regisss/math_qa huggingface dataset:
Problem: in a city where all streets run east - to - west , all avenues run north - to - south , and all intersections are right angles as shown below , jenn needs to walk from the corner of 1 st street and 1 st avenue to the corner of 6 th street and 3 rd avenue . if her friend amanda is sitting on a bench on 4 th street halfway between 1 st and 2 nd avenues , and jenn chooses her path randomly from any route that will allow her to walk exactly 7 blocks to her destination , what is the probability that jenn will walk down 4 th st . past amanda ?
Options: a ) 1 / 42 , b ) 1 / 21 , c ) 1 / 7 , d ) 1 / 3 , e ) 1 / 2
Rationale: all routes between ( 1,1 ) to ( 3,6 ) = 7 ! / ( 2 ! * 5 ! ) = 21 routes which pass 4 th st . between 1 st and 2 nd avenue = routs between ( 1,1 ) to ( 1,4 ) * routs between ( 2,4 ) to ( 3,6 ) = 1 * ( 3 ! / ( 2 ! * 1 ! ) ) = 3 the probability that jenn will walk down 4 th st . past amanda = 3 / 21 = 1 / 7 c is correct .
Answer: c
Problem: length of a rectangular plot is 50 mtr more than its breadth . if the cost of fencin g the plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ?
Options: a ) 46 m , b ) 60 m , c ) 58 m , d ) 75 m , e ) 80 m
Rationale: "let breadth = x metres . then , length = ( x + 50 ) metres . perimeter = 5300 / 26.5 m = 200 m . 2 [ ( x + 50 ) + x ] = 200 2 x + 50 = 100 2 x = 50 x = 25 . hence , length = x + 50 = 75 m d"
Answer: d
Problem: 10 camels cost as much as 24 horses , 16 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants . if the cost of 10 elephants is rs . 110000 , find the cost of a camel ?
Options: a ) s . 9800 , b ) s . 3800 , c ) s . 9800 , d ) s . 4400 , e ) s . 6880
Rationale: "cost of the camel = p 10 camels = 24 horses 16 horses = 4 oxen 6 oxen = 4 elephants 10 elephants = rs . 110000 p = rs . [ ( 24 * 4 * 4 * 110000 ) / ( 10 * 16 * 6 * 10 ) ] p = rs . ( 42240000 / 9600 ) = > p = rs . 4400 answer : d"
Answer: d
Problem: kyle , david , and catherine each try independently to solve a problem . if their individual probabilities for success are 1 / 3 , 2 / 7 and 5 / 9 , respectively , what is the probability that kyle and catherine , but not david will solve the problem ?
Options: a ) 35 / 189 , b ) 33 / 129 , c ) 25 / 189 , d ) 24 / 113 , e ) 20 / 189
Rationale: p ( kyle will solve ) = 1 / 3 p ( david will not solve ) = 1 - 2 / 7 = 5 / 7 p ( catherine will solve ) = 5 / 9 p = ( 1 / 3 ) * ( 5 / 7 ) * ( 5 / 9 ) = 25 / 189 answer : c
Answer: c
Problem: a car travels uphill at 30 km / hr and downhill at 60 km / hr . it goes 100 km uphill and 50 km downhill . find the average speed of the car ?
Options: a ) 32 kmph , b ) 33 kmph , c ) 34 kmph , d ) 35 kmph , e ) 36 kmph
Rationale: "avg speed = total distance / total time . total distance traveled = 100 + 50 = 150 km ; time taken for uphill journey = 100 / 30 = 10 / 3 ; time taken for down hill journey = 50 / 60 = 5 / 6 ; avg speed = 150 / ( 10 / 3 + 5 / 6 ) = 36 kmph answer : e"
Answer: e
Problem: a work which could be finished in 11 days was finished 3 days earlier after 10 more men joined . the number of men employed was ?
Options: a ) 22 , b ) 20 , c ) 88 , d ) 71 , e ) 12
Rationale: "x - - - - - - - 11 ( x + 10 ) - - - - 6 x * 11 = ( x + 10 ) 6 x = 12 \ answer : e"
Answer: e
Problem: the ratio of numbers is 3 : 4 and their h . c . f is 5 . their l . c . m is :
Options: a ) 12 , b ) 16 , c ) 24 , d ) 60 , e ) 98
Rationale: "let the numbers be 3 x and 4 x . then their h . c . f = x . so , x = 5 . so , the numbers are 15 and 20 . l . c . m of 15 and 20 = 60 . answer : d"
Answer: d
Problem: if the average ( arithmetic mean ) of a and b is 50 and the average of b and c is 70 , what is the value of c − a ?
Options: a ) 40 , b ) 50 , c ) 90 , d ) 140 , e ) it can not be determined from the information given .
Rationale: "- ( a + b = 100 ) b + c = 140 c - a = 40 a . 40"
Answer: a
Problem: a invested $ 15000 in a business after 6 months b invested $ 18000 in the business . end of the year if they got $ 16000 as profit . find b shares ?
Options: a ) $ 10000 , b ) $ 12000 , c ) $ 5000 , d ) $ 6000 , e ) $ 7500
Rationale: "a : b = 15000 * 12 : 18000 * 6 a : b = 5 : 3 a ' s share = 16000 * 5 / 8 = 10000 b ' s share = 16000 * 3 / 8 = 6000 answer is d"
Answer: d
Problem: if 85 percent of the test takers taking an old paper and pencil gmat exam answered the first question on a given math section correctly , and 70 percent of the test takers answered the second question correctly , and 5 percent of the test takers answered neither question correctly , what percent answered both correctly ?
Options: a ) 60 % , b ) 65 % , c ) 70 % , d ) 75 % , e ) 80 %
Rationale: "{ total } = { first correctly } + { second correctly } - { both correctly } + { neither correctly } 100 = 85 + 70 - { both correctly } + 5 { both correctly } = 60 . answer : a ."
Answer: a
Problem: a number when divided by 44 , gives 400 as quotient and 0 as remainder . what will be the remainder when dividing the same number by 35
Options: a ) a ) 30 , b ) b ) 3 , c ) c ) 4 , d ) d ) 6 , e ) e ) 7
Rationale: "explanation : p ÷ 44 = 400 = > p = 400 * 44 = 17600 p / 35 = 17600 / 35 = 502 , remainder = 30 answer : option a"
Answer: a
Problem: what is the area of a square field whose diagonal of length 22 m ?
Options: a ) 300 sq m , b ) 220 sq m , c ) 200 sq m , d ) 400 sq m , e ) 800 sq m
Rationale: "d 2 / 2 = ( 22 * 22 ) / 2 = 220 answer : b"
Answer: b
Problem: if p ( a ) = 0.18 , p ( b ) = 0.5 and p ( b | a ) = 0.2 , find p ( a n b ) ?
Options: a ) 0.28 , b ) 0.36 , c ) 0.45 , d ) 0.56 , e ) 0.7
Rationale: p ( b | a ) = p ( a n b ) / p ( a ) p ( a n b ) = p ( b | a ) × p ( a ) p ( a n b ) = 0.2 × 0.18 p ( a n b ) = 0.36 b )
Answer: b
Problem: an error 1 % in excess is made while measuring the side of a square . what is the percentage of error in the calculated area of the square ?
Options: a ) 4.05 % , b ) 4.02 % , c ) 4 % , d ) 3 % , e ) 2.01 %
Rationale: "percentage error in calculated area = ( 1 + 1 + ( 1 ã — 1 ) / 100 ) % = 2.01 % answer : e"
Answer: e
Problem: a survey of n people in the town of eros found that 50 % of them preferred brand a . another surveyof 100 people in the town of angie found that 60 % preferred brand a . in total , 55 % of all the people surveyed together preferred brand a . what is the total number of people surveyed ?
Options: a ) 50 , b ) 100 , c ) 150 , d ) 200 , e ) 250
Rationale: "50 % of n people from eros prefer brand a . 50 % of n is 50 / 100 x n = n / 2 . 60 % of 100 people from angie prefer brand a . 60 % of 100 is 60 / 100 x 100 = 60 . of the total n + 100 people surveyed , n / 2 + 60 prefer brand a . given that this is 55 % , we have ( n / 2 + 60 ) / ( n + 100 ) x 100 = 55 solving the equation ( n / 2 + 60 ) / ( n + 100 ) x 100 = 55 ( n / 2 + 60 ) = 55 / 100 x ( n + 100 ) ( n / 2 + 60 ) = 11 / 20 n + 55 0 = 11 n / 20 – n / 2 + 55 - 60 now subtracting n / 2 and 60 from both sides 0 = n / 20 - 5 adding 5 on both sides 5 = n / 20 n = 100 hence , the total number of people surveyed is n + 100 = 100 + 100 = 200 . answer : d"
Answer: d
Problem: 325.124 x 12.98 ã · 3.001 + 21.21 = ?
Options: a ) 1430.08 , b ) 1420.06 , c ) 781.189 , d ) 656.112 , e ) 456.512
Rationale: "explanation : ? = 325.124 x 12.98 ã · 3.001 + 21.21 = ? â ‰ ˆ ( 325.124 x 13 / 3 ) + 21.21 â ‰ ˆ 1408.87 + 21.21 â ‰ ˆ 1430.080 answer : option a"
Answer: a
Problem: gold is 19 times as heavy as water and copper is 9 times heavy . in what ratio must these metals be mixed so that the mixture may be 15 times as heavy as water ?
Options: a ) 2 : 3 , b ) 3 : 2 , c ) 1 : 3 , d ) 2 : 1 , e ) none of these
Rationale: "? required ratio = 6 ? 4 = 3 : 2 answer b"
Answer: b
Problem: in triangle pqr , the angle q = 90 degree , pq = 7 cm , qr = 8 cm . x is a variable point on pq . the line through x parallel to qr , intersects pr at y and the line through y , parallel to pq , intersects qr at z . find the least possible length of xz
Options: a ) 5.6 cm
b ) 2.4 cm
c ) 4.8 cm
d ) 2.16 cm
e ) 3.2 cm
Rationale: look at the diagram below : now , in case when qy is perpendicular to pr , two right triangles pqr and pqy are similar : qy : qp = qr : pr - - > qy : 7 = 8 : 10 - - > qy = 5.6 . answer : a .
Answer: a
Problem: in a family 15 people eat only vegetarian , 8 people eat only non veg . , 11 people eat both veg and non veg . . how many people eat veg in the family ?
Options: a ) 20 , b ) 11 , c ) 23 , d ) 26 , e ) 21
Rationale: "total people eat veg = only veg + both veg and non veg total = 15 + 11 = 26 answer = d"
Answer: d
Problem: two trains a and b are 125 m and 150 m long and are moving at one another at 54 km / hr and 36 km / hr respectively . arun is sitting on coach b 1 of train a . calculate the time taken by arun to completely cross train b .
Options: a ) 10 s , b ) 11 s , c ) 4 s , d ) 8 s , e ) 12 s
Rationale: "detailed solution speed of a = 54 ∗ 1000 / 60 ∗ 60 = 15 m / s speed of b = 36 ∗ 1000 / 60 ∗ 60 = 10 m / s relative speed = s 1 + s 2 = 15 + 10 m / s = 25 m / s the length that needs to be crossed = length of train b = 150 m . therefore time taken = 150 / 25 = 6 s . what is the time taken for trains to completely cross each other ? the length that needs to be crossed = 125 + 150 = 275 m . time taken = 275 / 25 = 11 s . correct answer b ."
Answer: b
Problem: together , 15 type a machines and 7 type b machines can complete a certain job in 4 hours . together 8 type b machines and 15 type c machines can complete the same job in 11 hours . how many hours t would it take one type a machine , one type b machine , and one type c machine working together to complete the job ( assuming constant rates for each machine ) ?
Options: a ) 22 hours , b ) 30 hours , c ) 44 hours , d ) 60 hours , e ) it can not be determined from the information above .
Rationale: "say the rates of machines a , b and c are a , b , and c , respectively . together 15 type a machines and 7 type b machines can complete a certain job in 4 hours - - > 15 a + 7 b = 1 / 4 ; together 8 type b machines and 15 type c machines can complete the same job in 11 hours - - > 8 b + 15 c = 1 / 11 . sum the above : 15 a + 15 b + 15 c = 1 / 4 + 1 / 11 = 15 / 44 - - > reduce by 15 : a + b + c = 1 / 44 - - > so , the combined rate of the three machines is 1 / 44 job / hour - - > time is reciprocal of the rate , thus machines a , b and c can do the t job in 44 hours . answer : c ."
Answer: c
Problem: a train running at a speed of 36 kmph crosses an electric pole in 12 seconds . in how much time will it cross a 320 m long platform ?
Options: a ) 44 min , b ) 55 min , c ) 47 min , d ) 67 min , e ) 45 min
Rationale: "a 44 min let the length of the train be x m . when a train crosses an electric pole , the distance covered is its own length . so , x = 12 * 36 * 5 / 18 m = 120 m . time taken to cross the platform = ( 120 + 320 ) / 36 * 5 / 18 = 44 min ."
Answer: a
Problem: the price of a book is increased from $ 300 to $ 450 . what is the % of increase in its price ?
Options: a ) 10 % , b ) 20 % , c ) 40 % , d ) 50 % , e ) 60 %
Rationale: "explanation : change in the price = rs 450 â € “ rs 300 = rs 150 percentage of increase = change in the price initial price * 100 . percentage increase in price = ( 150 300 ) * 100 = 50 % d"
Answer: d
Problem: a man can row downstream at 26 kmph and upstream at 22 kmph . find the speed of the man in still water and the speed of stream respectively ?
Options: a ) 24 , 2 , b ) 12 , 6 , c ) 15 , 3 , d ) 14 , 4 , e ) none of these
Rationale: "explanation : let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 26 - - - ( 1 ) and x - y = 22 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 48 = > x = 24 , y = 2 . answer : option a"
Answer: a
Problem: a train is walking at 6 / 7 of its usual speed , the train is 20 minutes too late . find its usual time to cover the journey .
Options: a ) 1 hour , b ) 30 min , c ) 3 hours 20 min , d ) 2 hours 30 min , e ) 2 hours
Rationale: new speed = 6 / 7 of the usual speed new time taken = 7 / 6 of the usual time taken so , ( 7 / 6 of the usual time ) - ( usual time ) = 20 min 1 / 6 of the usual time = 20 min usual time = 20 * 6 = 120 min = 2 hours correct option is e
Answer: e
Problem: what is the sum of all remainders obtained when the first 110 natural numbers are divided by 9 ?
Options: a ) 397 , b ) 401 , c ) 403 , d ) 405 , e ) 399
Rationale: "a positive integer can give only the following 9 remainders when divided by 9 : 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , and 0 . 1 divided by 9 gives the remainder of 1 ; 2 divided by 9 gives the remainder of 2 ; . . . 8 divided by 9 gives the remainder of 8 ; 9 divided by 9 gives the remainder of 0 . we ' ll have 11 such blocks , since 99 / 9 = 11 . the last will be : 91 divided by 9 gives the remainder of 1 ; 92 divided by 9 gives the remainder of 2 ; . . . 98 divided by 9 gives the remainder of 8 ; 99 divided by 9 gives the remainder of 0 . the last number , 100 , gives the remainder of 1 when divided by 9 , thus the sum of all remainders will be : 11 ( 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 0 ) + 1 = 403 . answer : c ."
Answer: c
Problem: by how much is 30 % of 80 greater than 4 / 5 th of 25 ?
Options: a ) 2 , b ) 4 , c ) 10 , d ) 15 , e ) 17
Rationale: "answer it is ( 30 x 80 ) / 100 - ( 4 x 25 ) / 5 = 24 - 20 = 4 correct option : b"
Answer: b
Problem: there are 4 people of different heights standing in order of increasing height . the difference is 2 inches between the first person and the second person , and also between the second person and the third person . the difference between the third person and the fourth person is 6 inches and the average height is 77 . how tall is the fourth person ?
Options: a ) 79 , b ) 81 , c ) 83 , d ) 85 , e ) 87
Rationale: "let x be the height of the first person . then the heights are x , x + 2 , x + 4 , and x + 10 . 4 x + 16 = 4 ( 77 ) = 308 x = 73 and the fourth person has a height of 73 + 10 = 83 inches the answer is c ."
Answer: c
Problem: t = { 2 , 3 , 4 , 5 } b = { 4 , 5 , 6 , 7 , 8 } two integers will be randomly selected from the sets above , one integer from set t and one integer from set b . what is the probability that the sum of the two integers will equal 9 ?
Options: a ) 0.15 , b ) 0.20 , c ) 0.25 , d ) 0.30 , e ) 0.33
Rationale: the total number of pairs t , b possible is 4 * 5 = 20 . out of these 20 pairs only 4 sum up to 9 : ( 2 , 7 ) ; ( 3 , 6 ) , ( 4 , 5 ) and ( 5 , 4 ) . the probability thus is 4 / 20 = 0.2 . answer : b .
Answer: b
Problem: a man whose speed is 7 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph , find his average speed for the total journey ?
Options: a ) 6.7 , b ) 4 , c ) 6 , d ) 9 , e ) 3
Rationale: "m = 7.0 s = 1.5 ds = 8.5 us = 5.5 as = ( 2 * 8.5 * 5.5 ) / 14 = 6.7 answer : a"
Answer: a
Problem: a sum was put at simple interest at a certain rate for 3 years . had it been put at 2 % higher rate , it would have fetched rs . 360 more . find the sum .
Options: a ) 3000 , b ) 6000 , c ) 2000 , d ) 4000 , e ) none of them
Rationale: "let sum = p and original rate = r . then , [ ( p * ( r + 2 ) * 3 ) / 100 ] – [ ( p * r * 3 ) / 100 ] = 360 . = 3 pr + 6 p - 3 pr = 36000  6 p = 36000  p = 6000 hence , sum = rs . 6000 . answer is b ."
Answer: b
Problem: 30 ^ 10 / 210 ^ 5 = ?
Options: a ) 6 ^ 5 , b ) 5 ^ 6 , c ) ( 30 / 7 ) ^ 5 , d ) 6 ^ 3 , e ) 15 ^ 3
Rationale: "30 ^ 10 / 210 ^ 5 = ? a . 6 ^ 5 b . 5 ^ 6 c . ( 30 / 7 ) ^ 5 d . 6 ^ 3 e . 15 ^ 3 - > 30 ^ 10 / 210 ^ 5 = ( 30 ^ 10 ) / ( 7 ^ 5 ) ( 30 ^ 5 ) = ( 30 ^ 5 ) / ( 7 ^ 5 ) = ( 30 / 7 ) ^ 5 . thus , c is the answer ."
Answer: c
Problem: the average salary of the employees in a office is rs . 120 / month . the avg salary of officers is rs . 420 and of non officers is rs 110 . if the no . of officers is 15 , then find the no of nonofficers in the office .
Options: a ) 400 , b ) 420 , c ) 430 , d ) 450 , e ) 510
Rationale: "let no . of non - officers be x 15 * 420 + x * 110 = ( x + 15 ) 120 x = 450 d"
Answer: d
Problem: if ( a - b - c + d = 13 ) and ( a + b - c - d = 9 ) , what is the value of ( b - d ) ^ 2 ?
Options: a ) 4 . , b ) 8 . , c ) 12 . , d ) 16 . , e ) 64 .
Rationale: "eq 1 : a - b - c + d = 13 eq 2 : a + b - c - d = 9 ( 1 ) subtract eq 1 from eq 2 a - b - c + d = 13 - a + b - c - d = 9 - - - - - - - - - - - - - - - - - - - - - - - - - 2 b + 2 d = 4 ( 2 ) simplify - b + d = 2 b - d = - 2 ( b - d ) ^ 2 = ( - 2 ) ^ 2 = 4 my answer : a"
Answer: a
Problem: in a certain state , the ratio of registered republicans to registered democrats is 3 to 2 , and every registered voter is either a republican or a democrat . if 70 percent of the republicans and 25 percent of the democrats are expected to vote for candidate x , and everyone else is expected to vote for candidate y , by what percent is candidate x expected to win the election ?
Options: a ) 2 % , b ) 4 % , c ) 8 % , d ) 10 % , e ) 15 %
Rationale: since we were expected to find a percentage figure - it thought that it might be easier to pick a ' smart number ' to represent the total number of voters ( republicans and democrats ) . therefore , i picked 100 ( as the total number of voters ) and thus 60 : 40 represents the number ratio of republicans : democrats . if 70 % of republicans ( which is ( 60 * 0.7 ) = 42 ) and 25 % of democrats ( 40 * 0.25 = 10 ) voted for candidate x , means that out of total of 100 voters ; 52 ( 42 + 10 ) voters voted for candidate x and 48 voted for candidate y . thus we can infer that candidate x is expected to win the election by 4 ( 52 - 48 ) votes . therefore candidate x is expected to win the election by ( 4 / 100 ) votes which is equivalent to 4 % . i think the answer is b .
Answer: b
Problem: a family pays $ 800 per year for an insurance plan that pays 85 percent of the first $ 1,000 in expenses and 100 percent of all medical expenses thereafter . in any given year , the total amount paid by the family will equal the amount paid by the plan when the family ' s medical expenses total .
Options: a ) $ 1,100 , b ) $ 1,200 , c ) $ 1,400 , d ) $ 1,800 , e ) $ 2,200
Rationale: "upfront payment for insurance plan = 800 $ family needs to pay 15 % of first 1000 $ in expense = 150 $ total amount paid by family when medical expenses are equal to or greater than 1000 $ = 800 + 150 = 950 $ total amount paid by insurance plan for first 1000 $ = 800 $ total amount paid by family will equal amount paid by plan when medical expense = 1100 $ ( since insurance plan will pay 100 % of amount that exceeds 950 $ ) answer a"
Answer: a
Problem: a vendor bought toffees at 6 for a dollar . how many for a dollar must he sell to gain 20 % ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 9 , e ) 8
Rationale: "c 5 c . p . of 6 toffees = $ 1 s . p . of 6 toffees = 120 % of $ 1 = $ 6 / 5 for $ 6 / 5 , toffees sold = 6 . for $ 1 . toffees sold = 6 * 5 / 6 = 5"
Answer: c
Problem: if each year the population of the country grows by 100 % , how many years will elapse before the population of the country doubles ?
Options: a ) 1 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "till year 2010 , population is 100 . year 2001 : population becomes 200 . . . . . . . . . . . . . 1 year elapsed answer : a"
Answer: a
Problem: positive integer y is 50 percent of 50 percent of positive integer x , and y percent of x equals 50 . what is the value of x ?
Options: a ) 50 , b ) 100 , c ) 200 , d ) 140 , e ) 2,000
Rationale: "y = 50 % of 50 % 0 f x = x / 4 and y / 100 of x = 50 y / 100 * 4 y = 50 y = 35 and x = 140 answer - d"
Answer: d
Problem: the number 149 can be written as the sum of the squares of 3 different positive integers . what is the sum of these 3 integers ?
Options: a ) 19 , b ) 16 , c ) 15 , d ) 14 , e ) 13
Rationale: "2 ^ 2 + 8 ^ 2 + 9 ^ 2 = 149 - - > 2 + 9 + 8 = 19 . a"
Answer: a
Problem: a cube of side 8 meter length is cut into small cubes of side 16 cm each . how many such small cubes can be obtained ?
Options: a ) 10780 , b ) 127600 , c ) 125000 , d ) 152000 , e ) 10000
Rationale: "along one edge , the number of small cubes that can be cut = 800 / 16 = 50 along each edge 50 cubes can be cut . ( along length , breadth and height ) . total number of small cubes that can be cut = 50 * 50 * 50 = 125000 answer : c"
Answer: c
Problem: in a group of 28 junior high school students , 7 take french , 10 take spanish , and 4 take both languages . the students taking both french and spanish are not counted with the 7 taking french or the 10 taking spanish . how many students are not taking either french or spanish ?
Options: a ) 7 , b ) 6 , c ) 8 , d ) 4 , e ) 3
Rationale: "a 7 seven students are not taking a language . add 7 + 10 + 4 to get 21 . then subtract 21 from the total students : 28 - 21 = 7 ."
Answer: a
Problem: on selling 17 balls at rs . 720 , there is a loss equal to the cost price of 5 balls . the cost price of a ball is
Options: a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60
Rationale: "( c . p . of 17 balls ) - ( s . p . of 17 balls ) = ( c . p . of 5 balls ) c . p . of 12 balls = s . p . of 17 balls = rs . 720 . c . p . of 1 ball = rs . 720 / 12 = rs . 60 . answer : e"
Answer: e
Problem: the ratio between the perimeter and the width of a rectangle is 5 : 1 . if the area of the rectangle is 384 square centimeters , what is the length of the rectangle in centimeters ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: "perimeter = 2 ( w + l ) = 5 w 3 w = 2 l w = 2 l / 3 wl = 384 2 l ^ 2 / 3 = 384 l ^ 2 = 576 l = 24 cm the answer is e ."
Answer: e
Problem: a hat company ships its hats , individually wrapped , in 8 - inch by 10 - inch by 12 - inch boxes . each hat is valued at $ 5.0 . if the company ’ s latest order required a truck with at least 288,000 cubic inches of storage space in which to ship the hats in their boxes , what was the minimum value of the order ?
Options: a ) $ 960 , b ) $ 1,500 , c ) $ 1,725 , d ) $ 2,050 , e ) $ 2,250
Rationale: "total volume is 288000 given lbh = 8 * 10 * 12 . the number of hats inside it = 288000 / 10 * 8 * 12 = 300 . price of each hat is 5 $ then total value is 300 * 5.0 = 1500 . imo option b is correct answer . ."
Answer: b
Problem: ramesh purchased a refrigerator for rs . 12500 after getting a discount of 20 % on the labelled price . he spent rs . 125 on transport and rs . 250 on installation . at what price should it be sold so that the profit earned would be 10 % if no discount was offered ?
Options: a ) 12880 , b ) 12789 , c ) 27108 , d ) 17600 , e ) 18291
Rationale: "explanation : price at which the tv set is bought = rs . 12,500 discount offered = 20 % marked price = 12500 * 100 / 80 = rs . 15625 the total amount spent on transport and installation = 125 + 250 = rs . 375 \ total price of tv set = 15625 + 375 = rs . 16000 the price at which the tv should be sold to get a profit of 10 % if no discount was offered = 16000 * 110 / 100 = rs . 17600"
Answer: d
Problem: 9873 + x = 13200 , then x is ?
Options: a ) 3327 , b ) 3237 , c ) 3337 , d ) 2337 , e ) none of these
Rationale: "answer x = 13200 - 9873 = 3327 option : a"
Answer: a
Problem: a library has an average of 510 visitors on sundays and 240 on other day . the average number of visitors in a month of 5 days starting with sunday is
Options: a ) 1215 , b ) 1314 , c ) 2900 , d ) 1710 , e ) 2750
Rationale: "explanation : as the month begin with sunday , so there will be five sundays in the month . so result will be : = ( 510 × 5 + 240 × 25 / 30 ) = ( 8550 / 5 ) = 1710 answer : option d"
Answer: d
Problem: in an election , candidate a got 70 % of the total valid votes . if 15 % of the total votes were declared invalid and the total numbers of votes is 560000 , find the number of valid vote polled in favor of candidate ?
Options: a ) 355600 , b ) 355800 , c ) 356500 , d ) 356800 , e ) 333200
Rationale: total number of invalid votes = 15 % of 560000 = 15 / 100 × 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 – 84000 = 476000 percentage of votes polled in favour of candidate a = 70 % therefore , the number of valid votes polled in favour of candidate a = 70 % of 476000 = 70 / 100 × 476000 = 33320000 / 100 = 333200 e )
Answer: e
Problem: a telephone company needs to create a set of 3 - digit area codes . the company is entitled to use only digits 2 , 4 and 5 , which can be repeated . if the product of the digits in the area code must be odd , how many different codes can be created ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 1 , e ) 30
Rationale: "total # of codes possible is 3 * 3 * 3 = 27 . oit of those 27 codes only the product of 555 will be odd , the remaining 26 will have either 2 or 4 in them , which ensures that their product will be even . therefore the number of codes where the product of the digits is even = ( total ) - ( restriction ) = 27 - 26 = 1 . answer : d ."
Answer: d
Problem: if a * b denotes the greatest common divisor of a and b , then ( ( 12 * 16 ) * ( 30 * 24 ) ) = ?
Options: a ) 24 , b ) 12 , c ) 6 , d ) 4 , e ) 2
Rationale: "the greatest common divisor of 12 and 16 is 4 . hence 12 * 16 = 4 ( note that * here denotes the function not multiplication ) . the greatest common divisor of 30 and 24 is 6 . hence 30 * 24 = 6 . hence ( ( 12 * 16 ) * ( 30 * 24 ) ) = 4 * 6 . the greatest common divisor of 4 and 6 is 2 . answer ; e ."
Answer: e
Problem: a certain number of horses and an equal number of men are going somewhere . half of the owners are on their horses ' back while the remaining ones are walking along leading their horses . if the number of legs walking on the ground is 60 , how many horses are there ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "legs 12 * 4 = 48 now half on their horses so remaining on the walk so 6 men 6 men has 12 legs so , 12 + 48 = 60 legs walking answer : b"
Answer: b
Problem: in a certain parking lot , 2 % of the cars are towed for parking illegally . however 90 % of the cars which are parked illegally are not towed . what percentage of cars in the parking lot are parked illegally ?
Options: a ) 10 % , b ) 12 % , c ) 16 % , d ) 18 % , e ) 20 %
Rationale: "let x be the number of cars and let y be the number of cars parked illegally . 2 % * x = 10 % * y y / x = 1 / 5 = 20 % the answer is e ."
Answer: e
Problem: a certain sky blue paint contains 10 percent blue pigment and 90 percent red pigment by weight . a certain green paint contains 70 percent blue pigment and 30 percent yellow pigment . when these paints are mixed to produce a brown paint , the brown paint contains 40 percent blue pigment . if the brown paint weighs 10 grams , then the red pigment contributes how many grams of that weight ?
Options: a ) 1.5 , b ) 2.5 , c ) 3.5 , d ) 4.5 , e ) 5.5
Rationale: 10 grams of combined mixture and 40 % blue pigment means that the mixtures were mixed 50 % each . thus 5 grams a piece . out of the 5 grams of the dark blue paint , 60 % is red . therefore , 5 * . 9 = 4.5 grams of red pigment
Answer: d
Problem: alok ordered 16 chapatis , 5 plates of rice , 7 plates of mixed vegetable and 6 ice - cream cups . the cost of each chapati is rs . 6 , that of each plate of rice is rs . 45 and that of mixed vegetable is rs . 70 . the amount that alok paid the cashier was rs . 985 . find the cost of each ice - cream cup ?
Options: a ) 25 , b ) 76 , c ) 29 , d ) 12 , e ) 20
Rationale: explanation : let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 985 96 + 225 + 490 + 6 x = 985 6 x = 174 = > x = 29 . answer : c
Answer: c
Problem: excluding stoppages , the speed of a bus is 65 kmph and including stoppages , it is 48 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 70 min , b ) 15 min , c ) 20.4 min , d ) 15.6 min , e ) 40 min
Rationale: "d 15.6 min due to stoppages , it covers 17 km less . time taken to cover 17 km = ( 17 / 65 x 60 ) min = 15.6 min"
Answer: d
Problem: a and b ’ s salaries together amount to rs . 2,000 . a spends 95 % of his salary and b spends 85 % of his . if now their savings are the same , what is b ’ s salary ?
Options: a ) 777 , b ) 500 , c ) 789 , d ) 776 , e ) 881
Rationale: "( 5 / 100 ) a = ( 15 / 100 ) b a = 3 b a + b = 2000 4 b = 2000 = > b = 500 answer b"
Answer: b
Problem: the inner circumference of a circular race track , 14 m wide is 440 m . find the radius of the outer circle .
Options: a ) 84 , b ) 12 , c ) 67 , d ) 28 , e ) 21
Rationale: "explanation : let inner radius be r meters . { \ color { black } then , 2 \ pi r = 440 \ rightarrow r = 440 \ times \ frac { 7 } { 22 } \ times \ frac { 1 } { 2 } = 70 m } radius of outer circle = 70 + 14 = 84 m answer : a ) 84 m"
Answer: a
Problem: the length of the rectangular field is double its width . inside the field there is square shaped pond 8 m long . if the area of the pond is 1 / 8 of the area of the field . what is the length of the field ?
Options: a ) 73 , b ) 32 , c ) 34 , d ) 43 , e ) 42
Rationale: "explanation : a / 8 = 8 * 8 = > a = 8 * 8 * 8 x * 2 x = 8 * 8 * 8 x = 16 = > 2 x = 32 answer : option b"
Answer: b
Problem: two goods train each 500 m long , are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one .
Options: a ) 12 sec , b ) 24 sec , c ) 48 sec , d ) 60 sec , e ) 65 sec
Rationale: "explanation : relative speed = = ( 45 + 30 ) km / hr = 75 x 5 / 18 m / sec = 125 / 6 m / sec we have to find the time taken by the slower train to pass the driver of the faster train and not the complete train . so , distance covered = length of the slower train . therefore , distance covered = 500 m . required time = 500 x 6 / 125 = 24 sec . answer is b"
Answer: b
Problem: the age of somu is one - third his father ' s . 5 years back he was one - fifth of his father ' s age . what is his persent age ?
Options: a ) 11 , b ) 13 , c ) 14 , d ) 12 , e ) 10
Rationale: "explanation : let somu ' s age be x and that of his father be 3 x . so , x - 5 = 3 x - 5 / 5 = x = 10 answer : option e"
Answer: e
Problem: a charitable association sold an average of 66 raffle tickets per member . among the female members , the average was 70 raffle tickets . the male to female ratio of the association is 1 : 2 . what was the average number w of tickets sold by the male members of the association
Options: a ) 50 , b ) 56 , c ) 58 , d ) 62 , e ) 66
Rationale: "given that , total average w sold is 66 , male / female = 1 / 2 and female average is 70 . average of male members isx . ( 70 * f + x * m ) / ( m + f ) = 66 - > solving this equation after substituting 2 m = f , x = 58 . ans c ."
Answer: c
Problem: amit and ananthu can do a work in 15 days and 90 days respectively . amit started the work and left after 3 days . ananthu took over and completed the work . in how many days was the total work completed ?
Options: a ) 68 days , b ) 70 days , c ) 73 days , d ) 75 days , e ) 77 days
Rationale: "amit ’ s one day ’ s work = 1 / 15 amit ’ s 3 day ’ s work = 1 / 15 * 3 = 1 / 5 work left = 1 - 1 / 5 = 4 / 5 ananthu ’ s one day ’ s work = 1 / 90 ananthu can do work in = 4 / 5 * 90 = 72 days so total days = 72 + 3 = 75 days answer : d"
Answer: d
Problem: city x has a population 6 times as great as the population of city y , which has a population twice as great as the population of city z . what is the ratio of the population of city x to the population of city z ?
Options: a ) 1 : 8 , b ) 1 : 4 , c ) 2 : 1 , d ) 4 : 1 , e ) 12 : 1
Rationale: "x = 6 y , y = 2 * z x : y , y : z 6 : 1 , 2 : 1 12 : 2 , 2 : 1 so , x : z = 12 : 1 ( e )"
Answer: e
Problem: a and b can do a work in 2 days , b and c in 4 days and c and a in 6 days . in how many days will the work be completed , if all three of them work together ?
Options: a ) 10 / 12 , b ) 16 / 28 , c ) 24 / 11 , d ) 42 / 16 , e ) 18 / 12
Rationale: one day work of a and b = 1 / 2 one day work of b and c = 1 / 4 one day work of c and a = 1 / 6 2 ( a + b + c ) = 1 / 2 + 1 / 4 + 1 / 6 . 2 ( a + b + c ) = 11 / 12 ( a + b + c ) = 11 / 24 number of days required = 24 / 11 days . answer : c
Answer: c
Problem: what is the sum of all the multiples of 7 between 30 and 100 ?
Options: a ) 692 , b ) 700 , c ) 677 , d ) 654 , e ) 665
Rationale: "you first have to know all the multiples of 7 between 30 and 100 . they are 35 , 42 , 49 , 56 , 63 , 70 , 77 , 84 , 91 , and 98 . if you add all these numbers together , you get 665 . final answer : e"
Answer: e
Problem: if { x } is the product of all even integers from 1 to x inclusive , what is the greatest prime factor of { 20 } + { 24 } ?
Options: a ) 23 , b ) 25 , c ) 11 , d ) 5 , e ) 2
Rationale: "soln : { 24 } + { 20 } = 24 * { 20 } + { 20 } = 25 * { 20 } answer : b"
Answer: b
Problem: the maximum number of students among them 1001 pens and 910 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils ?
Options: a ) 87 , b ) 91 , c ) 100 , d ) 96 , e ) 101
Rationale: "number of pens = 1001 number of pencils = 910 required number of students = h . c . f . of 1001 and 910 = 91 answer is b"
Answer: b
Problem: how many even integers n , such that 20 < = n < = 250 are of the form 3 k + 4 , where k is any natural number ?
Options: a ) 33 , b ) 36 , c ) 39 , d ) 42 , e ) 45
Rationale: "the first number is 22 = 16 + 6 ( 1 ) . we can continue adding 6 to make a list : 22 , 28 , 34 , . . . the last number is 250 = 16 + 6 ( 39 ) there are 39 numbers in the list . the answer is c ."
Answer: c
Problem: a trader sells 85 meters of cloth for $ 8925 at the profit of $ 15 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) $ 69 , b ) $ 78 , c ) $ 90 , d ) $ 86 , e ) $ 77
Rationale: c $ 90 sp of 1 m of cloth = 8925 / 85 = $ 105 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = $ 105 - $ 15 = $ 90 .
Answer: c
Problem: a fruit - salad mixture consists of apples , peaches , and grapes in the ratio 12 : 8 : 7 , respectively , by weight . if 54 pounds of the mixture is prepared , the mixture includes how many more pounds of apples than grapes ?
Options: a ) 15 , b ) 10 , c ) 9 , d ) 6 , e ) 4
Rationale: "we can first set up our ratio using variable multipliers . we are given that a fruit - salad mixture consists of apples , peaches , and grapes , in the ratio of 6 : 5 : 2 , respectively , by weight . thus , we can say : apples : peaches : grapes = 12 x : 8 x : 7 x we are given that 54 pounds of the mixture is prepared so we can set up the following question and determine a value for x : 12 x + 8 x + 7 x = 54 27 x = 54 x = 2 now we can determine the number of pounds of apples and of grapes . pounds of grapes = ( 7 ) ( 2 ) = 14 pounds of apples = ( 12 ) ( 2 ) = 24 thus we know that there are 24 - 14 = 10 more pounds of apples than grapes . answer is b ."
Answer: b
Problem: of the six - digit positive integers that have no digits equal to zero , how many have two digits that are equal to each other and the remaining digit different from the other two ?
Options: a ) 2443200 , b ) 3643200 , c ) 5443200 , d ) 1443200 , e ) 2163200
Rationale: "of the six - digit positive integers that have no digits equal to zero , how many have two digits that are equal to each other and the remaining digit different from the other two ? a . 24 b . 36 c . 72 d . 144 e . 216 choosing the digit for p - 9 ways ; choosing the digit for q - 8 ways ; choosing the digit for r - 7 ways ; choosing the digit for s - 6 ways ; choosing the digit for t - 5 ways ; # of permutations of 3 digits in ppqrst - 6 ! / 2 ! total : 9 * 8 * 7 * 6 * 5 * 6 ! / 2 ! = 5443200 . answer : c ."
Answer: c
Problem: two employees x and y are paid a total of rs . 330 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?
Options: a ) s . 150 , b ) s . 200 , c ) s . 250 , d ) s . 350 , e ) s . 400
Rationale: "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 330 but x = 120 % of y = 120 y / 100 = 12 y / 10 â ˆ ´ 12 y / 10 + y = 330 â ‡ ’ y [ 12 / 10 + 1 ] = 330 â ‡ ’ 22 y / 10 = 330 â ‡ ’ 22 y = 3300 â ‡ ’ y = 3300 / 22 = 300 / 2 = rs . 150 a )"
Answer: a
Problem: if the price of a certain computer increased 30 percent from d dollars to 338 dollars , then 2 d =
Options: a ) 540 , b ) 520 , c ) 619 , d ) 649 , e ) 700
Rationale: "before price increase price = d after 30 % price increase price = d + ( 30 / 100 ) * d = 1.3 d = 338 ( given ) i . e . d = 338 / 1.3 = $ 260 i . e . 2 d = 2 * 260 = 520 answer : option b"
Answer: b
Problem: simple interest on a certain sum of money for 2 years at 16 % per annum is one fourth the compound interest on rs . 4000 for 2 years at 8 % per annum . the sum placed on simple interest is
Options: a ) rs . 4000 , b ) rs . 665.6 , c ) rs . 520 , d ) rs . 166.4 , e ) none
Rationale: "solution c . i . = rs [ 4000 x ( 1 + 8 / 100 ) â ² - 4000 ] rs . ( 4000 x 108 / 100 x 108 / 100 - 4000 ) = rs . 665.6 . sum = rs . [ 166.4 x 100 / 2 x 16 ] = rs . 520 . answer c"
Answer: c
Problem: each digit 1 through 5 is used exactly once to create a 5 - digit integer . if the 1 and the 5 can not be adjacent digits in the integer , how many 5 - digit integers are possible ?
Options: a ) 48 , b ) 66 , c ) 76 , d ) 78 , e ) none of these
Rationale: "number of arrangements using 5 distinct digits = 5 ! number of arrangements in which 1 and 5 are adjacent - consider 1 and 5 together as one group . now you have 4 numbers / groups to arrange which can be done in 4 ! ways . in each of these arrangements , 1 and 5 can be arranged as 15 or 51 . number of arrangements in which 3 and 4 are not adjacent = 5 ! - 2 * 4 ! = 72 answer : e"
Answer: e
Problem: a pupil ' s marks were wrongly entered as 79 instead of 45 . due to that the average marks for the class got increased by half . the number of pupils in the class is :
Options: a ) 30 , b ) 80 , c ) 20 , d ) 68 , e ) 26
Rationale: "let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 . x / 2 = ( 79 - 45 ) = > x / 2 = 34 = > x = 68 . answer : d"
Answer: d
Problem: in a can , there is a mixture of milk and water in the ratio 2 : 5 . if it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 4 : 5 . find the capacity of the can ?
Options: a ) 40 , b ) 44 , c ) 48 , d ) 50 , e ) 8
Rationale: "let the capacity of the can be t litres . quantity of milk in the mixture before adding milk = 2 / 7 ( t - 8 ) after adding milk , quantity of milk in the mixture = 4 / 9 t . 4 t / 9 - 8 = 2 / 7 ( t - 8 ) 2 t = 72 - 56 = > t = 8 . answer : e"
Answer: e
Problem: 90 % of the population of a village is 45000 . the total population of the village is ?
Options: a ) 26799 , b ) 24000 , c ) 50000 , d ) 29973 , e ) 12312
Rationale: "x * ( 90 / 100 ) = 45000 x = 500 * 100 x = 50000 answer : c"
Answer: c
Problem: total 52 matches are conducted in knockout match type . how many players will be participated in that tournament ?
Options: a ) 60 , b ) 51 , c ) 53 , d ) 56 , e ) 50
Rationale: "51 players answer : b"
Answer: b
Problem: the ratio between the number of sheep and the number of horses at the stewart farm is 1 to 7 , if each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day , what is the number of sheep in the farm ?
Options: a ) 18 , b ) 28 , c ) 32 , d ) 56 , e ) 8
Rationale: "let the number of sheeps and horses be 1 x and 7 x . now total number of horses = total consumption of horse food / consumption per horse = 12880 / 230 = 56 , which is equal to 7 x . = > x = 8 sheeps = 1 x = 1 * 8 = 8 . hence e"
Answer: e
Problem: there are 12 teams in a soccer league and each team plays each of the other teams once . how many games will be played in total ?
Options: a ) 58 , b ) 62 , c ) 66 , d ) 70 , e ) 74
Rationale: 12 c 2 = 66 the answer is c .
Answer: c
Problem: the length of a rectangle is increased by 45 % and its breadth is decreased by 20 % . what is the effect on its area ?
Options: a ) 1288 , b ) 1299 , c ) 1000 , d ) 10000 , e ) 11600
Rationale: "100 * 100 = 10000 145 * 80 = 11600 answer : e"
Answer: e
Problem: michael cashed a check for $ 1270 and received only $ 10 and $ 50 bills in return . during the course of a day , he used 15 bills and then lost the rest of the money . if the number of $ 10 bills used was either one more or one less than the number of $ 50 bills used , what is the minimum possible amount of money that was lost ?
Options: a ) $ 830 , b ) $ 800 , c ) $ 770 , d ) $ 730 , e ) $ 700
Rationale: 1 . 15 bills spent 2 . number of $ 10 bills is one more or one less than number of $ 50 bills . so , 2 choices 1 . 7 * 10 + 8 * 50 = $ 470 2 . 8 * 10 + 7 * 50 = $ 430 least money lost implies most money spent . i . e $ 470 therefore , lost money = 1270 - 470 = 800 . answer b
Answer: b
Problem: a man ' s regular pay is $ 3 per hour up to 40 hours . overtime is twice the payment for regular time . if he was paid $ 180 , how many hours overtime did he work ?
Options: a ) 8 , b ) 5 , c ) 9 , d ) 6 , e ) 10
Rationale: "at $ 3 per hour up to 40 hours , regular pay = $ 3 x 40 = $ 120 if total pay = $ 168 , overtime pay = $ 180 - $ 120 = $ 60 overtime rate ( twice regular ) = 2 x $ 3 = $ 6 per hour = > number of overtime hours = $ 60 / $ 6 = 10 ans is e"
Answer: e
Problem: if a farmer sells 5 of his goats , his stock of feed will last for 4 more days than planned , but if he buys 10 more goats , he will run out of feed 3 days earlier than planned . if no goats are sold or bought , the farmer will be exactly on schedule . how many goats does the farmer have ?
Options: a ) 12 , b ) 20 , c ) 48 , d ) 55 , e ) 60
Rationale: say farmer has n goat and he is good for d days . : - we have 3 equations given in question : - ( n - 5 ) * d + 4 = ( n + 10 ) * ( d - 3 ) = n * d solving these : ( you can solve 1 st and 3 rd and 2 nd and 3 rd together ) we get : 10 d - 3 n = 30 4 n - 5 d = 20 = > n = 20 ans b it is !
Answer: b
Problem: cole drove from home to work at an average speed of 30 kmh . he then returned home at an average speed of 90 kmh . if the round trip took a total of 2 hours , how many minutes did it take cole to drive to work ?
Options: a ) 66 , b ) 70 , c ) 72 , d ) 75 , e ) 90
Rationale: "let the distance one way be x time from home to work = x / 30 time from work to home = x / 90 total time = 2 hrs ( x / 30 ) + ( x / 90 ) = 2 solving for x , we get x = 45 time from home to work in minutes = ( 45 ) * 60 / 30 = 90 minutes ans = e"
Answer: e
Problem: when tom works alone he chops 3 lb . salad in 2 minutes , and when tammy works alone she chops 2 lb . salad in 3 minutes . they start working together , and after some time finish chopping 65 lb . of salad . of those 80 lb . , the salad quantity chopped by tammy is what percent lesser than the quantifying chopped by tom ?
Options: a ) 44 % , b ) 100 % , c ) 15 % , d ) 125 % , e ) 400 %
Rationale: "tom chops 4 lbs in 6 minutes tammy chops 9 lbs in 6 minutes so in the same amount of time , tammy chops 125 % more than tom , since 9 is 125 % greater than 4 . so 125 % is the answer . note that the actual time does n ' t matter . if you multiply the time each work by x , you ' ll multiply the work each does by x , and 9 x is still 125 % greater than 4 x . 125 % lesser than tom ans : d"
Answer: d
Problem: what is the smallest integer y for which 27 ^ y > 3 ^ 24 ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 12
Rationale: "27 ^ y > 3 ^ 24 converting into the same bases : 27 ^ y > 27 ^ 8 therefore for the equation to hold true , y > 8 or y = 9 option c"
Answer: c
Problem: a and b together can do a piece of work in 4 days . if a alone can do the same work in 20 days , then b alone can do the same work in ?
Options: a ) 0.35 days , b ) 0.45 days , c ) 0.55 days , d ) 0.25 days , e ) 0.2 days
Rationale: "b = 1 / 4 – 1 / 20 = 0.2 days answer : e"
Answer: e
Problem: a bell curve ( normal distribution ) has a mean of − 1 and a standard deviation of 1 / 8 . how many integer values z are within 3 standard deviations of the mean ?
Options: a ) 0 , b ) 1 , c ) 3 , d ) 6 , e ) 7
Rationale: got the question correctly - - the second item - - [ highlight ] bthe list of elements in the set is required . [ / highlight ] is not required . with the new information , there is only one integer value ( - 1 ) that is between ( - 1.375 , - 0.625 ) i . e . , falls within the three 3 sd range . b
Answer: b
Problem: a man ' s speed with the current is 15 km / hr and the speed of the current is 2.8 km / hr . the man ' s speed against the current is ?
Options: a ) 9.4 , b ) 20 , c ) 50 , d ) 30 , e ) 40
Rationale: "man ' s speed with the current = 15 km / hr = > speed of the man + speed of the current = 15 km / hr speed of the current is 2.8 km / hr hence , speed of the man = 15 - 2.8 = 12.2 km / hr man ' s speed against the current = speed of the man - speed of the current = 12.2 - 2.8 = 9.4 km / hr answer is a ."
Answer: a
Problem: 1 / 3 + 1 / 2 - 5 / 6 + 1 / 5 + 1 / 4 - 9 / 20 - 2 / 15 =
Options: a ) 0 , b ) 2 / 15 , c ) 2 / 5 , d ) 9 / 20 , e ) 5 / 6
Rationale: "we need to determine the result of 1 / 3 + 1 / 2 - 5 / 6 + 1 / 5 + 1 / 4 - 9 / 20 let ’ s add the given fractions in two groups . in the group of the first three fractions , notice that 1 / 3 and 1 / 2 share a common denominator of 6 with 5 / 6 . 1 / 2 + 1 / 3 = 3 / 6 + 2 / 6 = 5 / 6 thus , 5 / 6 – 5 / 6 = 0 looking at the 2 nd group of the fractions ( 1 / 5 , 1 / 4 , and 9 / 20 ) , notice that 1 / 5 and 1 / 4 share a common denominator of 20 with 9 / 20 . 1 / 5 + 1 / 4 = 4 / 20 + 5 / 20 = 9 / 20 thus , 9 / 20 – 9 / 20 = 0 . thus , the result of 1 / 3 + 1 / 2 – 5 / 6 + 1 / 5 + 1 / 4 – 9 / 20 is 2 / 15 . answer : b"
Answer: b
Problem: a river 2 m deep and 45 m wide is flowing at the rate of 3 kmph the amount of water that runs into the sea per minute is ?
Options: a ) 4500 , b ) 2678 , c ) 2689 , d ) 2761 , e ) 2882
Rationale: "( 3000 * 2 * 5 ) / 60 = 4500 m 3 answer : a"
Answer: a
Problem: in a coconut grove , ( x + 2 ) trees yield 60 nuts per year , x trees yield 120 nuts per year and ( x – 2 ) trees yield 180 nuts per year . if the average yield per year per tree be 100 , find x .
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "( x + 2 ) × 60 + x × 120 + ( x − 2 ) × 180 / ( x + 2 ) + x + ( x − 2 ) = 100 ⇒ 360 x − 240 / 3 x = 100 ⇒ 60 x = 240 ⇒ x = 4 answer e"
Answer: e
Problem: tourist purchased a total of 30 travelers checks in $ 50 and $ 100 denominations . the total worth of the travelers checks is $ 1800 . how many checks of $ 50 denominations can he spend so that average amount ( arithmetic mean ) of the remaining travelers checks is $ 70 ?
Options: a ) 4 , b ) 12 , c ) 15 , d ) 20 , e ) 24
Rationale: "you could set - up a quick table and brute force the answer . a 4 * 50 200 1800 - 200 1600 26 61.54 b 12 * 50 600 1800 - 600 1200 18 66.67 c 15 * 50 750 1800 - 750 1050 15 70.00 d 20 * 50 1000 1800 - 1000 800 10 80.00 e 24 * 50 1200 1800 - 1200 600 6 100.00 answer is c"
Answer: c
Problem: in a graduating class , 40 percent of the students are male . in this class , 50 percent of the male students and 40 percent of the female students are 25 years old or older . if one student in the class is randomly selected , approximately what is the probability that he or she will be less than 25 years old ?
Options: a ) 0.44 , b ) 0.5 , c ) 0.56 , d ) 0.62 , e ) 0.68
Rationale: "let x be the total number of students . the number students who are younger than 25 is 0.5 * 0.4 x + 0.6 * 0.6 x = 0.56 x the answer is c ."
Answer: c
Problem: what is the remainder when 14,451 × 15,654 × 16,783 is divided by 5 ?
Options: a ) 1 , b ) 3 , c ) 2 , d ) 4 , e ) 5
Rationale: "only the unit ' s digit of the product will decide the remainder when divided by 5 . hence , 1 * 4 * 3 = will give units digit as 2 so , whatever be the number , if it ends in 2 , the remainder after dividing with 5 will be 2 . option c"
Answer: c
Problem: up to 20 , how many no . are odd and prime both ?
Options: a ) 9 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: we have to calculate it manually . odd 1,3 , 5,7 , 9,11 , 13,15 , 17,19 prime 2,3 , 5,7 , 11,13 , 17,19 common 3 , 5,7 , 11,13 , 17,19 total no . 7 answer d
Answer: d
Problem: the area of sector of a circle whose radius is 15 metro and whose angle at the center is 42 â ° is ?
Options: a ) 52.6 , b ) 52.9 , c ) 52.8 , d ) 52.1 , e ) 82.5
Rationale: "42 / 360 * 22 / 7 * 15 * 15 = 82.5 m 2 answer : e"
Answer: e