlike the images in symbolist poetry which are often vague and _______ , the images of surrealist poetry are startlingly ________ and bold.
A. B. C. D. E.
extraneous...furtive trivial...inadvertent obscure...concrete spectacular...pallid symmetrical…virulent
3. A good trial lawyer will argue only what is central to an issue, eliminating ___________ information or anything else that might __________ the client.
A. B. C. D. E.
Seminal...amuse Extraneous...jeopardize Erratic...enhance Prodigious...extol Reprehensible…initiate
4. Pollen grains and spores that are 200 millions old are now being extracted from shale and are ____________ the theory that the breakup of the continents occurred in stages; in fact, it seems that the breakups occurred almost __________ .
A. B. C. D. E.
refining...blatantly reshaping...simultaneously countermanding...imperceptibly forging...vicariously supporting...haphazardly
Each question below consists of a related pair of words or phrases, followed by five lettered pairs of words or phrases. Select the lettered pair that best expresses a relationship similar to that expressed in the original pair. 5. DETENTION : RELEASE :: A. B. C. D. E.
viciousness : attack calamity : repair qualification : employ induction : discharge therapy : confuse
6. PONDEROUS : WEIGHT :: A. B. C. D. E.
eternal : temporality convincing : decision gargantuan : size ancient : value prototypical : affection
7. FEBRILE : ILLNESS :: A. B. C. D. E. 8.
tenacious : astonishment juvenile : maturity classic : cultivation eccentric : discrimination delusional : insanity
EQUIVOCATION : MEANING :: A. B. C. D. E.
feint : intention secrecy : stealth geniality : amiability travesty : insight refinement : innovation
Choose the lettered word or phrase that is most nearly opposite in meaning to the word in capital letters. 9. WHIMSICAL : A. B. C. D. E.
chivalrous perfect predictable hidden backward
10.REVERE : A. B. C. D. E.
collide succumb threaten divide despise
11.INURED : A. B. C. D. E.
authoritative dissolute bereft sensitive taxing
12.ALACRITY : A. B. C. D. E.
skullduggery reluctance interment bellicosity specificity
Read the passages and answer the questions asked at its end. Art, like words, is a form of communication. Words, spoken and written, render accessible to humans of the latest generations all the knowledge discovered by the experience and reflection, both of preceding generations and of the best and foremost minds of their own times. Art renders accessible to people of the latest generations all the feelings experienced by their predecessors, and those already felt by their best and foremost contemporaries. Just as the evolution of knowledge proceeds by dislodging and replacing that which is mistaken, so too the evolution of feeling proceeds through art. Feelings less kind and less necessary for the well-being of humankind are replaced by others kinder and more essential to that end. This is the purpose of art, and the more art fulfills that purpose the better the art; the less it fulfills it, the worse the art. 13.The author develops the passage primarily by A. B. C. D. E.
theory and refutation example and generalization comparison and contrast question and answer inference and deduction
14.According to the author, knowledge is A. B. C. D. E.
evolutionary and emotional cumulative and progressive static and unmoving dynamic and cyclical practical and directionless
15.According to the passage, all of the following are true EXCEPT: A. B. C. D. E.
Art is a form of communication. Art helps to refine sensibilities. Art is a repository of experience. Real art can never be bad. Art is a progressive human endeavor.
II Analytical Reasoning Section
No. Of Questions
20
Choose the correct answer for each question and shade the corresponding CIRCLE in the answer sheet
Questions 16-19 are based on the following. The Western Derby is a race held annually at Bayshore Racetrack. There are eight gates at the racetrack, but only seven horses are entered in this race—Julius Caesar, King's Bounty, Longshot, Man Among Boys, Nocturnal, Odyssey, and Phantom. One of the gates is left empty. The horses are at the gate, waiting for the race to begin. Gate 1, on the inside of the racetrack, is occupied. Phantom is at a gate inside of Nocturnal. The number of gates separating Julius Caesar and King's Bounty equals the number of gates separating Longshot and Man among Boys. Nocturnal and Odyssey are next to each other.
16. If Odyssey is at Gate 2, which of the following must be true? A. B. C. D. E.
Nocturnal is at the innermost gate. King's Bounty is at the outermost gate. A horse occupies the outermost gate. Phantom is at the innermost gate. The outermost gate is not empty.
17. Which of the following is a possible assignment for the horses, from the inside to the outside?
A. Phantom, King's Bounty, Julius Caesar, Odyssey, Nocturnal, Man Among Boys, Longshot, vacant
B. vacant, Phantom, Julius Caesar, Longshot, King's Bounty, Man Among Boys, Nocturnal, Odyssey
C. Longshot, Man Among Boys, Nocturnal, vacant, Phantom, Odyssey, King's Bounty, Julius Caesar
D. Julius Caesar, King's Bounty, Longshot, Phantom, vacant, Man Among Boys, Nocturnal, Odyssey
E. Phantom, Julius Caesar, Nocturnal, vacant, Odyssey, King's Bounty, Longshot, Man Among Boys
18.If Julius Caesar is at Gate 6, King's Bounty is at Gate 7, and Odyssey is at Gate 4, which of the following must be true? I. Longshot is at Gate 1. II. Nocturnal is at Gate 5. III. Man Among Boys is at Gate 2. IV. Gate 8 is vacant. Building Standards in Education and Professional Testing
165
A.
I and II only
B. II and III only
C. II and IV only D. I, II, and III only E. I, II, III, and IV 19.If Julius Caesar and King's Bounty are at the second and fourth gates, respectively, all of the following can be true EXCEPT A. B. C. D. E.
Phantom is at Gate 1 Man Among Boys is at Gate 3 Longshot is at Gate 6 Odyssey is at Gate 7 Nocturnal is at Gate 7
20. Studies have shown that families who install smoke detectors and own fire extinguishers have a reduced risk of losing a child in a house fire. Therefore, no family who installs smoke detectors and owns a fire extinguisher will lose a child in a house fire. Of the following, the best criticism of the argument above is that the argument does not
A. take into account the possibility of losing a child in a house fire despite all B. C. D. E.
precautionary measures indicate that fire extinguishers are effective during early stages of a fire cite the fact that smoke detectors have proven to be effective in waking sleeping children during a house fire differentiate between the two major causes of house fires: cooking and heating take into account that families who buy smoke detectors are also more likely to purchase fire insurance
21.LSD is a drug known to cause synesthesia, a phenomenon in which sensory input somehow becomes interchanged in the brain: a person with synesthesia might smell a symphony, hear sun light, or taste a pinprick. While most cases are drug induced, some people suffer from synesthesia in various forms since birth. Which of the following can be most safely inferred from the information above?
A. Synesthesia is not always a drug-induced phenomenon. B. Some great artists of this century have been known for their synesthetic C.
D. E.
proclivities. LSD is an addictive drug. Synesthesia is rarely bothersome to those who experience it. Synesthesia at birth is a result of mothers who have tried LSD.
Building Standards in Education and Professional Testing
166
22. Palindromes are easier to solve than acrostics, but acrostics are more difficult to create than palindromes. Rebuses are more difficult to solve than acrostics, yet rebuses are easier to create than palindromes. If the above information is true, then it must also be true that
A. acrostics are more difficult to create than rebuses B. palindromes are more difficult to solve than rebuses C. rebuses are easier to solve than acrostics D. acrostics are easier to create than rebuses E. rebuses are easier to solve than palindromes Questions 23-25 are based on the following. A university has a procedure for registering and recording complaints. Due to strict bureaucratic regulations, the following system of passing complaints must be observed: A is the first registrar to receive all incoming complaints. F is the recorder and final administrator to handle a complaint. Personnel B, C, D, and E may pass complaints only as follows: A to B B to either C or D C to either B or E D to C E to either D or F 23.Which is an acceptable path for a complaint to follow, passing from A?
A. B. C. D. E.
B to C to D to F B to D to C to F B to C to E to F B to E to F D to C to F
24.If a complaint is received and is handled by each personnel member only one time, which of the following could be one of the passes?
A. B. C. D. E.
A to C C to B C to F D to C E to D
25.Between which two personnel may a complaint pass by means of two different paths without any duplication of passes?
A. B. C. D.
B to E C to D C to E D to B
Building Standards in Education and Professional Testing
167
E. E to B
Building Standards in Education and Professional Testing
168
Questions 26-31 are based on the following. In a baseball field, one team can practice at a time. There are seven teams—the Aces, the Bears, the Cubs, the Ducks, the Eagles, the Falcons, and the Giants. The baseball field is open seven evenings a week from Monday to Sunday (Sunday being considered the last day of the week), and the allocation of practice times is governed by the following rules: On any evening, only one team can play. The Aces must practice on Monday. The Ducks practice exactly one day before the Falcons practice. The Falcons practice exactly one day before the Giants practice. The Cubs and the Bears must practice earlier in the week than the Eagles. 26.The latest day in the week that the Bears can practice is A. B. C. D. E.
Tuesday Wednesday Thursday Friday Saturday
27.If a person went to the baseball field on three consecutive evenings, he or she could see which of the following teams in the order listed? A. B. C. D. E.
the the the the the
Falcons, the Giants, the Cubs Falcons, the Giants, the Ducks Aces, the Ducks, the Cubs Bears, the Cubs, the Falcons Ducks, the Eagles, the Falcons
28.One week, the Cubs practiced on Wednesday and the Ducks practiced the next day. That week, the Bears must have practiced on A. B. C. D. E.
Monday Tuesday Friday Saturday Sunday
29.If the Giants practice on Thursday, the Eagles and the Ducks must practice on which days, respectively? A. B. C. D. E.
Sunday and Tuesday Saturday and Tuesday Friday and Wednesday Wednesday and Thursday Tuesday and Monday
30.If the Falcons practice on Saturday, the Eagles must practice on what day? A.
Tuesday
Building Standards in Education and Professional Testing
169
B. C. D. E.
Wednesday Thursday Friday Sunday
31.The practice schedule has to adhere to which of the following?
A. B. C. D. E.
The The The The The
Ducks practice earlier in the week than the Eagles. Falcons practice on a later day than the Eagles. Falcons practice earlier in the week than the Giants. Cubs practice earlier in the week than the Ducks. Bears practice earlier in the week than the Cubs.
32.Wine, cheese, butter, and raisins are all examples of early techniques to preserve food. In modern times, food scientists have developed other techniques such as dehydration, hermetic sealing, and radiation. Of these, radiation is the most controversial because preliminary studies have shown that radiation alters the natural chemical bonds in fruits and vegetables. Instead of providing salutary effects, eating radiated produce may well introduce irritating chemicals into the body, creating a possible health hazard. Which of the following, if true, supports the conclusion that eating radiated produce poses a possible health hazard? A. Radiation affects only those chemical bonds associated with water, that is, hydrogen and oxygen. B. Radiation kills microorganisms that hasten food decay. C. The radiation-induced bonds are unlike any of those found in non-radiated produce. D. Certain microorganisms, namely those found in yogurt cultures, are essential for proper digestion. E. Radiation has no effect on foods preserved by drying.
33. Blue Blood, Inc., is a private blood products company that buys blood only from
qualified donors. To qualify, a person must weigh at least 105 pounds, must not have taken malaria medication in the last three years, must never have had hepatitis, and must never have used intravenous drugs. Blue Blood nurses know that traveling has an effect on the possibilities for blood donation: Everyone who travels to Malaysia is required to take malaria medication; no one who enters Singapore can have ever used intravenous drugs; everyone traveling to Gorisimi gets hepatitis. Which of the following situations would not automatically disqualify a person from selling blood to Blue Blood? A.
traveling to Malaysia two years ago
B. having once weighed 110 pounds and now weighing 95 pounds C. being denied admission to Singapore D. traveling to Gorisimi five years ago E. using intravenous drugs that were legal at the time
Building Standards in Education and Professional Testing
170
34.Before marriage, couples should be tested for AIDS and any other sexually communicable diseases. Negative results will guarantee the health and safe-ness of their marriage. Which of the following is an assumption of the argument in the passage above?
A. Current state laws require couples who are planning to get married to be B. C. D. E.
tested for infectious disease in order to prevent possible health problems in the future. There are many infectious diseases that can be sexually transmitted from one individual to another. Fortunately even if a test proves positive for a communicable disease, couples can still lead healthy marriages by taking the proper precautions. Due to advances in medical research over the years, infectious diseases that used to be fatal can now be effectively treated. All the diseases detectable through testing have no incubation period and the results of these tests can immediately indicate whether or not the individual has the disease.
Question 35 is based on the following. Nine athletes attend a sports banquet. Three of the athletes—}, K, and L—are varsity football players; two of the athletes—M and N—are varsity basketball players. The other four athletes— O, P, Q, and R—belong to the hockey club. All nine athletes will be seated at three small tables, each seating three athletes. The athletes must be seated according to the following rules: O and J do not sit at the same table. P sits together with at least one of K or M. There can be at most only one football player at a table. There can be at most only one basketball player at a table. 35.Suppose just one varsity athlete sits at a certain table, and that athlete happens to be J. If so, who else sits with J?
A. P, Q B.
C. D. E.
P, R Q, R O, Q O, P
Building Standards in Education and Professional Testing
171
III Quantitative Section
No of Questions
15
Choose the correct answer for each question and shade the corresponding CIRCLE in the answer sheet
36. If √y = 9, then y2 - √y = A. B. C. D. E.
√3-9 0 9-√3 6552 6561
37.If (x+3)/6 = 12/(x+4), what is the positive value of x? A. B. C. D. E.
2 3 5 √60 12
38. Cindy wants to paint her office. She can buy three cans of the same-priced paint and three identical brushes for $21, or she can buy four cans of the same paint and one brush for $22. How much does a can of paint cost? A. B. C. D. E.
$2 $3 $4 $5 $6
39.Which of the following must be true? I. (25 - 81) = (5 - 9) (5 + 9) II. 7(9 + 6) = 7(9) + 7(6) III. 6 ÷ (3 - 1) = (6 ÷ 3) - (6÷1) A. B. C. D. E.
I only II only III only I and II only I, II, and III
40.The sum of a and 9 - 2a is less than 8. Which of the following is (are) the value(s) of a? I.
II.
a<-1 a< 1
Building Standards in Education and Professional Testing
172
III. a>1 A. B. C. D. E.
I only II only III only I and II only I and III only
41.Susan is having a party. At 7:00 P.M., guests begin arriving at a uniform rate of 8 people every 15 minutes. If this pattern continues, how many guests will have arrived by 9:30 P.M.? F. G. H. I. J.
10 20 40 64 80
42. For positive integers p and q, if p2 + 2q2 = 41, and 2p2 +q2 = 34, then p2 = A. B. C. D. E.
2.5 7 3 9 16
43.If a:b is 7:6 and 3b:2c is 2:3, what is c/a ? A. B. C. D. E.
14/27 7/9 6/7 9/7 27/14
44.In the figure above, if the radius of the circle is 8, and triangle TRS is inscribed in the circle, then the length of arc TRS is A. 16π/3 B. (32 π)/3 C. 16 π D. (128 π)/3 E. 64 π
45. For developing pictures, XYZ Photo Lab charges a service fee of $3 for every order it receives in addition to a printing fee. If the order consists of 12 pictures or less, the printing fee per picture is $0.36. If Building Standards in Education and Professional Testing
173
the order consists of more than 12 pictures, the printing fee per picture is $0.24. What is the total cost per picture for an order consisting of 30 pictures? A. B. C. D. E.
$0.11 $0.24 $0.34 $0.46 $3.24
46.Lisa found an easy way to add up a sequence of positive even integers with an even number of terms. She formed pairs of equal sums by adding the first integer to the last, the second integer to the next-to-last, and so on. She then computed the total by adding these equal sums. If the total Lisa obtained was 930, how many terms were there in the sequence of positive even integers if the sequence started with the number 2? A. B. C. D. E.
30 39 40 60 465
47. December is the busiest month at Lamont's Gift Shoppe, where sales in December are 40 percent higher than average. If sales in February are typically 20 percent lower than average, what is the ratio of February sales to December sales? A. B. C. D. E.
1:2 4:2 4:5 4:7 6:7
48.How many 4-digit numbers are there that consist of only odd digits? A. B. C. D. E.
20 625 1,024 4,500 5,000
49. For some integer m, let [m] be defined by the equation {m} = m (1- m). If n + 1 = {n + 1}, then n = A. B. C. D. E.
-2 -1 0 1 2
Building Standards in Education and Professional Testing
174
50.Box A and box B have 6 cards each. Each card is marked with one integer, 1 through 6. Both boxes can have more than one card with the same integer, but the sum of all the integers in each box must be 18. Two of the cards in box/1 are 6's and two of the cards in box B are 5's. If one card is drawn from box A and one from box B, but neither a 6 nor a 5 is drawn, what is the largest possible sum of the integers on the cards drawn from the two boxes? A. B. C. D. E.
3 4 7 8 12
Building Standards in Education and Professional Testing
175
