To find out if a number is divisible by seven: Take the last digit, double it, and subtract it from the rest of the number. If the answer is more than a 2 digit number perform the above again. If the result is 0 or is divisible by 7 the original number is also divisible by 7. Example 1 ) 259 9*2= 18. 25-18 = 7 which is divisible by 7 so 259 is also divisible by 7. Example 2 ) 2793 3*2= 6 279-6= 273 now 3*2=6 27-6= 21 which is divisible by 7 so 2793 is also divisible by 7 . Now find out if following are divisible by 7 1) 2841 2) 3873 3) 1393 4) 2877
TO FIND SQUARE OF A NUMBER BETWEEN 40 to 50 Sq (44) . 1) Subtract the number from 50 getting result A. EXAMPLE 1 : 44 50-44=6 Sq of 6 =36 25-6 = 19 So answer 1936 EXAMPLE 2 : 47 50-47=3 Sq 0f 3 = 09 25-3= 22 So answer = 2209 NOW TRY To Find Sq of 48 ,26 and 49
2) Square A getting result X. 3) Subtract A from 25 getting result Y
TO FIND SQUARE OF A 3 DIGIT NUMBER : LET THE NUMBER BE XYZ SQ (XYZ) is calculated like this STEP 1. Last digit = last digit of SQ(Z) STEP 2. Second Last Digit = 2*Y*Z + any carryover from STEP 1. STEP 3. Third Last Digit 2*X*Z+ Sq(Y) + any carryover from STEP 2. STEP 4. Fourth last digit is 2*X*Y + any carryover from STEP 3. STEP 5 . In the beginning of result will be Sq(X) + any carryover from Step 4. EXAMPLE : SQ (431) STEP 1. Last digit = last digit of SQ(1) =1 STEP 2. Second Last Digit = 2*3*1 + any carryover from STEP 1.= 6 STEP 3. Third Last Digit 2*4*1+ Sq(3) + any carryover from STEP 2.= 2*4*1 +9= 17. so 7 and 1 carryover STEP 4. Fourth last digit is 2*4*3 + any carryover (which is 1) . = 24+1=25. So 5 and carry over 2. STEP 5 . In the beginning of result will be Sq(4) + any carryover from Step 4. So 16+2 =18. So the result will be 185761. If the option provided to you are such that the last two digits are different, then you need to carry out first two steps only , thus saving time. You may save up to 30 seconds on each calculations and if there are 4 such questions you save 2 minutes which may really affect UR Percentile score.
PYTHAGORAS THEROEM :
4) Answer is xy
In any given exam there are about 2 to 3 questions based on pythagoras theorem. Wouldn’t it be nice that you remember some of the pythagoras triplets thus saving up to 30 seconds in each question. This saved time may be used to attempt other questions. Remember one more right question may make a lot of difference in UR PERCENTILE score. The unique set of pythagoras triplets with the Hypotenuse less than 100 or one of the side less than 20 are as follows : (3,4,5), (5, 12, 13), (8, 15, 17), (7, 24, 25), (20, 21, 29), (12, 35, 37), (9, 40, 41), (28, 45, 53), (11, 60, 61), (33, 56, 65), (16, 63, 65), (48, 55, 73), (36, 77, 85), (13, 84, 85), (39, 80, 89), and (65, 72, 97). (15,112,113), (17,144,145), (19,180,181), (20,99,101) If you multiply the digits of the above mentioned sets by any constant you will again get a pythagoras triplet . Example : Take the set (3,4,5). Multiply it by 2 you get (6,8,10) which is also a pythagoras triplet. Multiply it by 3 you get ( 9,12,15) which is also a pythagoras triplet. Multiply it by 4 you get (12,16,20) which is also a pythagoras triplet. You may multiply by any constant you will get a pythagoras triplet Take another example (5,12,13) Multiply it by 5,6 and 7 and check if you get a pythagoras triplet. TIPS FOR SMART GUESSING :
You will notice that in any case, whether it is a unique triplet or it is a derived triplet (derived by multiplying a constant to a unique triplet), all the three numbers cannot be odd. In case of unique triplet , the hypotenuse is always odd and one of the remaining side is odd the other one is even. Below are the first few unique triplets with first number as Odd. 3 4 5 5 12 13 7 24 25 9 40 41 11 60 61 You will notice following trend for unique triplets with first side as odd. Hypotenuse = (Sq(first side) +1) / 2 Other side = Hypotenuse -1 Example : First side = 3 , so hypotenuse = (3*3+1)/2= 5 and other side = 5-1=4 Example 2: First side = 11 so hypotenuse = (9*9+1)/2= 41 and other side = 41-1=40 Please note that the above is not true for a derived triplet for example 9,12 and 15, which has been obtained from multiplying 3 to the triplet of 3,4,5. You may check for other derived triplets. Below are the first few unique triplets with first number as Even . 4 3 5 8 15 17 12 35 37 16 63 65 20 99 101 You will notice following trend for unique triplets with first side as Even. Hypotenuse = Sq( first side/ 2)+1 Other side = Hypotenuse-2 Example 1. First side =8 So hypotenuse = sq(8/2) +1= 17 Other side = 17-2=15 Example 2. First side = 16 So hypotenuse = Sq(16/2) +1 =65 Other side = 65-2= 63
PROFIT AND LOSS : In every exam there are from one to three questions on profit and loss, stating that the cost was first increased by certain % and then decreased by certain %. How nice it would be if there was an easy way to calculate the final change in % of the cost with just one formula. It would really help you in saving time and improving UR Percentile. Here is the formula for the same : Suppose the price is first increase by X% and then decreased by Y% , the final change % in the price is given by the following formula Final Difference % = X- Y – XY/100.
EXAMPLE 1. : The price of T.V set is increased by 40 % of the cost price and then decreased by 25% of the new price . On selling, the profit for the dealer was Rs.1,000 . At what price was the T.V sold. From the above mentioned formula you get : Final difference % = 40-25-(40*25/100)= 5 %. So if 5 % = 1,000 then 100 % = 20,000. C.P = 20,000 S.P = 20,000+ 1000= 21,000. EXAMPLE 2 : The price of T.V set is increased by 25 % of cost price and then decreased by 40% of the new price . On selling, the loss for the dealer was Rs.5,000 . At what price was the T.V sold.From the above mentioned formula you get : Final difference % = 25-40-(25*45/100)= -25 %. So if 25 % = 5,000 then 100 % = 20,000. C.P = 20,000 S.P = 20,000 – 5,000= 15,000. Now find out the difference in % of a product which was : First increased by 20 % and then decreased by 10 %. First Increased by 25 % and then decrease by 20 %. First Increased by 20 % and then decrease by 25 %. First Increased by 10 % and then decrease by 10 %. First Increased by 20 % and then decrease by 15 %.
TIPS TO IMPROVE UR PERCENTILE : HOW ABOUT SOLVING THE FOLLOWING QUESTION IN JUST 10 SECONDS Ajay can finish work in 21 days and Blake in 42 days. If Ajay, Blake and Chandana work together they finish the work in 12 days. In how many days Blake and Chandana can finish the work together ? (21*12 )/(24-12) = (21*12)/9= 7*4= 28 days. NOW CAREFULLY READ THE FOLLOWING TO SOLVE THE TIME AND WORK PROBLEMS IN FEW SECONDS. TIME AND WORK :
1. If A can finish work in X time and B can finish work in Y time then both together can finish work in (X*Y)/ (X+Y) time. 2. If A can finish work in X time and A and B together can finish work in S time then B can finish work in (XS)/(X-S) time. 3. If A can finish work in X time and B in Y time and C in Z time then they all working together will finish the work in (XYZ)/ (XY +YZ +XZ) time 4. If A can finish work in X time and B in Y time and A,B and C together in S time then : C can finish work alone in (XYS)/ (XY-SXSY) B+C can finish in (SX)/(X-S) and A+ C can finish in (SY)/(Y-S)
Here is another shortcut TYPE 1 : Price of a commodity is increased by 60 %. By how much % should the consumption be reduced so that the expense remain the same. TYPE 2 : Price of a commodity is decreased by 60 %. By how much % can the consumption be increased so that the expense remain the same. Solution : TYPE1 : (100* 60 ) / (100+60) = 37.5 % TYPE 2 : (100* 60 ) / (100-60) = 150 %
2. Properties of Integers (zero is an integer - both positive and negative numbers) 3. Consecutive Integers (follow one another and differ by 1. Example is 6,7,8,9 are consecutive) 4. Value of number (does not change when multiplied by 1. 13 x 1 = 13) 5. Real Numbers (ordering, arranging numbers from smallest to greatest or from greatest to smallest > <) 6. Order of Operations PEMDAS (Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction) 7. Decimals (place value starting from left of decimal point - tenths, hundredths, thousandths) 8. Multiplying, Dividing, Adding, Subtracting Decimals 9. Fractions, Rational Numbers, Scientific Notation 10. Reciprocal of any number (n is expressed as 1 over n or 1/n) 11. Product of a number and reciprocal (always 1. Reciprocal of 3 is 1/3 and 3 x 1/3 = 3/3 which is 1) 12. Fraction to Decimal (divide numerator by denominator 3/4 = 0.75)
13. Rational Number (fraction whose numerator and denominator are both integers and denominator does not equal 0) 14. Scientific notation (when numbers are very large or small 667,000,000 is written as 6.67 x 10 ^8 15. Ratio, proportion, percent 16. Ratio of 1 to 5 is 1/5 or 1:5 (be sure to differentiate between part-part and part-whole ratios) example: 2 cups of flour: 1 cup of sugar is a part-part ratio. One group of students being compared to entire class it is a part-whole ratio 13 girls: 27 students(
17. Squares and Square root (size=9)(a number is considered a perfect square when the square root of that number is a whole number. 25 is a perfect square because square root of 25 is 5)[/size] 18. Arithmetic sequence, Geometric sequence 19. Factors and multiples 20. Prime number factors, common factors, greatest common factor (gcf) 21. Common multiples, multiples, least common multiples (LCM) 22. Commutative property of multiplication 23. Distributive property of multiplication 24. Associative property of multiplication 25. Mean, Median, and Mode 26. Probability and outcomes 27. Absolute value 28. Factoring, Polynomials (use distributive property a(b + c) = ab + ac) 29. FOIL 30. Exponents, inequalities 31. Word problems - greater than, more than, and sum of (+) less than, fewer than, and difference (-) 32. Of and by means multiplication (x) and per means division (/) 33. Distance = rate x time 34. Simple annual interest - principal x interest rate x time Example: $10,000 at 6.0% interest for 1 year. You would earn 10,000 x 0.06 x 1 or $600 in interest during that year --- if interest was compounded, interest must be computed on the principal as well as on the interest that has already been earned
35. Geometry 36. Coordinate geometry (x,y) plane 37. Slope of line, slope intercept, parallel, perpendicular lines 38. Find distance between 2 points on plane- use distance formula 39. To find midpoint of line, use midpoint formula 40. Properties of triangles, equilateral triangle, isoceles, right and sum of interior angles 41. Perimeter (p) is sum of lengths 42. Area is 1/2 (base)(height) 43. Quadrilaterals, lines and angles 44. Paralleogram 45. Area, rectangle is a polygon 46. Squares, line, line segment (acute, obtuse, and right triangles) 47. Other polygons (pentagon, hexagon, octagon) 48. Circle, radius, and diameter (area circumference, complete arc is 360 degrees) 49. 3D figures 50. Formula for volume (v) of rectangular solid is v=lwh where l is length, w is width, and h is height. 51. Formula for surface area of rectangular solid is 2(wl + lh + wh) 52. Standard deviation, frequency distribution table
