regisss/math_qa huggingface dataset:
Problem: on dividing a number by 68 , we get 269 as quotient and 0 as remainder . on dividing the same number by 67 , what will be the remainder ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "number = 269 * 68 + 0 = 18292 67 ) 18292 ( 273 18291 - - - - - - - - 1 required number = 1 . answer : b"
Answer: b
Problem: a person want to give his money of $ 4500 to his 3 children a , b , c in the ratio 2 : 3 : 4 . what is the b ' s share ?
Options: a ) $ 2000 , b ) $ 1500 , c ) $ 2500 , d ) $ 1800 , e ) $ 1600
Rationale: b ' s share = 4500 * 3 / 9 = $ 1500 answer is b
Answer: b
Problem: how many integers between 100 and 180 , inclusive , can not be evenly divided by 3 nor 5 ?
Options: a ) 39 , b ) 41 , c ) 43 , d ) 45 , e ) 47
Rationale: "the total numbers between 100 and 180 , inclusive , is 81 . 3 * 34 = 102 and 3 * 60 = 180 so the number of multiples of 3 is 27 . 5 * 20 = 100 and 5 * 36 = 180 so the number of multiples of 5 is 17 . however , the multiples of 15 have been counted twice . 15 * 7 = 105 and 15 * 12 = 180 so the number of multiples of 15 is 6 . thus the total number is 81 - 27 - 17 + 6 = 43 . the answer is c ."
Answer: c
Problem: what is the least number of squares tiles required to pave the floor of a room 2 m 42 cm long and 1 m 76 cm broad ?
Options: a ) 88 , b ) 82 , c ) 84 , d ) 44 , e ) 54
Rationale: "length of largest tile = h . c . f . of 242 cm and 176 cm = 22 cm . area of each tile = ( 22 x 22 ) cm 2 . required number of tiles = 242 x 176 / ( 22 ^ 2 ) = 88 . answer : a"
Answer: a
Problem: rahul can do a work in 3 days while rajesh can do the same work in 2 days . both of them finish the work together and get $ 105 . what is the share of rahul ?
Options: a ) $ 50 , b ) $ 42 , c ) $ 60 , d ) $ 100 , e ) $ 90
Rationale: "rahul ' s wages : rajesh ' s wages = 1 / 3 : 1 / 2 = 2 : 3 rahul ' s share = 105 * 2 / 5 = $ 42 answer is b"
Answer: b
Problem: a number , x is chosen at random from the set of positive integers less than 12 . what is the probability that ( 9 / x ) > x ?
Options: a ) 1 / 11 , b ) 2 / 9 , c ) 2 / 11 , d ) 2 / 3 , e ) 7 / 9
Rationale: "number x has to be chosen from numbers 1 - 11 ( 9 / x ) > x = > 9 > x ^ 2 = > x ^ 2 - 9 < 0 x can have 2 values only 1 , 2 therefore , probability = 2 / 11 answer c"
Answer: c
Problem: a , b and c are partners . a receives 2 / 3 of profits , b and c dividing the remainder equally . a ' s income is increased by rs . 600 when the rate to profit rises from 5 to 7 percent . find the capital of b ?
Options: a ) 3999 , b ) 7799 , c ) 2500 , d ) 7500 , e ) 2912
Rationale: "a : b : c = 2 / 3 : 1 / 6 : 1 / 6 = 4 : 1 : 1 x * 2 / 100 * 2 / 3 = 600 b capital = 45000 * 1 / 6 = 7500 . answer : d"
Answer: d
Problem: what least number must be subtracted from 427398 so that remaining number is divisible by 15
Options: a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) none of these
Rationale: "explanation : on dividing 427398 by 15 we get the remainder 3 , so 3 should be subtracted answer : option a"
Answer: a
Problem: what is the value of 4 ^ 5 + 4 ^ 7 ?
Options: a ) 4 ^ 12 , b ) 4 ^ 35 , c ) 17 ( 4 ^ 5 ) , d ) 8 ^ 12 , e ) 7 ( 4 ^ 5 )
Rationale: "4 ^ 5 + 4 ^ 7 = 4 ^ 5 ( 1 + 4 ^ 2 ) = 4 ^ 5 * 17 answer c"
Answer: c
Problem: if 3 eighth of a number is 141 . what will be the approximately value of 32.08 % of this number ?
Options: a ) 119 , b ) 187 , c ) 181 , d ) 120 , e ) 891
Rationale: explanation : x * 3 / 8 = 141 = > x = 376 376 * 32.08 / 100 = 120 answer : d
Answer: d
Problem: the number of positive integers valued pairs ( x , y ) ssatisfying 4 x - 17 y = 1 and x < = 1000 ( x is less than or equal to 1000 ) is
Options: a ) fifty nine , b ) 57 , c ) 55 , d ) 58 , e ) 60
Rationale: 4 x - 17 y = 1 y = ( 4 x - 1 ) / 17 x has to be a positive integer such that 1 < = x < = 1000 ( 4 x - 1 ) is a factor of 17 so that y is also a positive integer so we need to know how many numbers in the set { 37 , 1115 , . . . . , 3999 } are divisible by 17 lets try to observe the pattern 1 . 3 mod 17 = 3 2 . 7 mod 17 = 7 3 . 11 mod 17 = 11 4 . 15 mod 17 = 15 5 . 19 mod 17 = 2 6 . 23 mod 17 = 6 7 . 27 mod 17 = 10 8 . 31 mod 17 = 14 9 . 35 mod 17 = 1 10 . 39 mod 17 = 5 11 . 43 mod 17 = 9 12 . 47 mod 17 = 13 13.51 mod 17 = 0 14 . 55 mod 17 = 4 15 . 59 mod 17 = 8 16 . 63 mod 17 = 12 17 . 67 mod 17 = 16 . . . and after this the remainders will repeat ( this is no co - incidence that the cyclicity is also 17 ) so the right choices are x = 1313 + 1713 + 17 + 17 , . . . . . the number of such numbers is 59 ( highest one being 999 ) a
Answer: a
Problem: a can do a piece of work in 4 hours ; b and c together can do it in 2 hours , while a and c together can do it in 2 hours . how long will b alone take to do it ?
Options: a ) 12 , b ) 9 , c ) 8 , d ) 6 , e ) 4
Rationale: "a ' s 1 hour ' s work = 1 / 4 ; ( b + c ) ' s 1 hour ' s work = 1 / 2 ; ( a + c ) ' s 1 hour ' s work = 1 / 2 . ( a + b + c ) ' s 1 hour ' s work = ( 1 / 4 + 1 / 2 ) = 3 / 4 . b ' s 1 hour ' s work = ( 3 / 4 - 1 / 2 ) = 1 / 4 . therefore a alone will take 4 hours to do the work . e"
Answer: e
Problem: a person buys an article at rs . 500 . at what price should he sell the article so as to make a profit of 40 % ?
Options: a ) 700 , b ) 882 , c ) 772 , d ) 652 , e ) 271
Rationale: "cost price = rs . 500 profit = 40 % of 500 = rs . 200 selling price = cost price + profit = 500 + 200 = 700 answer : a"
Answer: a
Problem: if both 5 ^ 2 and 3 ^ 3 are factors of n x ( 2 ^ 5 ) x ( 12 ^ 2 ) x ( 7 ^ 3 ) , what is the smallest possible positive value of n ?
Options: a ) 25 , b ) 75 , c ) 125 , d ) 150 , e ) 175
Rationale: "( 2 ^ 5 ) x ( 12 ^ 2 ) x ( 7 ^ 3 ) has two appearances of 3 ( in 12 ^ 2 ) and no appearances of 5 . thus n must include at least 3 * 5 ^ 2 = 75 the answer is b ."
Answer: b
Problem: find the compound interest on $ 56,000 at 20 % per annum for 9 months , compounded quarterly
Options: a ) 2532 , b ) 2552 , c ) 6524 , d ) 8827 , e ) 9512
Rationale: "principal = $ 56000 ; time = 9 months = 3 quarters ; rate = 20 % per annum = 5 % per quarter . amount = $ [ 56000 x ( 1 + ( 5 / 100 ) ) ^ 3 ] = $ 64827 . ci . = $ ( 64827 - 56000 ) = $ 8827 . answer d ."
Answer: d
Problem: the radius of the two circular fields is in the ratio 5 : 4 the area of the first field is what percent greater than the area of the second ?
Options: a ) 22 % , b ) 32 % , c ) 34 % , d ) 64 % , e ) 36 %
Rationale: "r = 5 ï € r 2 = 25 r = 4 ï € r 2 = 16 25 ï € â € “ 9 ï € 100 - - - - ? = > 36 % . answer : d"
Answer: d
Problem: rahul can do a work in 3 days while rajesh can do the same work in 2 days . both of them finish the work together and get $ 250 . what is the share of rahul ?
Options: a ) $ 50 , b ) $ 40 , c ) $ 60 , d ) $ 100 , e ) $ 90
Rationale: rahul ' s wages : rajesh ' s wages = 1 / 3 : 1 / 2 = 2 : 3 rahul ' s share = 250 * 2 / 5 = $ 100 answer is d
Answer: d
Problem: if n is a natural number , then ( 6 n 2 + 6 n ) is always divisible by ?
Options: a ) 6 only , b ) 6 and 12 both , c ) 12 only , d ) 6 or 12 only , e ) none
Rationale: "( 6 n 2 + 6 n ) = 6 n ( n + 1 ) , which is always divisible by 6 and 12 both , since n ( n + 1 ) is always even . b )"
Answer: b
Problem: how many numbers from 10 to 46 are exactly divisible by 3 ?
Options: a ) 13 , b ) 12 , c ) 16 , d ) 17 , e ) 18
Rationale: "12 , 15 , 18 , 21 , 24 , 27 , 30 , 33 , 36 , 39 , 42 , 45 . 12 numbers . 10 / 3 = 3 and 46 / 3 = 15 = = > 15 - 3 = 12 . therefore 12 digits b )"
Answer: b
Problem: what is the remainder when 54487 ^ ( 42787035 ) is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "we need to find the units digit of the number . the units digit of powers of seven repeats 7 , 9 , 3 , and 1 cyclically . since 42787035 has the form 4 a + 3 , the units digit is 3 . then the remainder when dividing by 5 is 3 . the answer is d ."
Answer: d
Problem: the total number of digits used in numbering the pages of a book having 366 pages is
Options: a ) 732 , b ) 990 , c ) 1098 , d ) 1305 , e ) 1605
Rationale: "explanation : total number of digits = ( no . of digits in 1 - digit page nos . + no . of digits in 2 - digit page nos . + no . of digits in 3 - digit page nos . ) = ( 1 x 9 + 2 x 90 + 3 x 267 ) = ( 9 + 180 + 801 ) = 990 . answer : b"
Answer: b
Problem: the sum of three consecutive numbers is 252 . the greatest among these three number is :
Options: a ) 45 , b ) 80 , c ) 85 , d ) 55 , e ) 40
Rationale: "let the numbers be x , x + 1 and x + 2 then , x + ( x + 1 ) + ( x + 2 ) = 252 3 x = 252 x = 83 greatest number , ( x + 2 ) = 85 answer : c"
Answer: c
Problem: two friends decide to get together ; so they start riding bikes towards each other . they plan to meet halfway . each is riding at 6 mph . they live 36 miles apart . one of them has a pet carrier pigeon and it starts flying the instant the friends start traveling . the pigeon flies back and forth at 15 mph between the 2 friends until the friends meet . how many miles does the pigeon travel ?
Options: a ) 54 , b ) 66 , c ) 80 , d ) 45 , e ) 96
Rationale: "d 45 it takes 3 hours for the friends to meet ; so the pigeon flies for 3 hours at 18 mph = 45 miles"
Answer: d
Problem: how many 3 - digit even numbers are possible such that if one of the digits is 4 , the next / succeeding digit to it should be 7 ?
Options: a ) 305 , b ) 5 , c ) 365 , d ) 405 , e ) 495
Rationale: 470 , 472 , 474 , 476 , and 478 , so total 5 . hence option b .
Answer: b
Problem: in a public show 45 % of the seats were filled . if there were 600 seats in the hall , how many seats were vacant ?
Options: a ) 330 , b ) 110 , c ) 120 , d ) 140 , e ) 150
Rationale: 75 % of 600 = 45 / 100 × 600 = 270 therefore , the number of vacant seats = 600 - 270 = 330 . answer : a
Answer: a
Problem: if ( 1 / 5 ) ^ m * ( 1 / 4 ) ^ 2 = 1 / ( ( 10 ) ^ 4 ) , then m =
Options: a ) 4 , b ) 5 , c ) 6 , d ) 3 , e ) 2
Rationale: 1 / 5 ^ m * 1 / 4 ^ 2 = 1 / 2 ^ 4 * 5 ^ 4 2 ^ 4 * 5 ^ 4 / 2 ^ 4 = 5 ^ m or 5 ^ 4 = 5 ^ m therefore m = 4 a
Answer: a
Problem: two workers completed the painting of a building in 10 days . if they were to paint the building separately , how many days will it take each worker , if one of them can complete it in approximately 2 days earlier than the other .
Options: a ) 9 and 11 , b ) 19 and 21 , c ) 8 and 10 , d ) 10 and 15 , e ) 10 and 12
Rationale: work = ( a ) ( b ) / ( a + b ) where a and b are the individual times of each entity . here , we ' re told that ( working together ) the two workers would complete a job in 10 days . this means that ( individually ) each of them would take more than 10 days to do the job . answers e , a and c are illogical , since the individual times must both be greater than 10 days . so we can test the values for answers b and d . using the values for answers b and d . . . answer b : ( 19 ) ( 21 ) / ( 19 + 21 ) = 399 / 40 = 9.97 this is a match ( complete it in approximately 2 days earlier than the other ) this is a match final answer : b
Answer: b
Problem: frank is 15 years younger then john . in 3 years john will be twice as old as frank . how old will frank be in 4 years ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: frank is 15 years younger then john - - > f + 15 = j ; in 5 years john will be twice as old as frank ( in 3 year john will be j + 3 years old and frank will be f + 3 years old ) - - > j + 3 = 2 * ( f + 3 ) - - > ( f + 15 ) + 3 = 2 * ( f + 3 ) - - > f = 12 ; in 4 years frank will be 12 + 4 = 16 years old . answer : e .
Answer: e
Problem: last year , for every 100 million vehicles that traveled on a certain highway , 50 vehicles were involved in accidents . if 5 billion vehicles traveled on the highway last year , how many of those vehicles were involved in accidents ? ( 1 billion = 1,000 , 000,000 )
Options: a ) 800 , b ) 850 , c ) 900 , d ) 500 , e ) 1000
Rationale: "to solve we will set up a proportion . we know that “ 100 million vehicles is to 50 accidents as 5 billion vehicles is to x accidents ” . to express everything in terms of “ millions ” , we can use 5,000 million rather than 5 billion . creating a proportion we have : 100 / 50 = 5,000 / x cross multiplying gives us : 100 x = 2,000 * 50 x = 20 * 50 = 1000 answer : e"
Answer: e
Problem: a man sitting in a train which is traveling at 30 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 ) 50 kmph , b ) 82 kmph , c ) 62 kmph , d ) 65 kmph , e ) 75 kmph
Rationale: "relative speed = 280 / 9 m / sec = ( ( 280 / 9 ) * ( 18 / 5 ) ) kmph = 112 kmph . speed of goods train = ( 112 - 30 ) kmph = 82 kmph . answer : b ."
Answer: b
Problem: in a certain school , 20 % of students are below 8 years of age . the number of students above 8 years of age is 2 / 3 of the number of students of 8 years of age which is 72 . what is the total number of students in the school ?
Options: a ) 72 , b ) 80 , c ) 120 , d ) 40 , e ) 150
Rationale: "explanation : let the number of students be x . then , number of students above 8 years of age = ( 100 - 20 ) % of x = 80 % of x . 80 % of x = 72 + 2 / 3 of 72 80 / 100 x = 120 x = 150 . answer : option e"
Answer: e
Problem: if 4 x + 3 y = 8 and y - 3 x = 8 , then what is the value of x + 4 y ?
Options: a ) 1 / 7 , b ) 16 , c ) 15 , d ) 52 / 7 , e ) 60 / 7
Rationale: "4 x + 3 y = 8 . . . equation 1 - 3 x + y = 8 . . . equation 2 adding both the equations x + 4 y = 16 correct answer option b"
Answer: b
Problem: mike needs 30 % to pass . if he scored 212 marks and falls short by 28 marks , what was the maximum marks he could have got ?
Options: a ) 343 , b ) 677 , c ) 800 , d ) 867 , e ) 932
Rationale: "if mike had scored 28 marks more , he could have scored 30 % therefore , mike required 212 + 28 = 240 marks let the maximum marks be m . then 30 % of m = 240 ( 30 / 100 ) × m = 240 m = ( 240 × 100 ) / 30 m = 24000 / 30 m = 800 answer : c"
Answer: c
Problem: a man can ride on motorcycle at 50 kmph upward road and 100 kmph downward road . he takes 12 hours to ride motorcycle uphill from lower point a to upper point b and back to a . what is the total distance traveled by him in 12 hours ? he must return back to base point a in remaining time .
Options: a ) 1000 , b ) 900 , c ) 800 , d ) 400 , e ) 1200
Rationale: upward distance traveled per hour - 50 km , distance traveled after 8 hours = 400 km . he remained with 4 hours travel downward , i . e . distance traveled in remaining 4 hours downward = 400 km so total distance traveled from a to b and back to point a = 400 km upward + 400 km downhill = 800 km ( answer : c )
Answer: c
Problem: 7 machines at a certain factory operate at the same constant rate . if 6 of these machines , operating simultaneously , take 42 hours to fill a certain production order , how many fewer hours does it take all 7 machines , operating simultaneously , to fill the same production order ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: the total work is 6 * 42 = 252 machine hours the time required for seven machines is 252 / 7 = 36 hours , thus 6 fewer hours . the answer is d .
Answer: d
Problem: what number is obtained by adding the units digits of 734 ^ 99 and 347 ^ 83 ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
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 ^ 83 is 3 because powers of 7 end in 7 , 9 , 3 , or 1 cyclically . since 83 is in the form 4 n + 3 , the units digit is 3 . then 4 + 3 = 7 . the answer is a .
Answer: a
Problem: the amount of principal rs . 8000 at compound interest at the ratio of 5 % p . a . for 1 year is
Options: a ) s . 9621 , b ) s . 6921 , c ) s . 8400 , d ) s . 6261 , e ) s . 6361
Rationale: "c . i = p ( 1 + r / 100 ) ^ n = 8000 ( 1 + 5 / 100 ) = rs 8400 answer : c"
Answer: c
Problem: the visitors of a modern art museum who watched a certain picasso painting were asked to fill in a short questionnaire indicating whether they had enjoyed looking at the picture and whether they felt they had understood it . according to the results of the survey , all 150 visitors who did not enjoy the painting also did not feel they had understood the painting , and the number of visitors who enjoyed the painting was equal to the number of visitors who felt they had understood the painting . if 3 / 4 of the visitors who answered the questionnaire both enjoyed the painting and felt they had understood the painting , then how many visitors answered the questionnaire ?
Options: a ) 90 , b ) 120 , c ) 160 , d ) 360 , e ) 600
Rationale: "if we exclude those cases and take the question at face value , then it seems straightforward . group # 1 = ( did n ' t like , did n ' t understand ) = 150 group # 2 = ( likeunderstood ) = 3 / 4 ( 1 / 4 ) n = 150 n = 600 answer = ( e )"
Answer: e
Problem: if x = 4 ^ 16 and x ^ x = 4 ^ k , what is k ?
Options: a ) 4 ^ 14 , b ) 4 ^ 16 , c ) 4 ^ 18 , d ) 4 ^ 20 , e ) 4 ^ 22
Rationale: "solution : we know that x = 4 ^ 16 which implies x ^ x = ( 4 ^ 16 ) ^ ( 4 ^ 16 ) = 4 ^ ( 16 * 4 ^ 16 ) [ because ( x ^ y ) ^ z = x ^ ( y * z ) ) ] so 4 ^ ( 4 ^ 2 * 4 ^ 16 ) = 4 ^ ( 4 ^ ( 2 + 16 ) ) [ because x ^ a * x ^ b = x ^ ( a + b ) ] therefore x ^ x = 4 ^ ( 4 ^ 18 ) given that x ^ x = 4 ^ k so 4 ^ ( 4 ^ 18 ) = 4 ^ k since the base is same the exponent will also be same therefore k = 4 ^ 18 answer : c"
Answer: c
Problem: what is the remainder when 123456789101112131415161718192021222324252627282930313233343536373839404142434481 is divided by 45 ?
Options: a ) 26 , b ) 36 , c ) 16 , d ) 06 , e ) 40
Rationale: explanation : let ' s call : a = 123456789101112131415161718192021222324252627282930313233343536373839404142434481 = > a = b * 100 + 81 [ with b = 1234567 . . . . . 424344 ] we have : b x 100 is divisible by 45 because : - sum of all digits in b = 1 + 2 + 3 + . . . . + 44 = ( 1 + 44 ) + ( 2 + 43 ) + . . . . + ( 22 + 23 ) ( 22 pairs ) = 22 * 45 = > b divisible for 9 since b is divisible by 9 , b * 100 will be divisible by 9 * 5 = 45 81 divided 45 gives a remainder of 36 therefore , a divided by 45 reminder 36 answer : b
Answer: b
Problem: a man can row 5 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and black . how far is the place ?
Options: a ) 2.25 , b ) 2.35 , c ) 2.45 , d ) 2.55 , e ) 2.65
Rationale: "m = 5 s = 1.2 ds = 5 + 1.2 = 6.2 us = 5 - 1.2 = 3.8 x / 6.2 + x / 3.8 = 1 x = 2.35 . answer : b"
Answer: b
Problem: a taxi company charges $ 1.15 for the first quarter of a mile and fifteen cents for each additional quarter of a mile . what is the maximum distance someone could travel with $ 4.90 ?
Options: a ) 4 miles , b ) 4 1 / 4 miles , c ) 4 3 / 4 miles , d ) 5 1 / 2 miles , e ) 6 1 / 2 miles
Rationale: if we start out with $ 4.90 and have to spend $ 1.15 for the first quarter - mile , we will have $ 3.75 left to spend on quarter - mile intervals . since $ 3.75 / $ 0.15 = 25 , we can buy 25 more quarter - miles , and will travel 26 quarter miles in all : 26 × 1 / 4 = 6 1 / 2 miles . the correct answer is choice ( e ) .
Answer: e
Problem: in a race where 10 cars are running , the chance that car x will win is 1 / 7 , that y will win is 1 / 3 and that z will win is 1 / 5 . assuming that a dead heat is impossible , find the chance that one of them will win .
Options: a ) 1 / 140 , b ) 1 / 180 , c ) 71 / 105 , d ) 21 / 113 , e ) 57 / 120
Rationale: "required probability = p ( x ) + p ( y ) + p ( z ) ( all the events are mutually exclusive ) . = 1 / 7 + 1 / 3 + 1 / 5 = 71 / 105 answer : c"
Answer: c
Problem: a person decided to build a house in 100 days . he employed 100 men in the beginning and 100 more after 20 days and completed the construction in stipulated time . if he had not employed the additional men , how many days behind schedule would it have been finished ?
Options: a ) 40 , b ) 80 , c ) 70 , d ) 60 , e ) 50
Rationale: "200 men do the rest of the work in 100 - 20 = 80 days 100 men can do the rest of the work in 80 * 200 / 100 = 160 days required number of days = 160 - 80 = 80 days answer is b"
Answer: b
Problem: find the cost of fencing around a circular field of diameter 32 m at the rate of rs . 1.50 a meter ?
Options: a ) 287 , b ) 132 , c ) 150.9 , d ) 158 , e ) 267
Rationale: "2 * 22 / 7 * 16 = 100.6 100.6 * 1 1 / 2 = rs . 150.9 answer : c"
Answer: c
Problem: bob wants to run a mile in the same time as his sister . if bob ’ s time for a mile is currently 10 minutes 40 seconds and his sister ’ s time is currently 5 minutes 20 seconds , by what percent does bob need to improve his time in order run a mile in the same time as his sister ?
Options: a ) 3 % , b ) 50 % , c ) 8 % , d ) 10 % , e ) 12 %
Rationale: "bob ' s time = 640 secs . his sis ' time = 320 secs . percent increase needed = ( 640 - 320 / 640 ) * 100 = 320 / 640 * 100 = 50 % . ans ( b ) ."
Answer: b
Problem: how much time does a train 100 metres long running at 72 km / hr take to pass a pole ?
Options: a ) 7.9 s , b ) 2.5 s , c ) 5 s , d ) 7.6 s , e ) 7.4 s
Rationale: explanation : 72 km / hr = 72 * 5 / 18 = 20 m / s speed = distance / time ; v = d / t 20 = 100 / t t = 5 s answer : c
Answer: c
Problem: sahil purchased a machine at rs 12000 , then got it repaired at rs 5000 , then gave its transportation charges rs 1000 . then he sold it with 50 % of profit . at what price he actually sold it .
Options: a ) rs . 22000 , b ) rs . 24000 , c ) rs . 26000 , d ) rs . 27000 , e ) none of these
Rationale: "explanation : question seems a bit tricky , but it is very simple . just calculate all cost price , then get 150 % of cp . c . p . = 12000 + 5000 + 1000 = 18000 150 % of 18000 = 150 / 100 * 18000 = 27000 option d"
Answer: d
Problem: find the simple interest on rs . 450 for 8 months at 5 paisa per month ?
Options: a ) 277 , b ) 270 , c ) 180 , d ) 266 , e ) 121
Rationale: "i = ( 450 * 8 * 5 ) / 100 = 180 answer : c"
Answer: c
Problem: in a division sum , the remainder is 0 . as student mistook the divisor by 12 instead of 21 and obtained 49 as quotient . what is the correct quotient ?
Options: a ) 0 , b ) 12 , c ) 13 , d ) 20 , e ) 28
Rationale: "12 * 49 = 588 588 % 21 = 28 answer : e"
Answer: e
Problem: 54671 - 18456 - 33466 = ?
Options: a ) 2749 , b ) 5449 , c ) 6749 , d ) 6449 , e ) 6468
Rationale: "a if we calculate we will get 2749"
Answer: a
Problem: uba capital recently bought brand new vehicles for office use . uba capital only went for toyota and honda and bought more of toyota than honda at the ratio of 4 : 6 . if 40 % of the toyota bought and 60 % of the honda bought were suv ã ¢ â ‚ ¬ â „ ¢ s . how many suv ã ¢ â ‚ ¬ â „ ¢ s did uba capital buy in the aforementioned purchase ?
Options: a ) 66 % , b ) 64 % , c ) 68 % , d ) 69 % , e ) 52 %
Rationale: "let total no of vehicles bought be 100 , toyota 40 and honda 60 , so total number of suv ' s bought for toyota and honda respectively 40 * 40 / 100 = 16 and 60 * 60 / 100 = 36 so total 52 suv ' s were bought out of 100 vehicles bought . . so required % is 52 % answer : e"
Answer: e
Problem: the effective annual rate of interest corresponding to a nominal rate of 12 % per annum payable half - yearly is ?
Options: a ) 16.06 % , b ) 16.07 % , c ) 12.36 % , d ) 6.09 % , e ) 6.19 %
Rationale: "amount of rs . 100 for 1 year when compounded half - yearly = [ 100 * ( 1 + 6 / 100 ) 2 ] = rs . 112.36 effective rate = ( 112.36 - 100 ) = 12.36 % answer : c"
Answer: c
Problem: an association of mathematics teachers has 1600 members . only 525 of these members cast votes in the election for president of the association . what percent of the total membership voted for the winning candidate if the winning candidate received 60 percent of the votes cast ?
Options: a ) 75 % , b ) 58 % , c ) 42 % , d ) 14.5 % , e ) 19.6 %
Rationale: total umber of members = 1600 number of members that cast votes = 525 since , winning candidate received 60 percent of the votes cast number of votes for winning candidate = ( 60 / 100 ) * 525 = 315 percent of total membership that voted for winning candidate = ( 315 / 1600 ) * 100 = 19.6 % answer e
Answer: e
Problem: if n is a prime number greater than 3 , what is the remainder when n ^ 2 is divided by 13 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 13 , e ) 5
Rationale: "there are several algebraic ways to solve this question including the one under the spoiler . but the easiest way is as follows : since we can not have two correct answersjust pick a prime greater than 3 , square it and see what would be the remainder upon division of it by 13 . n = 5 - - > n ^ 2 = 25 - - > remainder upon division 25 by 13 is 12 . answer : d ."
Answer: d
Problem: having received his weekly allowance , john spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 0.60 at the candy store . what is john ’ s weekly allowance ?
Options: a ) $ 2.25 , b ) $ 3.00 , c ) $ 3.25 , d ) $ 3.65 , e ) $ 4.80
Rationale: "x = 3 x / 5 + 1 / 3 * 2 x / 5 + 60 4 x / 15 = 60 x = 225 = $ 2.25 the answer is a ."
Answer: a
Problem: a certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 11 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ?
Options: a ) 42 , b ) 70 , c ) 140 , d ) 165 , e ) 385
Rationale: "ans : 385 7 c 1 * 11 c 2 answer e )"
Answer: e
Problem: in the year 1990 there are 5000 men 3000 women 2000 boys . in 1994 men are increased by 20 % women are increased by ratio of boys and women ?
Options: a ) 11000 , b ) 12000 , c ) 13000 , d ) 14000 , e ) 15000
Rationale: total population in year 1990 = 5000 + 3000 + 2000 = 10000 total population in year 1994 = ( ( 5000 * 120 / 100 ) + ( 3000 + ( 3000 * 2 / 3 ) ) + ( 2000 ) ) = 13000 answer : c
Answer: c
Problem: a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 27 , the how old is b
Options: a ) 10 , b ) 8 , c ) 6 , d ) 5 , e ) 7
Rationale: "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 27 5 x = 25 x = 5 . hence , b ' s age = 2 x = 10 years answer : a"
Answer: a
Problem: what is the sum of the multiples of 4 between 13 and 125 inclusive ?
Options: a ) 1,890 , b ) 1,960 , c ) 2,200 , d ) 3,780 , e ) 4,400
Rationale: "the first multiple of 12 between 13 and 125 is 16 while the last is 124 total number of terms is given by 124 = 16 + ( n - 1 ) 4 4 n - 4 = 108 n = 112 / 4 = 28 or , ( 124 - 16 ) / 4 + 1 = 28 so , we have 28 multiples of 12 between 13 and 125 sum = 14 ( 2 * 16 + ( 27 ) 4 ) = 14 ( 140 ) = 1960 answer : b"
Answer: b
Problem: the volume of a rectangular swimming pool is 840 cubic meters and water is flowing into the swimming pool . if the surface level of the water is rising at the rate of 0.5 meters per minute , what is the rate s , in cubic meters per minutes , at which the water is flowing into the swimming pool ?
Options: a ) 0.125 , b ) 0.25 , c ) 0.5 , d ) 0.75 , e ) not enough information to determine the rate
Rationale: "the correct answer is e . there are not enough info to answer the question . a 840 cubic meters rectangle is built from : height * length * width . from the question we know the volume of the pool and the filling rate . a pool can have a height of 10 * width 8.4 * length 10 and have a volume of 840 cubic meters , and it can have a height of 1 meter , width of 100 meters and length of 8.4 . in both cases the pool will fill up in a different rate = e"
Answer: e
Problem: four horses are tethered at 4 corners of a square field of side 70 metres so that they just can not reach one another . the area left ungrazed by the horses is :
Options: a ) 1050 sq . m
b ) 3850 sq . m
c ) 950 sq . m
d ) 1075 sq . m
e ) 1065 sq . m
Rationale: area ungrazed is given by total area - 4 * area grazed by each horse = 70 * 70 - 4 * ( 90 / 360 ) * pi * ( 70 / 2 ) ^ 2 as the angle made by the horse is 90 degree , so applying the area of the sector , = theta / 360 * pi * radius ^ 2 above = 70 * 70 - pi * ( 70 / 2 ) * ( 70 / 2 ) = 70 * 70 { 1 - pi / 4 } = 70 * 70 { 6 / ( 7 * 4 ) } , expanding pi = 22 / 7 = ( 70 * 70 * 6 ) / ( 7 * 4 ) = 1050 sq m answer : a
Answer: a
Problem: a dealer purchases 15 articles for rs . 25 and sells 12 articles for rs . 38 . find the profit percentage ?
Options: a ) 80 % , b ) 90 % , c ) 59 % , d ) 40 % , e ) 53 %
Rationale: l . c . m of 15 and 12 = 60 cp of 60 articles = rs . 100 ( 25 * 4 ) sp of 60 articles = rs . 190 ( 30 * 5 ) profit percentage = ( 190 - 100 ) / 100 * 100 = 90 % answer : b
Answer: b
Problem: redo ’ s manufacturing costs for sets of horseshoes include a $ 10000 initial outlay , and $ 20 per set . they can sell the sets $ 50 . if profit is revenue from sales minus manufacturing costs , and the company producessells 500 sets of horseshoes , what was their profit ?
Options: a ) $ 4500 , b ) $ 3500 , c ) $ 5500 , d ) $ 5000 , e ) $ 6300
Rationale: total manufacturing cost = 10000 + 500 * 20 = 20000 total selling cost = 500 * 50 = 25000 profit = 25000 - 20000 = 5000 answer : d
Answer: d
Problem: from below option 50 is divisible by which one ?
Options: a ) 3 , b ) 2 , c ) 7 , d ) 8 , e ) 9
Rationale: "50 / 2 = 25 b"
Answer: b
Problem: in n is a positive integer less than 200 , and 24 n / 60 is an integer , then n has how many different positive prime factors ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) 8
Rationale: "( a ) . 24 n / 60 must be an integer . = > 2 n / 5 must be an integer . hence n must be a multiple of 5 . = > n has 1 different prime integers ."
Answer: a
Problem: on rainy mornings , mo drinks exactly n cups of hot chocolate ( assume that n is an integer ) . on mornings that are not rainy , mo drinks exactly 4 cups of tea . last week mo drank a total of 42 cups of tea and hot chocolate together . if during that week mo drank 14 more tea cups than hot chocolate cups , then how many rainy days were there last week ?
Options: a ) 0 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "t = the number of cups of tea c = the number of cups of hot chocolate t + c = 42 t - c = 14 - > t = 28 . c = 14 . mo drinks 4 cups of tea a day then number of days that are not rainy = 28 / 4 = 7 so number of rainy days = 7 - 7 = 0 a is the answer ."
Answer: a
Problem: 469157 * 9999
Options: a ) 1691100843 , b ) 4591100843 , c ) 4691100843 , d ) 3691100843 , e ) none of these
Rationale: "explanation : 469157 * ( 10000 - 1 ) = 4691570000 - 469157 = 4691100843 option c"
Answer: c
Problem: what is the largest 4 digit number exactly divisible by 72 ?
Options: a ) 4676 , b ) 4678 , c ) 8888 , d ) 9504 , e ) 9936
Rationale: "largest 4 digit number = 9999 9999 ÷ 72 = 138 , remainder = 63 hence largest 4 digit number exactly divisible by 88 = 9999 - 63 = 9936 answer : e"
Answer: e
Problem: apple costs l rupees per kilogram for first 30 kgs and q rupees per kilogram for each additional kilogram . if the price of 33 kilograms is 360 and for 36 kgs of apples is 420 then the cost of first 25 kgs of apples is
Options: a ) 100 , b ) 250 , c ) 125 , d ) 110 , e ) 115
Rationale: "ans : by framing equations we get 30 l + 3 q = 360 30 l + 6 q = 420 eliminate q by multiplying the first equation by 2 and subtracting second equation from the first then we get l = 10 cost of 10 kgs of apples = 25 x 10 = 250 answer : b"
Answer: b
Problem: if x = 3 ^ 27 and x ^ x = 3 ^ k , what is k ?
Options: a ) 3 ^ 9 , b ) 3 ^ 12 , c ) 3 ^ 27 , d ) 3 ^ 30 , e ) 3 ^ 33
Rationale: "solution : we know that x = 3 ^ 27 which implies x ^ x = ( 3 ^ 27 ) ^ ( 3 ^ 27 ) = 3 ^ ( 27 * 3 ^ 27 ) [ because ( x ^ y ) ^ z = x ^ ( y * z ) ) ] so 3 ^ ( 3 ^ 3 * 3 ^ 27 ) = 3 ^ ( 3 ^ ( 3 + 27 ) ) [ because x ^ a * x ^ b = x ^ ( a + b ) ] therefore x ^ x = 3 ^ ( 3 ^ 30 ) given that x ^ x = 3 ^ k so 3 ^ ( 3 ^ 30 ) = 3 ^ k since the base is same the exponent will also be same therefore k = 3 ^ 30 answer : d"
Answer: d
Problem: find the least number which when divided by 5,6 , 7,8 leaves a remainder 3 but when divided by 9 leaves no remainder
Options: a ) 9632 , b ) 7896 , c ) 8741 , d ) 1683 , e ) 8523
Rationale: "l . c . m of 5,6 , 7,8 = 840 required number is of the form of 840 k + 3 least value of k for which ( 840 k + 3 ) is divided by 9 is k = 2 required number = ( 840 * 2 + 3 ) = 1683 answer ( d )"
Answer: d
Problem: the ratio of the radius of two circles is 3 : 4 , and then the ratio of their areas is ?
Options: a ) 1 : 7 , b ) 9 : 16 , c ) 1 : 9 , d ) 3 : 7 , e ) 3 : 4
Rationale: "r 1 : r 2 = 3 : 4 î r 1 ^ 2 : î r 2 ^ 2 r 1 ^ 2 : r 2 ^ 2 = 9 : 16 answer : b"
Answer: b
Problem: evaluate : 30 - | - x + 6 | for x = 10
Options: a ) 16 , b ) 26 , c ) 36 , d ) 46 , e ) 56
Rationale: substitute x by 10 in the given expression and evaluate 30 - | - ( 10 ) + 6 | = 30 - | - 10 + 6 | = 30 - | - 4 | = 30 - 4 = 26 correct answer b ) 26
Answer: b
Problem: in a partnership , a invests 1 ⁄ 6 of the capital for 1 ⁄ 6 of the time , b invests 1 ⁄ 3 of the capital for 1 ⁄ 3 of the time and c , the rest of the capital for whole time . find a ’ s share of the total profit of 2300
Options: a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) none of these
Rationale: remaining capital = 1 - ( 1 ⁄ 6 + 1 ⁄ 3 ) = 1 ⁄ 2 ratio of their profit = 1 ⁄ 6 × [ 1 ⁄ 6 × 12 ] : 1 ⁄ 3 × [ 1 ⁄ 3 × 12 ] : 1 ⁄ 2 × 12 = 1 ⁄ 3 : 4 ⁄ 3 : 6 = 1 : 4 : 18 ∴ a ' s share = 1 / 1 + 4 + 18 × 2300 = 100 answer a
Answer: a
Problem: a shopkeeper has 280 kg of apples . he sells 40 % of these at 20 % profit and remaining 50 % at 30 % profit . find his % profit on total .
Options: a ) 23 % , b ) 25 % , c ) 26 % , d ) 28 % , e ) 35 %
Rationale: "if the total quantity was 100 then 40 x 20 % + 50 x 30 % = 23 this profit will remain same for any total quantity unless the % of products remains the same . hence ' a ' is the answer"
Answer: a
Problem: car x began traveling at an average speed of 35 miles per hour . after 48 minutes , car y began traveling at an average speed of 39 miles per hour . when both cars had traveled the same distance , both cars stopped . how many miles did car x travel from the time car y began traveling until both cars stopped ?
Options: a ) 105 , b ) 140 , c ) 175 , d ) 210 , e ) 245
Rationale: "in 48 minutes , car x travels 28 miles . car y gains 4 miles each hour , so it takes 7 hours to catch car x . in 7 hours , car x travels 245 miles . the answer is e ."
Answer: e
Problem: how many 4 - digit positive integers are there in which all 4 digits are even ?
Options: a ) 625 , b ) 600 , c ) 500 , d ) 400 , e ) 256
Rationale: "positive integers - 2 , 4,6 , 8,0 let the integers of a four digit positive number be abcd a can take four values ( 2,4 , 6,8 ) b can take five values ( 0 , 2,4 , 6,8 ) c can take five values ( 0 , 2,4 , 6,8 ) d can take five values ( 0 , 2,4 , 6,8 ) the total is 5 * 5 * 5 * 4 the answer according to me is 500 answer : c"
Answer: c
Problem: benny goes to the market for buying some apples to be distributed between her 9 kids equally . she takes 360 dollars with her . the cost of each apple is 4 dollars . how many apples does she buy to share them equally between her eighteen kids ?
Options: a ) 8 , b ) 9 , c ) 5 , d ) 7 , e ) 10
Rationale: cost of each apple = 4 dollars apples that benny can buy with the amount she has = 360 / 4 = 90 . apples that each kid gets evenly = 90 / 18 = 5 apples . so the answer is c = 5
Answer: c
Problem: it takes nine minutes to load a certain video on a cellphone , and fifteen seconds to load that same video on a laptop . if the two devices were connected so that they operated in concert at their respective rates , how many seconds would it take them to load the video , rounded to the nearest hundredth ?
Options: a ) 13.58 , b ) 13.87 , c ) 14.24 , d ) 14.59 , e ) 14.85
Rationale: the laptop can load the video at a rate of 1 / 15 of the video per second . the phone can load the video at a rate of 1 / ( 60 * 9 ) = 1 / 540 of the video per second . the combined rate is 1 / 15 + 1 / 540 = 37 / 540 of the video per second . the time required to load the video is 540 / 37 = 14.59 seconds . the answer is d .
Answer: d
Problem: a sum of money invested at compound interest to rs . 800 in 3 years and to rs 820 in 4 years . the rate on interest per annum is .
Options: a ) 0.4 % , b ) 5.0 % , c ) 2.5 % , d ) 7 % , e ) 8 %
Rationale: explanation : s . i . on rs 800 for 1 year = 20 rate = ( 100 * 20 ) / ( 800 * 1 ) = 2.5 % answer : c
Answer: c
Problem: if two positive numbers are in the ratio 1 / 9 : 1 / 7 , then by what percent is the second number more than the first ?
Options: a ) 67 % . , b ) 70 % . , c ) 60 % . , d ) 28.6 % . , e ) 80 % .
Rationale: "given ratio = 1 / 9 : 1 / 7 = 7 : 9 let first number be 7 x and the second number be 9 x . the second number is more than first number by 2 x . required percentage = 2 x / 7 x * 100 = 28.6 % . answer : d"
Answer: d
Problem: find compound interest on rs . 7500 at 4 % per annum for 2 years , compounded annually
Options: a ) rs 312 , b ) rs 412 , c ) rs 512 , d ) rs 612 , e ) none of these
Rationale: explanation : please apply the formula amount = p ( 1 + r 100 ) nc . i . = amount - p answer : d
Answer: d
Problem: the front wheels of a wagon are 2 π feet in circumference and the rear wheels are 3 π feet in circumference . when the front wheels have made 10 more revolutions than the rear wheels , how many feet has the wagon travelled ?
Options: a ) 30 π , b ) 45 π , c ) 60 π , d ) 90 π , e ) none
Rationale: solution let the rear wheel make x revolutions . then , the front wheel makes ( x + 10 ) revolutions . ( x + 10 ) x 3 π = x × 2 π ‹ = › 3 x + 30 = 2 x ‹ = › x = 30 . distance travelled by the wagon = ( 2 π x 30 ) ft ‹ = › ( 60 π ) ft . answer c
Answer: c
Problem: lcm of two numbers is 7700 and hcf is 11 . if one number is 308 then other number is
Options: a ) 269 , b ) 285 , c ) 300 , d ) 275 , e ) none of these
Rationale: option d
Answer: d
Problem: a car is running at a speed of 80 kmph . what distance will it cover in 20 sec ?
Options: a ) 100 m , b ) 440 m , c ) 180 m , d ) 200 m , e ) 250 m
Rationale: speed = 80 kmph = 80 * 5 / 18 = 22 m / s distance covered in 20 sec = 22 * 10 = 440 m answer is b
Answer: b
Problem: a , b , c subscribe rs . 50,000 for a business . a subscribes rs . 4000 more than b and b rs . 5000 more than c . out of a total profit of rs . 35,000 , a receives
Options: a ) rs . 8400 , b ) rs . 11,900 , c ) rs . 13,600 , d ) rs . 14,700 , e ) none
Rationale: "solution : let c = x . then , b = x + 5000 and a = x + 5000 + 4000 = x + 9000 . so , x + x + 5000 + x + 9000 = 50000 . = > 3 x = 36000 . = > x = 12000 . a : b : c = 21000 : 17000 : 12000 = 21 : 17 : 12 . so a ' s share = rs . ( 35000 x 21 / 50 ) = rs . 14,700 . answer : option d"
Answer: d
Problem: the radius of a cylindrical vessel is 7 cm and height is 2 cm . find the whole surface of the cylinder ?
Options: a ) 281 , b ) 396 , c ) 440 , d ) 767 , e ) 1981
Rationale: "r = 7 h = 2 2 π r ( h + r ) = 2 * 22 / 7 * 7 ( 9 ) = 396 answer : b"
Answer: b
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 r 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 r 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: a train 880 m long is running at a speed of 78 km / hr . if it crosses a tunnel in 1 min , then the length of the tunnel is ?
Options: a ) 510 , b ) 540 , c ) 500 , d ) 420 , e ) 589
Rationale: "speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 1 min = 60 sec . let the length of the train be x meters . then , ( 880 + x ) / 60 = 65 / 3 x = 420 m . answer : option d"
Answer: d
Problem: if x is less than y by 50 % then y exceed x by :
Options: a ) 33.33 % , b ) 100 % , c ) 75 % , d ) 66.66 % , e ) none of these
Rationale: "using formula ( x / ( 100 - x ) * 100 ) where x is percentage decrease ( here it is 25 % ) = > 50 ( 100 - 50 ) * 100 = 100 % answer : b"
Answer: b
Problem: arun purchased 30 kg of wheat at the rate of rs . 11.50 per kg and 20 kg of wheat at the rate of 14.25 per kg . he mixed the two and sold the mixture . approximately what price per kg should be sell the mixture to make 30 % profit ?
Options: a ) 66.3 , b ) 76.3 , c ) 86.3 , d ) 16.3 , e ) 36.3
Rationale: "explanation : c . p . of 50 kg wheat = ( 30 * 11.50 + 20 * 14.25 ) = rs . 630 . s . p . of 50 kg wheat = 130 % of rs . 630 = 130 / 100 * 630 = rs . 819 . s . p . per kg = 819 / 50 = rs . 16.38 = 16.30 . answer : d"
Answer: d
Problem: what was the principal , if at 5 % per annum the interest after 10 years amounted to rs . 3100 less than the sum lent ?
Options: a ) 6200 , b ) 3000 , c ) 3000 , d ) 2000 , e ) 1000
Rationale: "p - 2336 = ( p * 10 * 5 ) / 100 p = 6200 answer : a"
Answer: a
Problem: the list price of an article is rs . 68 . a customer pays rs . 56.16 for it . he was given two successive discounts , one of them being 10 % . the other discount is ?
Options: a ) 3.23 % , b ) 4.23 % , c ) 5.23 % , d ) 7.23 % , e ) 8.23 %
Rationale: "68 * ( 90 / 100 ) * ( ( 100 - x ) / 100 ) = 56.16 x = 8.23 % answer : e"
Answer: e
Problem: the cost of the paint is rs . 36.50 per kg . if 1 kg of paint covers 16 square feet , how much will it cost to paint outside of a cube having 8 feet each side .
Options: a ) rs . 850 , b ) rs . 860 , c ) rs . 876 , d ) rs . 886 , e ) none of these
Rationale: "explanation : we will first calculate the surface area of cube , then we will calculate the quantity of paint required to get answer . here we go , surface area = 6 a 2 = 6 ∗ 8 ( 2 ) = 384 sq feet quantity required = 38416 = 24 kg cost of painting = 36.50 ∗ 24 = rs . 876 option c"
Answer: c
Problem: two consultants can type up a report in 12.5 hours and edit it in 7.5 hours . if mary needs 30 hours to type the report and jim needs 12 hours to edit it alone , how many w hours will it take if jim types the report and mary edits it immediately after he is done ?
Options: a ) 41.4 , b ) 34.1 , c ) 13.4 , d ) 12.4 , e ) 10.8
Rationale: "break down the problem into two pieces : typing and editing . mary needs 30 hours to type the report - - > mary ' s typing rate = 1 / 30 ( rate reciprocal of time ) ( point 1 in theory below ) ; mary and jim can type up a report in 12.5 and - - > 1 / 30 + 1 / x = 1 / 12.5 = 2 / 25 ( where x is the time needed for jim to type the report alone ) ( point 23 in theory below ) - - > x = 150 / 7 ; jim needs 12 hours to edit the report - - > jim ' s editing rate = 1 / 12 ; mary and jim can edit a report in 7.5 and - - > 1 / y + 1 / 12 = 1 / 7.5 = 2 / 15 ( where y is the time needed for mary to edit the report alone ) - - > y = 20 ; how many w hours will it take if jim types the report and mary edits it immediately after he is done - - > x + y = 150 / 7 + 20 = ~ 41.4 answer : a ."
Answer: a
Problem: a scuba diver descends at a rate of 35 feet per minute . a diver dive from a ship to search for a lost ship at the depth of 3500 feet below the sea level . . how long will he take to reach the ship ?
Options: a ) 160 minutes , b ) 120 minutes , c ) 100 minutes , d ) 76 minutes , e ) 77 minutes
Rationale: "time taken to reach = 3500 / 35 = 100 minutes answer : c"
Answer: c
Problem: a snail , climbing a 42 feet high wall , climbs up 4 feet on the first day but slides down 2 feet on the second . it climbs 4 feet on the third day and slides down again 2 feet on the fourth day . if this pattern continues , how many days will it take the snail to reach the top of the wall ?
Options: a ) 20 , b ) 26 , c ) 32 , d ) 39 , e ) 51
Rationale: "total transaction in two days = 4 - 2 = 2 feet in 38 days it will climb 38 feet on the 39 th day , the snail will climb 4 feet , thus reaching the top therefore , total no of days required = 39 d"
Answer: d
Problem: at what rate percent on simple interest will rs . 900 amount to rs . 950 in 5 years ?
Options: a ) 1.11 % , b ) 5.93 % , c ) 4.33 % , d ) 5.33 % , e ) 6.33 %
Rationale: "50 = ( 900 * 5 * r ) / 100 r = 1.11 % answer : a"
Answer: a
Problem: if the price of sugar rises from rs . 10 per kg to rs . 12 per kg , a person , to have no increase in the expenditure on sugar , will have to reduce his consumption of sugar by
Options: a ) 17 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) none
Rationale: "sol . let the original consumption = 100 kg and new consumption = x kg . so , 100 x 10 = x × 12 = x = 83 kg . ∴ reduction in consumption = 17 % . answer a"
Answer: a
Problem: initially , the men and women in a room were in the ratio of 4 : 5 . then , 2 men entered the room and 3 women left the room . then , the number of women doubled . now there are 14 men in the room . how many e women are currently in the room ?
Options: a ) 12 , b ) 14 , c ) 15 , d ) 24 , e ) 36
Rationale: "the number of women doubled means that they have become 24 from 12 . . and we have to tell the current strength so 24 is the answer . . let the number be 4 x and 5 x . . given 4 x + 2 = 14 . . so x = 3 . . women number = 5 * 3 - 3 = 12 , then doubled = 24 . . ans d"
Answer: d
Problem: find the compound ratio of ( 2 : 3 ) , ( 3 : 4 ) and ( 1 : 4 ) is
Options: a ) 1 : 2 , b ) 2 : 3 , c ) 1 : 8 , d ) 4 : 5 , e ) 3 : 2
Rationale: "required ratio = 2 / 3 * 3 / 4 * 1 / 4 = 1 / 8 = 1 : 8 answer is c"
Answer: c
Problem: in a neighborhood having 90 households , 11 did not have either a car or a bike . if 16 households had a both a car and a bike and 44 had a car , how many had bike only ?
Options: a ) 30 , b ) 35 , c ) 20 , d ) 18 , e ) 10
Rationale: "{ total } = { car } + { bike } - { both } + { neither } - - > 90 = 44 + { bike } - 16 + 11 - - > { bike } = 51 - - > # those who have bike only is { bike } - { both } = 51 - 16 = 35 . answer : b ."
Answer: b
Problem: a bag marked at $ 150 is sold for $ 120 . the rate of discount is ?
Options: a ) 10 % , b ) 25 % , c ) 20 % , d ) 50 % , e ) 45 %
Rationale: "rate of discount = 30 / 150 * 100 = 20 % answer is c"
Answer: c
Problem: a man swims downstream 70 km and upstream 30 km taking 10 hours each time ; what is the speed of the current ?
Options: a ) 1 , b ) 4 , c ) 2 , d ) 6 , e ) 8
Rationale: "70 - - - 10 ds = 7 ? - - - - 1 30 - - - - 10 us = 3 ? - - - - 1 s = ? s = ( 7 - 3 ) / 2 = 2 answer : c"
Answer: c
Problem: a certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 8 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ?
Options: a ) 42 , b ) 70 , c ) 140 , d ) 196 , e ) 315
Rationale: "ans : 196 7 c 1 * 8 c 2 answer d )"
Answer: d
Problem: a certain store sells all maps at one price and all books at another price . on monday the store sold 12 maps and 10 books for a total of $ 38.00 , and on tuesday the store sold 12 maps and 9 books for a total of $ 30.00 . at this store , how much less does a map sell for than a book ?
Options: a ) $ 0.25 , b ) $ 0.50 , c ) $ 0.75 , d ) $ 1.00 , e ) $ 4.5
Rationale: "12 x + 10 y = 38 12 x + 9 y = 30 subtracting 1 from 2 y = 8 therefore x = 3.5 difference in price = 4.5 e"
Answer: e
Problem: if an object travels at three feet per second , how many feet does it travel in one hour ?
Options: a ) 3488 , b ) 10800 , c ) 12788 , d ) 1800 , e ) 2881
Rationale: explanation : if an object travels at 2 feet per second it covers 3 x 60 feet in one minute , and 3 x 60 x 60 feet in one hour . answer = 10800 answer : b ) 10800
Answer: b
Problem: the length of a rectangle is twice its breadth . if its length is decreased by 5 cm and breadth is increased by 5 cm , the area of the rectangle is increased by 55 sq . cm . find the length of the rectangle .
Options: a ) 16 cm , b ) 18 cm , c ) 15 cm , d ) 20 cm , e ) 23 cm
Rationale: "explanation : let breadth = x . then , length = 2 x . then , ( 2 x - 5 ) ( x + 5 ) - 2 x * x = 55 = > 5 x - 25 = 55 = > x = 16 . length of the rectangle = 16 cm . answer : option a"
Answer: a