regisss/math_qa huggingface dataset:
Problem: the average weight of a group of boys is 30 kg . after a boy of weight 37 kg joins the group , the average weight of the group goes up by 1.00001 kg . find the number of boys in the group originally ?
Options: a ) a ) 4 , b ) b ) 8 , c ) c ) 6 , d ) d ) 2 , e ) e ) 1
Rationale: "let the number off boys in the group originally be x . total weight of the boys = 30 x after the boy weighing 37 kg joins the group , total weight of boys = 30 x + 37 so 30 x + 37 = 31 ( x + 1 ) = > x = 6 . answer : c"
Answer: c
Problem: of 55 players on a cricket team , 37 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?
Options: a ) 49 , b ) 55 , c ) 59 , d ) 71 , e ) 92
Rationale: "total = 55 thrower = 37 rest = 55 - 37 = 18 left handed = 18 / 3 = 6 right handed = 12 if all thrower are right handed then total right handed is 37 + 12 = 49 so a . 49 is the right answer"
Answer: a
Problem: a person want to give his money of $ 900 to his 3 children a , b , c in the ratio 2 : 3 : 4 . what is the b ' s share ?
Options: a ) $ 400 , b ) $ 300 , c ) $ 500 , d ) $ 180 , e ) $ 200
Rationale: "b ' s share = 900 * 3 / 9 = $ 300 answer is b"
Answer: b
Problem: a can do a piece of work in 21 days and b in 28 days . together they started the work and b left after 4 days . in how many days can a alone do the remaining work ?
Options: a ) 22 , b ) 88 , c ) 27 , d ) 14 , e ) 99
Rationale: "let a worked for x days . x / 21 + 4 / 28 = 1 = > x / 21 = 6 / 7 = > x = 18 a worked for 18 days . so , a can complete the remaining work in 18 - 4 = 14 days . answer : d"
Answer: d
Problem: if a and b are the two values of t that satisfy the equation t ^ 2 â € “ 12 t + 20 = 0 , with a > b , what is the value of a â € “ b ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: factor the left side of the equation : t ^ 2 â € “ 12 t + 20 = 0 ( t â € “ 2 ) ( t â € “ 10 ) = 0 t = 2 , t = 10 thus , a = 10 and b = 2 . so a â € “ b = 10 â € “ 2 = 8 . the answer is d .
Answer: d
Problem: the average ( arithmetic mean ) of 4 different integers is 74 . if the largest integer is 90 , what is the least possible value of the smallest integer ?
Options: a ) 1 , b ) 19 , c ) 29 , d ) 30 , e ) 33
Rationale: "total of integers = 74 * 4 = 296 lowest of the least possible integer is when the middle 2 intergers are at the maximum or equal to the highest possible integer . but all integers are distinct . so if the largest integer is 90 , then the middle 2 will be 88 and 89 lowest of least possible integer = 296 - ( 90 + 89 + 88 ) = 296 - 267 = 29 answer : c"
Answer: c
Problem: how many numbers from 2 to 11 are exactly divisible by 2 ?
Options: a ) a ) 2 , b ) b ) 3 , c ) c ) 5 , d ) d ) 7 , e ) e ) 8
Rationale: "2 / 2 = 1 and 11 / 2 = 5 5 - 1 = 4 4 + 1 = 5 numbers . answer : c"
Answer: c
Problem: if w is the set of all the integers between 35 and 64 , inclusive , that are either multiples of 3 or multiples of 2 or multiples of both , then w contains how many numbers ?
Options: a ) 18 , b ) 19 , c ) 61 , d ) 31 , e ) 11
Rationale: "official solution : number of multiples of 3 step 1 . subtract the extreme multiples of 3 within the range ( the greatest is 63 , the smallest is 36 ) : 63 - 36 = 27 step 2 . divide by 3 : 27 / 3 = 9 step 3 . add 1 : 9 + 1 = 10 . so there are 10 multiples of 3 within the range : examples are 51 , 54 , 57 , 60 , etc . number of multiples of 2 step 1 . subtract the extreme multiples of 2 within the range ( the greatest is 64 , the smallest is 36 ) : 64 - 36 = 28 step 2 . divide by 2 : 28 / 2 = 14 step 3 . add 1 : 14 + 1 = 15 . so there are 15 multiples of 2 within the range : examples are 50 , 52 , 54 , 56 , 58 , 60 etc . add the 10 multiples of 3 and the 15 multiples of 2 : 10 + 15 = 25 . however , by adding the multiples of 2 and the multiples of 3 , we are effectively counting several numbers twice : for example , 54 and 60 are parts of both the lists above . so we ca n ' t just take 10 + 15 = 25 . find the number of multiples of 6 ( which are the double counted , as 6 is divisible by both 2 and 3 ) , and subtract it from 25 : step 1 . subtract the extreme multiples of 6 within the range ( the greatest is 72 , the smallest is 54 ) : 60 - 30 = 30 step 2 . divide by 6 : 30 / 6 = 5 step 3 . add 1 : 5 + 1 = 6 . so there are 6 multiples of 6 within the range : we counted 6 numbers twice . subtract the 6 multiples of 6 from the sum of the multiples of 2 and 3 : = 10 + 15 - 6 = 25 - 6 = 19 therefore , the final number of multiples of 2 , 3 or 6 is 19 . hence , this is the correct answer . ( b )"
Answer: b
Problem: 4 milkmen rented a pasture . a grazed 24 cows for 3 months ; b 10 for 5 months ; c 35 cows for 4 months and d 21 cows for 3 months . if a ' s share of rent is rs . 1440 , find the total rent of the field .
Options: a ) 6500 , b ) 3550 , c ) 4250 , d ) 2250 , e ) 3250
Rationale: ratio of shares of a , b , c , d = ( 24 x 3 ) : ( 10 x 5 ) : ( 35 x 4 ) : ( 21 x 3 ) = 72 : 50 : 140 : 63 . let total rent be rs . x . then , a ’ s share = rs . ( 72 x ) / 325 ( 72 x ) / 325 = 1440 = x = ( 1440 x 325 ) / 72 = 6500 hence , total rent of the field is rs . 6500 . answer is a .
Answer: a
Problem: how many multiples of 4 are there between 12 and 108 , inclusive ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: "the multiples of 4 are from 4 * 3 up to 4 * 27 . 27 - 3 + 1 = 25 . the answer is e ."
Answer: e
Problem: 123 : 36 : : 221 : ?
Options: a ) 52 , b ) 69 , c ) 72 , d ) 25 , e ) 32
Rationale: "( 1 + 2 + 3 ) ^ 2 = 36 ( 2 + 2 + 1 ) ^ 2 = 25 answer : d"
Answer: d
Problem: an inspector rejects 0.02 % of the meters as defective . how many will he examine to reject 2 ?
Options: a ) a ) 1500 , b ) b ) 10000 , c ) c ) 2500 , d ) d ) 3000 , e ) e ) 3100
Rationale: "let the number of meters to be examined be x then , 0.02 % of x = 2 ( 2 / 100 ) * ( ( 1 / 100 ) * x = 2 x = 10000 answer is b"
Answer: b
Problem: if a - b = 10 and a ^ 2 + b ^ 2 = 150 , find the value of ab
Options: a ) 10 , b ) 12 , c ) 25 , d ) 18 , e ) 19
Rationale: "2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 150 - 100 = 50 = > ab = 25 answer : c"
Answer: c
Problem: eddy and freddy start simultaneously from city a and they travel to city b and city c respectively . eddy takes 3 hours and freddy takes 4 hours to complete the journey . if the distance between city a and city b is 900 kms and city a and city c is 300 kms . what is the ratio of their average speed of travel ? ( eddy : freddy )
Options: a ) 8 / 3 , b ) 3 / 8 , c ) 8 / 5 , d ) 4 / 1 , e ) 5 / 3
Rationale: "distance traveled by eddy = 900 km time taken by eddy = 3 hours average speed of eddy = 900 / 3 = 300 km / hour distance traveled by freddy = 300 km time taken by freddy = 4 hours average speed of freddy = 300 / 4 = 75 km / hour ratio of average speed of eddy to freddy = 300 / 75 = 4 / 1 answer d"
Answer: d
Problem: if 40 honey bees make 40 grams of honey in 40 days , then 1 honey bee will make 1 gram of honey in how many days ?
Options: a ) 1 , b ) 3.5 , c ) 40 , d ) 49 , e ) 30
Rationale: "explanation : let the required number days be x . less honey bees , more days ( indirect proportion ) less honey , less days ( direct proportion ) honey bees 1 : 40 : : 40 : x honey 40 : 1 = > 1 x 40 x x = 40 x 1 x 40 = > x = 40 . answer : c"
Answer: c
Problem: a dog takes 5 leaps for every 8 leaps of a hare . if one leap of the dog is equal to 5 leaps of the hare , the ratio of the speed of the dog to that of the hare is :
Options: a ) 25 : 10 , b ) 25 : 8 , c ) 25 : 9 , d ) 8 : 25 , e ) 24 : 8
Rationale: "explanation : dog : hare = ( 5 * 5 ) leaps of hare : 8 leaps of hare = 25 : 8 answer : b"
Answer: b
Problem: of the families in city x in 2001 , 25 percent owned a personal computer . the number of families in city x owning a computer in 2008 was 15 percent greater than it was in 2001 , and the total number of families in city x was 6 percent greater in 2008 than it was in 2001 . what percent of the families in city x owned a personal computer in 2008 ?
Options: a ) 27.12 % , b ) 23.12 % , c ) 25.55 % , d ) 31.22 % , e ) 56.22 %
Rationale: "say a 100 families existed in 1994 then the number of families owning a computer in 1994 - 25 number of families owning computer in 1998 = 25 * 115 / 100 = 28.75 number of families in 1998 = 106 the percentage = 28.75 / 106 * 100 = 27.12 % . answer : a"
Answer: a
Problem: the mass of 1 cubic meter of a substance is 100 kg under certain conditions . what is the volume in cubic centimeters of 1 gram of this substance under these conditions ? ( 1 kg = 1,000 grams and 1 cubic meter = 1 , 000,000 cubic centimeters )
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "100 kg - 1 cubic meter ; 100,000 g - 1 cubic meter ; 100,000 g - 1 , 000,000 cubic centimeters ; 1 g - 1 , 000,000 / 100,000 = 10 / 1 = 10 cubic centimeters . answer : c ."
Answer: c
Problem: two pipes a and b can fill a tank in 12 and 24 minutes respectively . if both the pipes are used together , how long will it take to fill the tank ?
Options: a ) 9 min , b ) 8 min , c ) 4 min , d ) 6 min , e ) none of these
Rationale: "explanation : tank can be filled by pipe a in 12 minutes and pipe b in 24 minutes . = > part filled by a in 1 minute = 1 / 12 = > part filled by b in 1 minute = 1 / 24 = > part filled by both in 1 minute = 1 / 12 + 1 / 24 = 3 / 24 = 1 / 8 time taken to fill the entire tank = 8 minutes answer b"
Answer: b
Problem: what number is obtained by adding the units digits of 734 ^ 99 and 347 ^ 82 ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "the units digit of 734 ^ 99 is 4 because 4 raised to the power of an odd integer ends in 4 . the units digit of 347 ^ 82 is 9 because powers of 7 end in 7 , 9 , 3 , or 1 cyclically . since 82 is in the form 4 n + 2 , the units digit is 9 . then 4 + 9 = 13 . the answer is d ."
Answer: d
Problem: the ratio between the number of sheep and the number of horses at the stewar farm is 3 to 7 . if each of horse is fed 230 ounces of horse food per day and the farm needs a total 12880 ounces of horse food per day . what is number sheep in the form ? ?
Options: a ) 24 , b ) 28 , c ) 32 , d ) 56 , e ) 58
Rationale: et no of sheep and horses are 3 k and 7 k no of horses = 12880 / 230 = 56 now 7 k = 56 and k = 8 no of sheep = ( 3 * 8 ) = 24 answer : a
Answer: a
Problem: a pump can fill a tank with a water in 2 hours . because of a leak , it took 2 and 4 / 5 hours to fill the tank . the leak can drain all the water of the full tank in how many hours ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: the rate of the pump + leak = 5 / 14 1 / 2 - leak ' s rate = 5 / 14 leak ' s rate = 1 / 2 - 5 / 14 = 1 / 7 the leak will empty the tank in 7 hours . the answer is d .
Answer: d
Problem: the sum of number of boys and girls in a school is 100 . if the number of boys is x , then the number of girls becomes x % of the total number of students . the number of boys is ?
Options: a ) 50 , b ) 40 , c ) 60 , d ) 100 , e ) 70
Rationale: "we have x + x % of 100 = 100 x + x / 100 * 100 = 100 2 * x = 100 x = 50 answer is a"
Answer: a
Problem: the food in a camp lasts for 20 men for 50 days . if 20 more men join , how many days will the food last ?
Options: a ) 22 days , b ) 25 days , c ) 28 days , d ) 16 days , e ) 27 days
Rationale: one man can consume the same food in 20 * 50 = 1000 days . 20 more men join , the total number of men = 40 the number of days the food will last = 1000 / 40 = 25 days . answer : b
Answer: b
Problem: three numbers are in the ratio of 2 : 3 : 4 and their l . c . m . is 264 . what is their h . c . f . ?
Options: a ) 18 , b ) 22 , c ) 24 , d ) 28 , e ) 32
Rationale: "let the numbers be 2 x , 3 x , and 4 x . lcm of 2 x , 3 x and 4 x is 12 x . 12 x = 264 x = 22 hcf of 2 x , 3 x and 4 x = x = 22 the answer is b ."
Answer: b
Problem: in a class of students , 1 / 2 of the number of girls is equal to 1 / 3 of the total number of students . what is the ratio of boys to girls in the class ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 2 / 3 , d ) 1 / 4 , e ) 3 / 4
Rationale: "( 1 / 2 ) g = ( 1 / 3 ) ( b + g ) 3 g = 2 b + 2 g g = 2 b b / g = 1 / 2 . the answer is a ."
Answer: a
Problem: two circles are there one with arc area 60 digree equal to 45 digree of another circle find the area of circle 1 : circle 2 ratio
Options: a ) 3 : 4
b ) 1 : 4
c ) 1 : 2
d ) 2 : 3
e ) 1 : 3
Rationale: area for first circle = ( 3.14 * r ^ 2 ) / 6 area of second circke = ( 3.14 * r ^ 2 ) / 8 therefore , ratio = 3 : 4 answer : a
Answer: a
Problem: in a recent head - to - head run - off election , 12,000 absentee ballets were cast . 1 / 6 of the absentee ballets were thrown out and 3 / 5 of the remaining absentee ballets were cast for candidate a . how many absentee votes did candidate b receive ?
Options: a ) 2,000 , b ) 3,000 , c ) 4,000 , d ) 8,000 , e ) 9,000
Rationale: 5 / 6 * 2 / 5 ( total absentee votes ) = 1 / 3 ( total votes ) = 1 / 3 * 12000 = 4000 answer is c
Answer: c
Problem: a train 300 m long can cross an electric pole in 30 sec and then find the speed of the train ?
Options: a ) 76 kmph , b ) 54 kmph , c ) 72 kmph , d ) 36 kmph , e ) 91 kmph
Rationale: "length = speed * time speed = l / t s = 300 / 30 s = 10 m / sec speed = 10 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 36 kmph answer : d"
Answer: d
Problem: at what rate percent of simple interest will a sum of money double itself in 66 years ?
Options: a ) 6.54 % , b ) 4.54 % , c ) 1.51 % , d ) 1.94 % , e ) 5.54 %
Rationale: "let sum = x . then , s . i . = x . rate = ( 100 * s . i . ) / ( p * t ) = ( 100 * x ) / ( x * 66 ) = 100 / 66 = 1.51 % answer : c"
Answer: c
Problem: an = 2 an - 1 + 4 and qn = 4 qn - 1 + 8 for all n > 1 . if a 5 = q 4 and a 7 = 316 , what is the first value of n for which qn is an integer ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: assuming i have understood the symbols used correctly answer is c - 3 a 7 = 2 s 6 + 4 = 316 a 6 = 312 / 2 = 156 = 2 a 5 + 4 a 5 = 152 / 2 = 76 = q 4 q 4 = 4 q 3 + 8 = 76 q 3 = 68 / 4 = 17 q 3 = 4 q 2 + 8 = 17 q 2 = 9 / 4 = 2.25 q 2 = 4 q 1 + 8 q 1 will not be integer = c
Answer: c
Problem: courtyard 3.78 meters long 5.95 meters wide is to be paved exactly with square tiles , all of the same size . what is the largest size of the tile which could be used for the purpose ?
Options: a ) 22 , b ) 77 , c ) 877 , d ) 99 , e ) 88
Rationale: 3.78 meters = 378 cm = 2 × 3 × 3 × 3 × 7 5.25 meters = 525 cm = 5 × 5 × 3 × 7 hence common factors are 3 and 7 hence lcm = 3 × 7 = 21 hence largest size of square tiles that can be paved exactly with square tiles is 77 cm . answer : b
Answer: b
Problem: in a college the ratio of the numbers of boys to the girls is 8 : 5 . if there are 160 girls , the total number of students in the college is ?
Options: a ) 562 , b ) 356 , c ) 452 , d ) 416 , e ) 512
Rationale: "let the number of boys and girls be 8 x and 5 x then , 5 x = 160 x = 32 total number of students = 13 x = 13 * 32 = 416 answer is d"
Answer: d
Problem: x is a positive integer less than 500 . when x is divided by 5 , the remainder is 1 ; when x is divided by 3 , the remainder is 2 . how many x are there ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: "the nubmer which when divided by 5 leaves remainder 1 should be of the form 7 k + 1 this number when divided by 3 leaves remainder 2 . so , ( 7 k + 1 ) - 2 should be divisible by 3 or 7 k - 1 should be divisible by 3 . we now put the values of k starting from 0 to find first number divisible by 3 we find 1 st number at k = 1 thus smallest number will be 7 ( 1 ) + 1 = 8 now , next number will be = 8 + lcm of 37 i . e 29 now we will find number of all such values less than 500 by using the formula for last term of an a . p 8 + ( n - 1 ) 21 = 500 n = 24.42 or n = 24 answer : - d"
Answer: d
Problem: john distributes his pencil among his 4 friends rose , mary , ranjan , and rohit in the ratio 1 / 4 : 1 / 3 : 1 / 4 : 1 / 5 . what is the minimum no . of pencils that the person should have ?
Options: a ) 45 , b ) 62 , c ) 70 , d ) 77 , e ) 98
Rationale: "rakesh : rahul : ranjan : rohit = 1 / 4 : 1 / 3 : 1 / 4 : 1 / 5 step 1 : at first we need to do is lcm of 2 , 3,4 and 5 is 60 . step 2 : then pencil are distributed in ratio among friends , rakesh = ( 1 / 4 x 60 ) = 15 . rahul = ( 1 / 3 x 60 ) = 20 . ranjan = ( 1 / 4 x 60 ) = 15 . rohit = ( 1 / 5 x 60 ) = 12 . step 3 : total number of pencils are ( 15 x + 20 x + 15 x + 12 x ) = 62 x . for minimum number of pencils x = 1 . the person should have at least 62 pencils . b )"
Answer: b
Problem: tough and tricky questions : word problems . a salesman ' s income consists of commission and base salary . his weekly income totals over the past 5 weeks have been $ 406 , $ 413 , $ 420 , $ 436 and $ 395 . what must his average ( arithmetic mean ) income over the next 5 weeks be to increase his average weekly income to $ 500 over the 10 - week period ?
Options: a ) $ 570 , b ) $ 586 , c ) $ 630 , d ) $ 686 , e ) $ 715
Rationale: official solution : ( b ) first , we need to add up the wages over the past 5 weeks : $ 406 + $ 413 + $ 420 + $ 436 + $ 395 = $ 2070 . to average $ 500 over 10 weeks , the salesman would need to earn : $ 500 × 10 = $ 5000 . subtract $ 2070 from $ 5000 to determine how much he would need to earn , in total , over the next 5 weeks to average $ 500 for the 10 weeks : $ 5000 – $ 2070 = $ 2930 . dividing $ 2930 by 5 will give us the amount he needs to earn on average over the next 5 weeks : $ 2930 / 5 = $ 586 . the correct answer is choice ( b ) .
Answer: b
Problem: when a random experiment is conducted , the probability that event a occurs is 1 / 3 . if the random experiment is conducted 4 independent times , what is the probability that event a occurs exactly twice ?
Options: a ) 8 / 27 , b ) 10 / 31 , c ) 12 / 37 , d ) 14 / 41 , e ) 16 / 49
Rationale: "one case is : 1 / 3 * 1 / 3 * 2 / 3 * 2 / 3 = 4 / 81 the total number of possible cases is 4 c 2 = 6 p ( event a occurs exactly twice ) = 6 * ( 4 / 81 ) = 8 / 27 the answer is a ."
Answer: a
Problem: if 16 % of 40 % of a number is 6 , then the number is
Options: a ) 200 , b ) 225 , c ) 93.75 , d ) 320 , e ) none of these
Rationale: explanation : let 16 / 100 × 40 / 100 × a = 6 a = 6 × 100 × 100 / 16 × 40 = 93.75 correct option : c
Answer: c
Problem: one day a car rental agency rented 2 / 3 of its cars , including 3 / 5 of its cars with cd players . if 3 / 5 of its cars have cd players , what percent of the cars that were not rented had cd players ?
Options: a ) 18 / 25 , b ) 17 / 20 , c ) 11 / 15 , d ) 7 / 10 , e ) 3 / 5
Rationale: "the cars with cd players which were not rented is ( 2 / 5 ) ( 3 / 5 ) = 6 / 25 of all the cars . the cars which were not rented is 1 / 3 of all the cars . the percent of non - rented cars which had cd players is ( 6 / 25 ) / ( 1 / 3 ) = 18 / 25 the answer is a ."
Answer: a
Problem: a certain number when divided by 39 leaves a remainder 19 , what is the remainder when the same number is divided by 13 ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 6 , e ) 4
Rationale: explanation : 39 + 19 = 58 / 13 = 6 ( remainder ) answer : d
Answer: d
Problem: if the price of gasoline increases by 20 % and a driver intends to spend only 8 % more on gasoline , by how much percent should the driver reduce the quantity of gasoline that he buys ?
Options: a ) 4 % , b ) 5 % , c ) 6 % , d ) 8 % , e ) 10 %
Rationale: "let x be the amount of gasoline the driver buys originally . let y be the new amount of gasoline the driver should buy . let p be the original price per liter . ( 1.2 * p ) y = 1.08 ( p * x ) y = ( 1.08 / 1.2 ) x = 0.9 x which is a reduction of 10 % . the answer is e ."
Answer: e
Problem: the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 50 kg . what might be the weight of the new person ?
Options: a ) 70 kg , b ) 80 kg , c ) 85 kg , d ) 90 kg , e ) 95 kg
Rationale: "total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 50 + 20 ) kg = 70 kg . a )"
Answer: a
Problem: machine a can finish a job in 4 hours , machine в can finish the job in 2 hours , and machine с can finish the job in 6 hours . how many hours will it take for a , b , and с together to finish the job ?
Options: a ) 4 / 3 , b ) 6 / 5 , c ) 8 / 7 , d ) 10 / 9 , e ) 12 / 11
Rationale: "the combined rate is 1 / 4 + 1 / 2 + 1 / 6 = 11 / 12 of the job per hour . the time to complete the job is 12 / 11 hours . the answer is e ."
Answer: e
Problem: a cubical block of metal weighs 3 pounds . how much will another cube of the same metal weigh if its sides are twice as long ?
Options: a ) 48 , b ) 32 , c ) 24 , d ) 18 , e ) 12
Rationale: "for example our cube have a side 1 meter , so we have 1 cubical meter in this cube and this cubical meter weigth 3 pounds if we take cube with side 2 meters we will have 8 cubical meters in this cube 8 meters * 3 pounds = 24 pounds so answer is c and similar but more theoretical approach : if we have sides a and b than they have equal ration with their areas : a / b = a ^ 2 / b ^ 2 and they have equal ration with their volumes : a / b = a ^ 3 / b ^ 3 we have two sides 1 / 2 so their volume will be in ratio 1 / 8 weight of one cube * volume of another cube 3 * 8 = 24 so answer is c"
Answer: c
Problem: two coins are tossed . find the probability of at most 2 tails ?
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 1 / 3 , d ) 1 , e ) 3 / 4
Rationale: "n ( s ) = 2 ^ 2 = 4 . . . . ( 2 coins are tossed ) let e is the event of getting at most 2 tails n ( e ) = hh , tt , ht , th = 4 p ( e ) = n ( e ) / n ( s ) = 4 / 4 = 1 ans - d"
Answer: d
Problem: a trader sells 85 meters of cloth for rs . 8925 at the profit of rs . 35 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) 21 , b ) 28 , c ) 90 , d ) 26 , e ) 70
Rationale: "explanation : sp of 1 m of cloth = 8925 / 85 = rs . 105 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 105 - rs . 35 = rs . 70 . answer : e"
Answer: e
Problem: how many seconds will a train 200 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph ?
Options: a ) 22 sec , b ) 35 sec , c ) 25 sec , d ) 18 sec , e ) 17 sec
Rationale: "d = 200 + 150 = 350 s = 36 * 5 / 18 = 10 mps t = 350 / 10 = 35 sec answer : b"
Answer: b
Problem: a sum of rs . 427 is to be divided among a , b and c in such a way that 3 times a ’ s share , 4 times b ’ s share and 7 times c ’ s share are all equal . the share of c is
Options: a ) 82 , b ) 83 , c ) 84 , d ) 85 , e ) 86
Rationale: "a + b + c = 427 3 a = 4 b = 7 c = > ( 7 c / 3 ) + ( 7 c / 4 ) + c = 427 = > c = 84 answer : c"
Answer: c
Problem: find the average of first 4 multiples of 12 ?
Options: a ) 10 , b ) 12.6 , c ) 22.5 , d ) 30 , e ) 40.8
Rationale: "average = ( 12 + 24 + 36 + 48 ) / 4 = 30 answer is d"
Answer: d
Problem: there is a rectangular prism made of 1 in cubes that has been covered in tin foil . there are exactly 128 cubes that are not touching any tin foil on any of their sides . if the width of the figure created by these 128 cubes is twice the length and twice the height , what is the p measure in inches of the width of the foil covered prism ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 9 , e ) 10
Rationale: "if the width is w , then length and height would be w / 2 . so , w * w / 2 * w / 2 = 128 = > w ^ 3 = ( 2 ^ 3 ) * 64 = ( 2 ^ 3 ) * ( 4 ^ 3 ) = > w = 2 * 4 = 8 in . along the width of the cuboid , 8 cubes do n ' t touch the tin foil . so the actual width will be non - touching cubes + touching cubes = 8 + 2 = p = 10 ans e ."
Answer: e
Problem: if 15 students in a class average 80 % on an english exam and 10 students average 90 % on the same exam , what is the average in percent for all 25 students ?
Options: a ) 83 % , b ) 83 1 ⁄ 2 % , c ) 84 % , d ) 85 % , e ) 86 2 ⁄ 3 %
Rationale: the average percentage = ( 15 x 80 % + 10 x 90 % ) / 25 = ( 15 x 80 % + 10 x 80 % + 10 x 10 % ) / 25 . . . . . . ( as 90 % = 10 % + 80 % ) = ( 25 x 80 % + 10 x 10 % ) / 25 = 80 % + 10 x 10 % / 25 = 80 % + 4 % = 84 % answer : c
Answer: c
Problem: a man sitting in a train which is traveling at 50 kmph observes that a goods train , traveling in opposite direction , takes 9 seconds to pass him . if the goods train is 280 m long , find its speed
Options: a ) 52 kmph , b ) 56 kmph , c ) 58 kmph , d ) 62 kmph , e ) 72 kmph
Rationale: "explanation : relative speed = 280 / 9 m / sec = ( ( 280 / 9 ) × ( 18 / 5 ) ) kmph = 112 kmph . speed of goods train = ( 112 - 50 ) kmph = 62 kmph answer : option d"
Answer: d
Problem: how many positive factors do 160 and 96 have in common ?
Options: a ) 6 , b ) 12 , c ) 16 , d ) 18 , e ) 24
Rationale: "the number of common factors will be same as number of factors of the highest common factor ( hcf ) hcf of 160 and 96 is 32 number of factors of 32 = 6 answer : a"
Answer: a
Problem: how many odd prime numbers are there less than 50 ?
Options: a ) 15 , b ) 1 , c ) 2 , d ) 14 , e ) 17
Rationale: "odd prime number less than 50 : 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43 , 47 there is 14 the odd prime number answer is d"
Answer: d
Problem: at a local appliance manufacturing facility , the workers received a 15 % hourly pay raise due to extraordinary performance . if one worker decided to reduce the number of hours that he worked so that his overall pay would remain unchanged , by approximately what percent would he reduce the number of hours that he worked ?
Options: a ) 13 % , b ) 80 % , c ) 20 % , d ) 17 % , e ) 12 %
Rationale: "let ' s say he works usually 10 hours and earns 100 per hour . 10 * 100 = 1000 10 * 115 = 1150 ( this are the new earnings after the raise ) to figure out how much he needs to work with the new salary in order to earn the original 1000 : 1000 / 115 = 8.7 so he can reduce his work by 1.3 hours . which is > 13 % . answer a"
Answer: a
Problem: if the simple interest on $ 2000 increase by $ 40 , when the time increase by 4 years . find the rate percent per annum .
Options: a ) 1.2 % , b ) 0.5 % , c ) 0.7 % , d ) 0.9 % , e ) 0.3 %
Rationale: "applying the above formula , we have 40 = 2000 * r * 4 / 100 r = 40 * 100 / 2000 * 4 = 0.5 % . answer is b"
Answer: b
Problem: in a room filled with 7 people , 4 people have exactly 1 sibling in the room and 3 people have exactly 2 siblings in the room . if two individuals are selected from the room at random , what is the probability that those two individuals are not siblings ?
Options: a ) 5 / 21 , b ) 3 / 7 , c ) 4 / 7 , d ) 5 / 7 , e ) 16 / 21
Rationale: "# of selections of 2 out of 7 - c 27 = 21 c 72 = 21 ; # of selections of 2 people which are not siblings - c 12 ∗ c 12 c 21 ∗ c 21 ( one from first pair of siblings * one from second pair of siblings ) + c 12 ∗ c 13 c 21 ∗ c 31 ( one from first pair of siblings * one from triple ) + c 1 ^ _ 2 * c ^ 1 _ 3 ( one from second pair of siblings * one from triple ) = 4 + 6 + 6 = 16 = 4 + 6 + 6 = 16 . p = 16 / 21 answer : e"
Answer: e
Problem: working at their respective constant rates , machine a makes 100 copies in 12 minutes and machine b makes 150 copies in 15 minutes . if these machines work simultaneously at their respective rates for 30 minutes , what is the total number of copies that they will produce ?
Options: a ) 250 , b ) 425 , c ) 550 , d ) 700 , e ) 750
Rationale: machine a can produce 100 * 30 / 12 = 250 copies and , machine b can produce 150 * 30 / 15 = 300 copies total producing 550 copies . c is the answer
Answer: c
Problem: which number can we add to 897326 to get a number exactly divisible by 456 ?
Options: a ) 58 , b ) 66 , c ) 74 , d ) 82 , e ) 90
Rationale: 897326 / 456 = 1967 with a remainder of 374 . we need to add 456 - 374 = 82 the answer is d .
Answer: d
Problem: when two dice are rolled , what is the probability that the sum is either 7 or 11 ?
Options: a ) 1 / 4 , b ) 1 / 9 , c ) 4 / 3 , d ) 3 / 9 , e ) 2 / 9
Rationale: total number of outcomes possible = 36 probability of getting sum of 7 = 6 / 36 probability of getting sum of 11 = 2 / 36 probability that the sum is either 7 or 11 = 6 / 36 + 2 / 36 = 2 / 9 answer : e
Answer: e
Problem: the radius of a wheel is 24.2 cm . what is the distance covered by the wheel in making 500 resolutions ?
Options: a ) 708 m , b ) 704 m , c ) 774 m , d ) 760.57 m , e ) 744 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 500 resolutions . = 500 * 2 * 22 / 7 * 24.2 = 76057 cm = 760.57 m answer : d"
Answer: d
Problem: after spending rs . 5000 on rent , rs . 1500 on milk , rs . 4500 on groceries , rs . 2500 on childrens education rs . 2000 on petrol and rs . 3940 on miscellaneous expenses , mr . kishore saved 10 % of his monthly salary . how much did he save in rs . ?
Options: a ) 2160 , b ) 2350 , c ) 2000 , d ) 2300 , e ) none of these
Rationale: "explanation : total exp = 5000 + 1500 + 4500 + 2500 + 2000 + 3940 = 19440 exp in % = 100 - 10 = 90 % , 19440 = 90 % saving = 10 % = 19440 x 10 / 90 = rs . 2160 answer : a"
Answer: a
Problem: the standard deviation of a normal distribution of data is 2 , and 3 standard deviations below the mean is greater than 44 . what is a possible value for the mean of the distribution ?
Options: a ) 46 , b ) 47 , c ) 48 , d ) 49 , e ) 51
Rationale: "the standard deviation ( { sd } ) = 2 ; 3 standard deviations below the mean is greater than 44 : { mean } - 3 * { sd } > 44 ; { mean } - 6 > 44 ; { mean } > 50 . answer : e ."
Answer: e
Problem: the set x = { 78 , 910 } . the set y = { 23 , 45 } . we will randomly choose one element x from set x and one element y from set y . what is the probability that x / y will be an integer ?
Options: a ) 7 / 16 , b ) 5 / 16 , c ) 3 / 16 , d ) 7 / 8 , e ) 5 / 8
Rationale: the total number of x and y pairs is 4 * 4 = 16 . there are five pairs such that x / y is an integer . the probability that x / y is an integer is 5 / 16 . the answer is b .
Answer: b
Problem: what is the value of 4 ^ 5 + 4 ^ 8 ?
Options: a ) 4 ^ 12 , b ) 4 ^ 35 , c ) 17 ( 4 ^ 5 ) , d ) 8 ^ 12 , e ) 65 ( 4 ^ 5 )
Rationale: "4 ^ 5 + 4 ^ 8 = 4 ^ 5 ( 1 + 4 ^ 3 ) = 4 ^ 5 * 65 answer e"
Answer: e
Problem: john bought a total of 12 mangoes and oranges . each mango costs 80 cents and each orange costs 50 cents . if the average price of the 12 mangoes and oranges that john originally purchased was 65 cents , then how many oranges needs to return to raise the average price of his purchase to 72 cents ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "let number of mangoes be x , number of oranges be 12 - x 0.80 x + ( 12 - x ) 0.50 / 12 = 0.65 solving for x , we get x = 6 - - > mangoes 6 , oranges 6 now , number of oranges to be returned be y [ 0.80 * 6 + ( 6 - y ) * 0.50 ] / 12 - y = 0.72 solving for y , y = 4 ans : a"
Answer: a
Problem: two vessels contains equal number of mixtures milk and water in the ratio 4 : 2 and 5 : 1 . both the mixtures are now mixed thoroughly . find the ratio of milk to water in the new mixture so obtained ?
Options: a ) 3 : 1 , b ) 9 : 13 , c ) 5 : 11 , d ) 11 : 3 , e ) 15 : 4
Rationale: "the ratio of milk and water in the new vessel is = ( 4 / 6 + 5 / 6 ) : ( 2 / 6 + 1 / 6 ) = 9 / 6 : 3 / 6 = 3 : 1 answer is a"
Answer: a
Problem: for any positive integer n , the sum of the first n positive integers equals n ( n + 1 ) / 2 . what is the sum of all the even integers between 99 and 201 ?
Options: a ) 7650 , b ) 9250 , c ) 12,650 , d ) 14,250 , e ) 15,150
Rationale: "100 + 102 + . . . + 200 = 100 * 51 + ( 2 + 4 + . . . + 100 ) = 100 * 51 + 2 * ( 1 + 2 + . . . + 50 ) = 100 * 51 + 2 ( 50 ) ( 51 ) / 2 = 100 * 51 + 50 * 51 = 150 ( 51 ) = 7650 the answer is a ."
Answer: a
Problem: in what time will a train 90 m long cross an electric pole , it its speed be 72 km / hr ?
Options: a ) 1.5 , b ) 2.5 , c ) 3.5 , d ) 4.5 , e ) 5.5
Rationale: "speed = 72 * 5 / 18 = 20 m / sec time taken = 90 / 20 = 4.5 sec . answer : d"
Answer: d
Problem: a can give b 200 meters start and c 400 meters start in a kilometer race . how much start can b give c in a kilometer race ?
Options: a ) 111.12 , b ) 250 , c ) 111.64 , d ) 111.11 , e ) 101.12
Rationale: "a runs 1000 m while b runs 800 m and c runs 600 m . the number of meters that c runs when b runs 1000 m , = ( 1000 * 600 ) / 800 = 750 m . b can give c = 1000 - 750 = 250 m . answer : b"
Answer: b
Problem: a reduction of 40 % in the price of bananas would enable a man to obtain 65 more for rs . 40 , what is reduced price per dozen ?
Options: a ) 1.95 , b ) 2.95 , c ) 4.95 , d ) 3.95 , e ) 5.95
Rationale: "40 * ( 40 / 100 ) = 16 - - - 65 ? - - - 12 = > rs . 2.95 answer : b"
Answer: b
Problem: a shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 20 % while buying and by 10 % while selling . what is his percentage profit ?
Options: a ) 10.22 % , b ) 20.22 % , c ) 21.22 % , d ) 20 % , e ) ca n ' t be calculated
Rationale: "the owner buys 100 kg but actually gets 120 kg ; the owner sells 100 kg but actually gives 90 kg ; profit : ( 120 - 90 ) / 90 * 100 = 20 % answer : d ."
Answer: d
Problem: for the past n days , the average ( arithmetic mean ) daily production at a company was 50 units . if today ' s production of 115 units raises the average to 55 units per day , what is the value of n ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: the daily production was raised by 5 units for n days , which has a weighting of 5 n . 5 n = 115 - 55 = 60 n = 12 the answer is c .
Answer: c
Problem: the h . c . f . of two numbers is 11 and their l . c . m . is 7700 . if one of the numbers is 275 , then the other is :
Options: a ) 279 , b ) 283 , c ) 308 , d ) 318 , e ) 338
Rationale: other number = ( 11 x 7700 ) / 275 = 308 . answer : c
Answer: c
Problem: excluding stoppages , the speed of a bus is 54 kmph and including stoppages , it is 41 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 7 min , b ) 8 min , c ) 14.4 min , d ) 10 min , e ) 11 min
Rationale: due to stoppages , it covers 13 km less . time taken to cover 13 km = ( 13 / 54 ) x 60 = 14.4 min answer : c
Answer: c
Problem: a train length 100 m going with speed 10 m / sec another train 150 m long going with speed 15 m / sec . the distance between two train is 50 m . then how much time second train will take to cross the first train ?
Options: a ) 60 sec , b ) 40 sec , c ) 30 sec , d ) 45 sec , e ) 1 min 10 sec
Rationale: net speed = 15 - 10 = 5 m / sec net distance = 100 + 150 + 50 = 300 total time = 300 / 5 = 60 sec answer a
Answer: a
Problem: one copy machine can make 15 copies a minute , and a second copy machine makes 10 copies a minute . if the two copiers work together , how long would it take them to make 1,000 copies ?
Options: a ) 20 minutes , b ) 30 minutes , c ) 40 minutes , d ) 50 minutes , e ) 60 minutes
Rationale: total work done by both machines in a minute = 15 + 10 = 25 copies total number of copies required = 1000 time = 1000 / 25 = 40 mins answer c
Answer: c
Problem: a and b start walking towards each other at 6 pm at speed of 6 kmph and 4 kmph . they were initially 50 km apart . at what time do they meet ?
Options: a ) 8 pm , b ) 6 pm , c ) 11 pm , d ) 10 pm , e ) 5 pm
Rationale: "time of meeting = distance / relative speed = 50 / 4 + 6 = 50 / 10 = 5 hrs after 6 pm = 11 pm answer is c"
Answer: c
Problem: what is the units digit of 33 ^ 2 * 17 ^ 3 * 49 ^ 3 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "the units digit of 33 ^ 2 is the units digit of 3 * 3 = 9 which is 9 . the units digit of 17 ^ 3 is the units digit of 7 * 7 * 7 = 343 which is 3 . the units digit of 49 ^ 3 is the units digit of 9 * 9 * 9 = 729 which is 9 . the units digit of 9 * 3 * 9 = 243 is 3 . the answer is b ."
Answer: b
Problem: solution y is 30 percent liquid x and 70 percent water . if 2 kilograms of water evaporate from 10 kilograms of solution y and 2 kilograms of solution y are added to the remaining 6 kilograms of liquid , what percent of this new solution is liquid x ?
Options: a ) 34 , b ) 35 , c ) 36 , d ) 37 1 / 25 , e ) 40
Rationale: "in 8 kilograms of solution y there are 0.3 * 10 = 3 kilograms of solution x ; after 2 kilograms of water are replaced by 2 kilograms of solution y , to the existing 2.4 kilograms of solution x , 0.3 * 2 = 0.6 kilograms of solution x are added , so in the new solution of 8 kilograms there are 3 + 0.6 = 3.6 kilograms of solution x , which is 3.6 / 10 * 100 = 36 % of this new solution . answer : c ."
Answer: c
Problem: water is poured into a tank so that the tank is being filled at the rate of 4 cubic feet per hour . if the empty rectangular tank is 6 feet long , 4 feet wide , and 3 feet deep , approximately how many hours does it take to fill the tank ?
Options: a ) 16 , b ) 18 , c ) 20 , d ) 22 , e ) 24
Rationale: "the volume the tank is : length * width * depth = 6 * 4 * 3 = 72 cubic feet . 72 cubic feet / 4 cubic feet per hour = 18 hours . it will take 18 hours to fill the tank . the answer is b ."
Answer: b
Problem: two pipes a and b can separately fill a cistern in 60 min and 75 min respectively . there is a third pipe in the bottom of the cistern to empty it . if all the 3 pipes are simultaneously opened , then the cistern is full in 50 min . in how much time , the third pipe alone can empty the cistern ?
Options: a ) 197 min , b ) 100 min , c ) 177 min , d ) 176 min , e ) 186 min
Rationale: work done by the third pipe in 1 min = 1 / 50 - ( 1 / 60 + 1 / 75 ) = - 1 / 100 . [ - ve sign means emptying ] the third pipe alone can empty the cistern in 100 min . answer : b
Answer: b
Problem: a and b undertake to do a piece of work for rs . 1200 . a alone can do it in 6 days while b alone can do it in 8 days . with the help of c , they finish it in 3 days . find the share of b .
Options: a ) 250 , b ) 450 , c ) 750 , d ) 800 , e ) none of them
Rationale: "c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 24 a : b : c = ratio of their 1 day ' s work = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 . a ’ s share = rs . ( 1200 * 4 / 8 ) = rs . 600 , b ' s share = rs . ( 1200 * 3 / 8 ) = rs . 450 c ' s share = rs . [ 1200 - ( 300 + 225 » ) = rs . 150 . answer is b"
Answer: b
Problem: a trader sells 92 meters of cloth for rs . 9890 at the profit of rs . 24 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) 22 , b ) 89.5 , c ) 76.9 , d ) 83.5 , e ) 11
Rationale: "sp of 1 m of cloth = 9890 / 92 = rs . 107.5 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 107.5 - rs . 24 = rs . 83.5 answer : d"
Answer: d
Problem: what is the least value of x . so that 21 x 57 is divisible by 3 .
Options: a ) 2 , b ) 0 , c ) 1 , d ) 3 , e ) 4
Rationale: "explanation : the sum of the digits of the number is divisible by 3 , then the number is divisible by 3 . 2 + 1 + x + 5 + 7 = 15 + x least value of x may be 0 therefore 15 + 0 = 15 is divisible by 3 . answer : option b"
Answer: b
Problem: the ratio of numbers is 3 : 4 and their h . c . f is 3 . their l . c . m is :
Options: a ) 12 , b ) 16 , c ) 36 , d ) 48 , e ) 98
Rationale: "let the numbers be 3 x and 4 x . then their h . c . f = x . so , x = 3 . so , the numbers are 9 and 12 . l . c . m of 9 and 12 = 36 . answer : c"
Answer: c
Problem: the average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 65 kg . what is the correct weight ?
Options: a ) 67.4 kg , b ) 57.75 kg , c ) 58.85 kg , d ) 49.4 kg , e ) none of these
Rationale: "actual total weight is ( 20 ã — 58.4 - 56 + 65 ) = 1177 kgs actual average weight is 1177 / 20 = 58.85 kgs answer is c"
Answer: c
Problem: the sale price sarees listed for rs . 400 after successive discount is 30 % and 20 % is ?
Options: a ) 297 , b ) 879 , c ) 342 , d ) 762 , e ) 224
Rationale: "400 * ( 70 / 100 ) * ( 80 / 100 ) = 224 answer : e"
Answer: e
Problem: a runs 1 ¾ times as fast as b . if a gives b a start of 84 m , bow far must winning post be so that a and b might reach it at the same time ?
Options: a ) 196 m , b ) 194 m , c ) 186 m , d ) 296 m , e ) 106 m
Rationale: . ratio of the rates of a and b = 7 / 4 : 1 = 7 : 4 . so , in a race of 7 m , a gains 3 m over b . : . 3 m are gained by a in a race of 7 m . : . 84 m are gained by a in a race of ( 7 / 3 x 84 ) m = 196 m . : . winning post must be 196 m away from the starting point . answer is a .
Answer: a
Problem: a box contains 13 apples , 12 of which are red . an apple is drawn from the box and its color is noted before it is eaten . this is done a total of n times , and the probability that a red apple is drawn each time is less than 0.5 . what is the smallest possible value of n ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "p ( choosing a red apple 7 times in a row ) = 12 / 13 * 11 / 12 * 10 / 11 * 9 / 10 * 8 / 9 * 7 / 8 * 6 / 7 = 6 / 13 < 0.5 the answer is e ."
Answer: e
Problem: a soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price . during the annual summer sale , everything in the store is an additional 40 percent off the original list price . if a replica jersey ' s list price is $ 80 , approximately what percent of the list price is the lowest possible sale price ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 40 , e ) 50
Rationale: "let the list price be 2 x for min sale price , the first discount given should be 50 % , 2 x becomes x here now , during summer sale additional 20 % off is given ie sale price becomes 0.8 x it is given lise price is $ 80 = > 2 x = 80 = > x = 20 and 0.8 x = 32 so lowest sale price is 32 , which is 40 % of 80 hence , a is the answer"
Answer: a
Problem: a = { 2 , 3 , 5 , 7 , 11 } b = { 2 , 4 , 6 , 19 } two integers will be randomly selected from sets a and b , one integer from set a and one from set b , and then multiplied together . how many different products can be obtained ?
Options: a ) 15 , b ) 16 , c ) 19 , d ) 24 , e ) 36
Rationale: step 1 : find out the number of products you get . 5 distinct numbers in set a and 4 distinct in set b so number of products = 5 * 4 = 20 step 2 : remove the products that appear more than once . notice that 5 , 7 , 11 and 13 are primes and none of their multiples are in either set . so ignore them . we just need to focus on 2 and 3 of set a and 2 , 4 and 6 of set b . 2 , 3 2 , 4 , 6 the only product repeated when you take a number from each set is 12 . ( 3 * 4 and 2 * 6 ) rest all are distinct . answer = 20 - 1 = 24 note here that the second step will involve manual calculation since it will depend on the specific numbers you have in the two sets . d
Answer: d
Problem: if one - seventh of a number exceeds its eleventh part by 100 then the number is …
Options: a ) 770 , b ) 870 , c ) 1825 , d ) 1925 , e ) 925
Rationale: let no be : x 1 / 7 x - 1 / 11 x = 100 4 x / 77 = 100 x = 7700 / 4 = 1925 answer : d
Answer: d
Problem: a regular 10 sided area is inscribed in a circle . if a and b are adjacent vertices of the pentagon and o is the center of the circle , what is the value of ∠ oab ?
Options: a ) 48 degrees
b ) 54 degrees
c ) 72 degrees
d ) 84 degrees
e ) 72 degrees
Rationale: its a regular 10 sided so divide the globe by 10 . = 360 / 10 = 36 36 would be the angle at o . angles at a and b are equivalent , so 36 + 2 x = 180 2 x = 144 x = 72 angles oab and oba will be 72 degrees each . e
Answer: e
Problem: a rower whose speed is 6 km / hr in still water rows to a certain point upstream and back to the starting point in a river which flows at 3 km / hr . what is the rower ' s average speed ( in km / hr ) for the total journey ?
Options: a ) 3.9 , b ) 4.2 , c ) 4.5 , d ) 4.8 , e ) 5.1
Rationale: "time upstream = d / 3 time downstream = d / 9 total time = d / 3 + d / 9 = 4 d / 9 average speed = 2 d / ( 4 d / 9 ) = 4.5 km / hr the answer is c ."
Answer: c
Problem: list i : 3 , 4 , 8 , 19 list ii : x , 3 , 4 , 8 , 19
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: we start by calculating the median of the numbers of list i : 3 , 4 , 8 , 19 . we see that the numbers in the list are in order already and , since we have an even number of numbers , the median is the average of the two middle numbers . median = ( 4 + 8 ) / 2 median = 12 / 2 median = 6 the median of list i is 6 . looking at list ii : x , 3 , 4 , 8 , 19 , we see that we have an odd number of terms . thus , when the list is ordered from least to greatest the median must be the middle term . since the medians of the two lists must be equal , we know that the median of list ii must be 6 and therefore x is 6 . the answer is a .
Answer: a
Problem: there are 4 more women than there are men on a local co - ed softball team . if there are a total of 20 players on the team , what is the ratio of men to women ?
Options: a ) 8 / 12 , b ) 6 / 16 , c ) 4 / 16 , d ) 6 / 10 , e ) 4 / 10
Rationale: "w = m + 4 w + m = 20 m + 4 + m = 20 2 m = 16 m = 8 w = 12 ratio : 8 : 12 ans : a"
Answer: a
Problem: it is currently 9 : 53 pm . what time was it in the morning exactly 149,061 minutes ago ?
Options: a ) 9 : 12 , b ) 9 : 18 , c ) 9 : 26 , d ) 9 : 32 , e ) 9 : 38
Rationale: divide by 60 to convert 149,061 minutes to hours : 149,061 / 60 = 2,484 r 21 . that is 2,484 hours and 21 minutes . all of the answers are in the 9 am hour before : 53 , thus we can assume 2,484 previous must be 9 : 53 am . 21 minutes before that is 9 : 32 am . d
Answer: d
Problem: a man can row his boat with the stream at 20 km / h and against the stream in 4 km / h . the man ' s rate is ?
Options: a ) 1 kmph , b ) 7 kmph , c ) 98 kmph , d ) 6 kmph , e ) 8 kmph
Rationale: "ds = 20 us = 4 s = ? s = ( 20 - 4 ) / 2 = 8 kmph answer : e"
Answer: e
Problem: 6 chess players take part in a tournament . every player plays twice with each of his opponents . how many games are to be played ?
Options: a ) 19 , b ) 20 , c ) 30 , d ) 33 , e ) 34
Rationale: "though 2 * ( 6 c 2 ) is the correct approcah to do this , but for people like me who find perm , comb n prob a nightmare , an easy approach can be used . the first guy has to play 2 matches with the rest of 5 , so he ' ll play 10 matches . similarly , second guy has to play with the rest of 4 as his 2 games with the first guy are already played . so he plays 8 matches . this continues like this and the total matches are 10 + 8 + 6 . . . + 2 10 + 8 + . . . + 2 = 2 ( 5 + 4 + . . . + 1 ) = 2 ( ( 5 * 6 ) / 2 ) = 5 * 6 = 30 . answer : c"
Answer: c
Problem: the time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 51 kmph , find the speed of the stream ?
Options: a ) 12 kmph , b ) 13 kmph , c ) 14 kmph , d ) 15 kmph , e ) 17 kmph
Rationale: "the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 51 / 3 = 17 kmph answer : e"
Answer: e
Problem: the average ( arithmetic man ) of 3 integers a , b , and c is exactly 4 times the median . if a < b < c and a = 0 , what is the value of c / b ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 11 , e ) can not be determined from the information given .
Rationale: the average of three integers a , b , and c is exactly twice the median - - > ( a + b + c ) / 3 = 4 b - - > since a = 0 , then ( 0 + b + c ) / 3 = 4 b - - > c = 11 b - - > c / b = 11 . answer : d .
Answer: d
Problem: in 1950 , richard was 4 times as old as robert . in 1955 , richard was 3 times as old as robert . in which year was richard 1.75 times as old as robert ?
Options: a ) 1960 , b ) 1965 , c ) 1970 , d ) 1975 , e ) 1980
Rationale: "in 1950 : ri = 4 ro - - - - - - - - - - - - - - eq 1 in 1955 : ri + 5 = 3 ( ro + 5 ) - - - - - - - - - eq 2 thus in 1950 , solving eq 1 and eq 2 ro = 10 , ri = 40 now for each year we can calculate : 1960 : ri = 50 , ro = 20 1965 : ri = 55 , ro = 25 1980 : ri = 40 , ro = 70 thus 8 ans : e"
Answer: e
Problem: raman ' s salary was decreased by 50 % and subsequently increased by 50 % . how much percent does he loss
Options: a ) 75 , b ) 65 , c ) 45 , d ) 25 , e ) 35
Rationale: "explanation : let the origianl salary = rs . 100 it will be 150 % of ( 50 % of 100 ) = ( 150 / 100 ) * ( 50 / 100 ) * 100 = 75 so new salary is 75 , it means his loss is 25 % answer : option d"
Answer: d
Problem: a dishonest shopkeeper professes to sell pulses at the cost price , but he uses a false weight of 930 gm . for a kg . his gain is … % .
Options: a ) 5.26 % , b ) 5.36 % , c ) 4.26 % , d ) 6.26 % , e ) 7.53 %
Rationale: "his percentage gain is 100 * 7 / 930 as he is gaining 70 units for his purchase of 930 units . so 7.53 % . answer : e"
Answer: e