regisss/math_qa huggingface dataset:
Problem: when x is even , [ x ] = x / 2 + 1 , when x is odd [ x ] = 2 x + 1 then [ 5 ] * [ 4 ] = ?
Options: a ) [ 33 ] , b ) [ 44 ] , c ) [ 45 ] , d ) [ 88 ] , e ) [ 90 ]
Rationale: "[ 5 ] * [ 4 ] = ( 2 * 5 + 1 ) ( 4 / 2 + 1 ) = [ 33 ] . ans - a"
Answer: a
Problem: 765 chairs are to be arranged in a column in such a way that the number of chairs in each column should be equal to the columns . how many chairs will be excluded to make this arrangement possible ?
Options: a ) 6 , b ) 36 , c ) 19 , d ) 27 , e ) none of these
Rationale: 27 ( 2 ) < 765 < 28 ( 2 ) ∴ required no . of chairs to be excluded = 765 – 729 = 36 answer b
Answer: b
Problem: a mobile battery in 1 hour charges to 20 percent . how much time ( in minute ) will it require more to charge to 40 percent .
Options: a ) 120 , b ) 150 , c ) 175 , d ) 160 , e ) 130
Rationale: 1 hr = 20 percent . thus 15 min = 5 percent . now to charge 40 percent 120 min . answer : a
Answer: a
Problem: if a lends rs . 3500 to b at 10 % per annum and b lends the same sum to c at 11 % per annum then the gain of b in a period of 3 years is ?
Options: a ) 110 , b ) 106 , c ) 105 , d ) 107 , e ) 109
Rationale: "( 3500 * 1 * 3 ) / 100 = > 105 answer : c"
Answer: c
Problem: x and y began business with rs . 10000 and rs . 8000 after 6 months , x advances rs . 2000 and y advances rs . 2000 more . at the end of the year , their profits amounted to rs . 2000 find the share of x and y respectively .
Options: a ) 10001000 , b ) 9001100 , c ) 1200800 , d ) 8001200 , e ) 1100 , 900
Rationale: ( 10 * 6 + 12 * 6 ) : ( 8 * 6 + 10 * 6 ) 11 : 9 x share = 11 / 20 * 2000 = 1100 . y share = 9 / 20 * 2000 = 900 . x and y share respectively is 1100 , 900 . answer : e
Answer: e
Problem: in a group of ducks and cows , the total number of legs are 30 more than twice the no . of heads . find the total no . of buffaloes .
Options: a ) 11 , b ) 12 , c ) 14 , d ) 15 , e ) 18
Rationale: "let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 30 = > 2 x = 30 = > x = 15 d"
Answer: d
Problem: the l . c . m of two numbers is 48 . the numbers are in the ratio 1 : 2 . the sum of numbers is :
Options: a ) 28 , b ) 30 , c ) 40 , d ) 50 , e ) 72
Rationale: "let the numbers be 1 x and 2 x . then , their l . c . m = 2 x . so , 2 x = 48 or x = 24 . the numbers are 24 and 48 . hence , required sum = ( 24 + 48 ) = 72 . answer : e"
Answer: e
Problem: a certain fraction has the same ratio to 1 / 36 , as 4 / 7 does to 5 / 9 . what is this certain fraction ?
Options: a ) 1 / 35 , b ) 1 / 42 , c ) 1 / 49 , d ) 1 / 56 , e ) 1 / 63
Rationale: x / ( 1 / 36 ) = ( 4 / 7 ) / ( 5 / 9 ) x = 4 * 9 * 1 / 36 * 7 * 5 = 1 / 35 the answer is a .
Answer: a
Problem: there are 780 male and female participants in a meeting . half the female participants and one - quarter of the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ?
Options: a ) 75 , b ) 100 , c ) 125 , d ) 130 , e ) 225
Rationale: "female = x male = 780 - x x / 2 + 780 - x / 4 = 1 / 3 * ( 780 ) = 260 x = 260 x / 2 = 130 is supposed to be the answer m is missing something correct option d"
Answer: d
Problem: two goods trains each 2000 m long are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 228 , b ) 278 , c ) 192 , d ) 27 , e ) 21
Rationale: "relative speed = 45 + 30 = 75 km / hr . 75 * 5 / 18 = 125 / 6 m / sec . distance covered = 2000 + 2000 = 4000 m . required time = 4000 * 6 / 125 = 192 sec . answer : c"
Answer: c
Problem: what sum of money will produce rs . 70 as simple interest in 4 years at 3 1 / 2 percent ?
Options: a ) 289 , b ) 500 , c ) 188 , d ) 666 , e ) 155
Rationale: "70 = ( p * 4 * 7 / 2 ) / 100 p = 500 answer : b"
Answer: b
Problem: a man is 34 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is ?
Options: a ) 16 , b ) 19 , c ) 15 , d ) 32 , e ) 40
Rationale: "let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . ( x + 34 ) + 2 = 2 ( x + 2 ) x + 36 = 2 x + 4 = > x = 32 . answer : d"
Answer: d
Problem: a jogger running at 9 km / hr along side a railway track is 240 m ahead of the engine of a 130 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?
Options: a ) 28 sec , b ) 16 sec , c ) 37 sec , d ) 18 sec , e ) 17 sec
Rationale: "speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 240 + 120 = 370 m . time taken = 370 / 10 = 37 sec . answer : c"
Answer: c
Problem: a train running at a speed of 36 km / h passes an electric pole in 14 seconds . in how many seconds will the whole train pass a 360 - meter long platform ?
Options: a ) 44 , b ) 46 , c ) 48 , d ) 50 , e ) 52
Rationale: "let the length of the train be x meters . when a train crosses an electric pole , the distance covered is its own length x . speed = 36 km / h = 36000 m / 3600 s = 10 m / s x = 14 * 10 = 140 m . the time taken to pass the platform = ( 140 + 360 ) / 10 = 50 seconds the answer is d ."
Answer: d
Problem: if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer m that must divide n is ?
Options: a ) 6 , b ) 12 , c ) 24 , d ) 36 , e ) 48
Rationale: "q : if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer m that must divide n is : a 6 , b 12 , c 24 , d 36 , e 48 n ^ 2 is divisible by 72 , but it must also be greater than 72 . if n is an integer , then n ^ 2 must be a perfect square . the factorization of 72 is ( 8 ) ( 9 ) , so if it is multiplied by 2 , it will be ( 2 ) ( 8 ) ( 9 ) = ( 16 ) ( 9 ) = 144 , a perfect square . so n ^ 2 must be at least 144 or a multiple of 144 , which means that n must be 12 or a multiple of 12 . b"
Answer: b
Problem: a brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 27 m * 2 m * 0.75 m ?
Options: a ) 29798 , b ) 27908 , c ) 78902 , d ) 25000 , e ) 27000
Rationale: 27 * 2 * 0.75 = 20 / 100 * 10 / 100 * 7.5 / 100 * x 27 = 1 / 100 * x = > x = 27000 answer : e
Answer: e
Problem: one - fourth of the workers in palabras bookstore have read the latest book by j . saramago , and 5 / 8 of the workers have read the latest book by h . kureishi . the number of workers that have read neither book is one less than the number of the workers that have read the latest saramago book and have not read the latest kureishi book . if there are 72 workers in the palabras bookstore , how many of them have read both books ?
Options: a ) 13 , b ) 12 , c ) 9 , d ) 8 , e ) 4
Rationale: "there are total 72 workers . one - fourth of the workers in palabras bookstore have read the latest book by j . saramago , so 18 have read saramago . 5 / 8 of the workers have read the latest book by h . kureishi . so ( 5 / 8 ) * 72 = 45 have read kureishi the number of workers that have read neither book is one less than the number of the workers that have read the latest saramago book and have not read the latest kureishi book if b workers have read both books , 18 - b have read saramago but not kureishi . so , ( 18 - b - 1 ) have read neither . total = n ( a ) + n ( b ) - both + neither 72 = 18 + 45 - b + ( 18 - b - 1 ) b = 4 answer ( e )"
Answer: e
Problem: in traveling from a dormitory to a certain city , a student went 1 / 4 of the way by foot , 1 / 2 of the way by bus , and the remaining 10 kilometers by car . what is the distance , in kilometers , from the dormitory to the city ?
Options: a ) 10 , b ) 45 , c ) 30 , d ) 20 , e ) 40
Rationale: "whole trip = distance by foot + distance by bus + distance by car x = 1 / 4 x + 1 / 2 x + 10 x - 1 / 4 x - 1 / 2 x = 10 x = 40 km option : e"
Answer: e
Problem: if ( 1 / 5 ) ^ m * ( 1 / 4 ) ^ 4 = 1 / ( 16 * ( 10 ) ^ 4 ) , then m =
Options: a ) 3 , b ) 2 , c ) 1 , d ) 4 , e ) 8
Rationale: "( 1 / 5 ) ^ m ( 1 / 4 ) ^ 4 = 1 / { 16 ( 10 ) ^ 4 } 16 ( 10 ) ^ 4 / 4 ^ 4 = 5 ^ m [ 16 ( 2 ^ 4 ) ( 5 ^ 4 ) ] / [ 2 ^ 8 ] = 5 ^ m 5 ^ 4 = 5 ^ m m = 4 d"
Answer: d
Problem: in the faculty of reverse - engineering , 220 second year students study numeric methods , 423 second year students study automatic control of airborne vehicles and 134 second year students study them both . how many students are there in the faculty if the second year students are approximately 80 % of the total ?
Options: a ) 515 . , b ) 545 . , c ) 618 . , d ) 644 . , e ) 636 .
Rationale: answer is e : 636 solution : total number of students studying both are 423 + 220 - 134 = 509 ( subtracting the 134 since they were included in the both the other numbers already ) . so 80 % of total is 509 , so 100 % is approx . 636 .
Answer: e
Problem: what would be the minimum number of pumps required to fill a tank of 1000 m 3 to 85 % in one hour ? the capacity of the pump is 150 m 3 / hour and operates at an efficiency of 75 % .
Options: a ) 6 , b ) 8 , c ) 10 , d ) 11 , e ) 12
Rationale: volume handled by pump in one hour = 150 x . 75 = 112.5 volume of the tank that needs to be filled = 1000 x . 85 = 850 number of pumps needed = 850 / 112.5 = 7.55 â ‰ ˆ 8 answer : b
Answer: b
Problem: of the land owned by a farmer , 90 percent was cleared for planting . of the cleared land , 60 percent was planted with grapes and 30 percent of the cleared land was planted with potato . if the remaining 360 acres of cleared land was planted with tomato , how many acres did the farmer own ?
Options: a ) 3250 , b ) 3450 , c ) 4000 , d ) 3750 , e ) 3800
Rationale: 60 % of 90 % = 54 % , 30 % 0 f 90 % = 27 % so the remaining 90 - 54 - 27 = 9 % = 360 acres or 10 % of 90 % = 9 % - - > 360 / 9 * 100 = 4000 acres answer ( c )
Answer: c
Problem: the ratio of investments of two partners p and q is 7 : 5 and the ratio of their profits is 7 : 10 . if p invested the money for 8 months , find for how much time did q invest the money ?
Options: a ) 11 , b ) 10 , c ) 18 , d ) 16 , e ) 12
Rationale: "7 * 5 : 8 * x = 7 : 10 x = 16 answer : d"
Answer: d
Problem: a monkey ascends a greased pole 12 metres high . he ascends 2 metres in first minute and slips down 1 metre in the alternate minute . in which minute , he reaches the top ?
Options: a ) 21 st , b ) 22 nd , c ) 23 rd , d ) 24 th , e ) none of these
Rationale: in 2 minutes , he ascends = 1 metre ∴ 10 metres , he ascends in 20 minutes . ∴ he reaches the top in 21 st minute . answer b
Answer: b
Problem: what will be the remainder when 17 ^ 200 is divided by 18
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "17 ^ 200 % 18 ( 17 - 18 ) ^ 200 % 18 ( - 1 ) ^ 200 % 18 1 % 18 = 1 answer : a"
Answer: a
Problem: sakshi invests a part of rs . 12000 in 12 % stock at rs . 120 and the remainder in 15 % stock at rs . 125 . if his total dividend per annum is rs . 1360 , how much does he invest in 12 % stock at rs . 120 ?
Options: a ) rs . 4000 , b ) rs . 4500 , c ) rs . 5500 , d ) rs . 6000 , e ) rs . 6500
Rationale: let investment in 12 % stock be rs . x . then , investment in 15 % stock = rs . ( 12000 - x ) . 12 / 120 * x + 15 / 125 * ( 12000 - x ) = 1360 x / 10 + 3 / 25 ( 12000 - x ) = 1360 5 x + 72000 - 6 x = 1360 x 50 x = 4000 . answer = a
Answer: a
Problem: xavier , yvonne , and zelda each try independently to solve a problem . if their individual probabilities for success are 1 / 5 , 1 / 2 and 5 / 8 , respectively , what is the probability that xavier and yvonne , but not zelda , will solve the problem ?
Options: a ) 11 / 8 , b ) 3 / 80 , c ) 9 / 64 , d ) 5 / 64 , e ) 3 / 64
Rationale: "p ( xavier will solve ) = 1 / 5 p ( yvonne will solve ) = 1 / 2 p ( zelda will not solve ) = 1 - 5 / 8 = 3 / 8 . now , we need to multiply all this ps to find an answer : p = ( 1 / 5 ) * ( 1 / 2 ) * ( 3 / 8 ) = 3 / 80 . ans . b ."
Answer: b
Problem: in a college , the ratio of the number of boys to girls is 8 : 5 . if there are 400 girls , the total number of students in the college is
Options: a ) 1040 , b ) 920 , c ) 980 , d ) 720 , e ) 820
Rationale: "explanation : let the boy are 8 x and girls are 5 x = > 5 x = 400 = > x = 80 total students = 8 x + 5 x = 13 x = 13 ( 80 ) = 1040 option a"
Answer: a
Problem: the tax on a commodity is diminished by 18 % and its consumption increased by 15 % . the effect on revenue is ?
Options: a ) 2 % , b ) 8.7 % , c ) 5.7 % , d ) 6.7 % , e ) 1 %
Rationale: "100 * 100 = 10000 82 * 115 = 9430 - - - - - - - - - - - 10000 - - - - - - - - - - - 570 100 - - - - - - - - - - - ? = > 5.7 % decrease answer : c"
Answer: c
Problem: a can do a job in 10 days and b can do it in 30 days . a and b working together will finish twice the amount of work in - - - - - - - days ?
Options: a ) 21 ½ days , b ) 22 ½ days , c ) 23 ½ days , d ) 15 days , e ) none of these
Rationale: "explanation : 1 / 10 + 1 / 30 = 4 / 30 = 2 / 15 15 / 2 = 15 / 2 * 2 = 15 days answer : d"
Answer: d
Problem: if jamie ' s income is rs 20000 , calculate his savings given that his income and expenditure are in the ratio 7 : 5 . ?
Options: a ) rs 7500 , b ) rs 4000 , c ) rs 2000 , d ) rs 8000 , e ) rs 7000
Rationale: let the income and the expenditure of the person be rs . 7 x and rs . 7 x respectively . income , 7 x = 28000 = > x = 4000 savings = income - expenditure = 7 x - 5 x = 2 x so , savings = rs . 8000 answer : d
Answer: d
Problem: a sum fetched a total simple interest of rs . 4016.25 at the rate of 1 % p . a . in 5 years . what is the sum ?
Options: a ) 82762 , b ) 12877 , c ) 82882 , d ) 80925 , e ) 80325
Rationale: "principal = ( 100 * 4016.25 ) / ( 1 * 5 ) = rs . 80325 . answer : e"
Answer: e
Problem: on thrusday mabel handled 90 transactions . anthony handled 10 % more transaction than mabel , cal handled 2 / 3 rds of the transactions that anthony handled and jade handled 16 more transaction than cal . how much transaction did jade handled ?
Options: a ) 92 , b ) 80 , c ) 72 , d ) 82 , e ) 28
Rationale: mabel handled 90 transaction , anthony 10 % more transaction the mabel . anthony = 90 + 90 * 10 % , = 90 + 90 * 0.10 , = 90 + 9 , = 99 , cal handled 2 / 3 rds than anthony handled , cal = 2 / 3 * 99 = 66 , jade handled 16 more than cal . jade = 66 + 16 = 82 , jade handled = 82 tranasactions . correct answer : ( d )
Answer: d
Problem: jar x is 1 / 3 full of water . jar y , which has half the capacity of jar x , is 1 / 2 full of water . if the water in jar y is poured into jar x , then jar x will be filled to what fraction of its capacity ?
Options: a ) 5 / 6 , b ) 5 / 12 , c ) 7 / 12 , d ) 7 / 18 , e ) 11 / 18
Rationale: "let p be the capacity of jar x . the amount of water in jar y is 1 / 2 * p / 2 = p / 4 then the total amount in jar x is p / 3 + p / 4 = 7 p / 12 the answer is c ."
Answer: c
Problem: a cement mixture is composed of 3 elements . by weight , 1 / 3 of the mixture is sand , 1 / 4 of the mixture is water , and the remaining 10 pounds of the mixture is gravel . what is the weight of the entire mixture in pounds ?
Options: a ) 24 , b ) 26 , c ) 28 , d ) 30 , e ) 36
Rationale: "let the total weight be x . sand content = ( 1 / 3 ) x water content = ( 1 / 4 ) x gravel = x - ( 1 / 3 ) x - ( 1 / 4 ) x = ( 5 / 12 ) x = 10 x = 24 then answer will be a = 24"
Answer: a
Problem: 0.01 is what percent of 0.1 ?
Options: a ) 1 % , b ) 10 % , c ) 100 % , d ) 50 % , e ) 25 %
Rationale: "required percentage = 0.01 * 100 / 0.1 = 100 / 10 = 10 % answer is b"
Answer: b
Problem: a 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 26 sec . what is the length of the platform ?
Options: a ) 389 m , b ) 150 m , c ) 289 m , d ) 299 m , e ) 219 m
Rationale: "speed = 300 / 26 = 150 / 13 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 39 = 150 / 13 = > x = 150 m . answer : b"
Answer: b
Problem: 9 persons went to a hotel for taking their meals . 8 of them spent rs 12 each on their meals and the ninth spent rs . 8 more than the average expenditure of all the 9 . what was the total money spent by them ?
Options: a ) 117 , b ) 180 , c ) 150 , d ) 200 , e ) 250
Rationale: exp . let the total expenditure be x , then the average = x / 9 , 8 * 12 + [ x / 9 + 8 ] = x or [ x - x / 9 ] = 104 . 8 x / 9 = 104 , x = 104 * 9 / 8 = 117 . answer : a
Answer: a
Problem: a car started running at a speed of 30 km / hr and the speed of the car was increased by 2 km / hr at the end of every hour . find the total distance covered by the car in the first 7 hours of the journey .
Options: a ) 342 km , b ) 352 km , c ) 252 km , d ) 742 km , e ) 382 km
Rationale: "the total distance covered by the car in the first 7 hours = 30 + 32 + 34 + 36 + 38 + 40 + 42 = sum of 7 terms in ap whose first term is 30 and last term is 42 = 7 / 2 [ 30 + 42 ] = 252 km . answer : c"
Answer: c
Problem: the average ( arithmetic mean ) of 4 positive integers is 40 . if the average of 2 of these integers is 45 , what is the greatest possible value that one of the other 2 integers can have ?
Options: a ) 55 , b ) 69 , c ) 100 , d ) 109 , e ) 115
Rationale: a + b + c + d = 160 a + b = 90 c + d = 70 greatest possible = 69 ( just less than 1 ) answer = b
Answer: b
Problem: what is the least number of square tiles required to pave the floor of a room 12 m 12 cm long and 1 m 20 cm broad ?
Options: a ) 1010 , b ) 804 , c ) 814 , d ) 844 , e ) none
Rationale: "solution length of largest tile = h . c . f . of 1212 cm & 120 cm = 12 cm . area of each tile = ( 12 x 12 ) cm 2 ∴ required number of tiles = [ 1212 x 120 / 12 x 12 ] = 1010 . answer a"
Answer: a
Problem: if 2 x = 3 √ 32 , then x is equal to :
Options: a ) 3 / 5 , b ) 5 / 3 , c ) 15 , d ) 25 , e ) none
Rationale: "sol . 2 x = 3 √ 32 ⇔ 2 x = ( 32 ) 1 / 3 = ( 25 ) 1 / 3 = 25 / 3 ⇔ x = 5 / 3 . answer b"
Answer: b
Problem: a train running at the speed of 48 km / hr crosses a pole in 9 seconds . find the length of the train ?
Options: a ) 120 meter , b ) 299 meter , c ) 666 meter , d ) 155 meter , e ) 144 meter
Rationale: "speed = 48 * ( 5 / 18 ) m / sec = 40 / 3 m / sec length of train ( distance ) = speed * time ( 40 / 3 ) * 9 = 120 meter answer : a"
Answer: a
Problem: a cricket player whose bowling average was 20.5 runs per wicket , takes 5 wicket for 52 runs in a match . due to this his average decreases by 0.5 . what will be the number of wickets taken by him till the last match ?
Options: a ) 64 , b ) 72 , c ) 101 , d ) 111 , e ) 128
Rationale: "average = total runs / total wickets total runs after last match = 20.5 w + 52 total wickets after last match = w + 5 ( 20.5 w + 52 ) / ( w + 5 ) = 20.5 - 0.5 = 20 w = 96 so total wickets aftr last match = w + 5 = 101 answer : c"
Answer: c
Problem: if a trader sold two cars each at rs . 325475 and gains 11 % on the first and loses 11 % on the second , then his profit or loss percent on the whole is ?
Options: a ) 1.21 % , b ) 1.74 % , c ) 1.84 % , d ) 1.47 % , e ) 1.24 %
Rationale: "sp of each car is rs . 325475 , he gains 11 % on first car and losses 11 % on second car . in this case , there will be loss and percentage of loss is given by = [ ( profit % ) ( loss % ) ] / 100 = ( 11 ) ( 11 ) / 100 % = 1.21 % answer : a"
Answer: a
Problem: 3 buffaloes eat as much as 4 cows or 2 oxen . at a farm , there are 15 buffaloes , 8 oxen , and 24 cows . the fodder for these cattle is available for 36 days . if 40 more cows and 15 more buffaloes are brought in , how many days will the fodder last ?
Options: a ) 15 days , b ) 18 days , c ) 21 days , d ) 24 days , e ) 27 days
Rationale: "2 oxen = 3 buffaloes = 4 cows also : 15 buffaloes + 8 oxen + 24 cows = 10 oxen + 8 oxen + 12 oxen = 30 oxen there is enough fodder for 1 oxen for 30 * 36 days . 40 cows + 15 buffaloes = 20 oxen + 10 oxen = 30 oxen the new total is equal to 60 oxen instead of 30 oxen . 30 * 36 / 60 oxen = 18 days the answer is b ."
Answer: b
Problem: for any non - zero a and b that satisfy | ab | = ab and | a | = a | b - 4 | + | ab - b | = ?
Options: a ) ab - 4 , b ) 2 b - ab - 4 , c ) ab + 4 , d ) ab - 2 b + 4 , e ) 4 - ab
Rationale: | ab | = ab and | a | = - a = > b is also negative . so | b - 4 | + | ab - b | = ( b - 4 ) + ab - b ( as ab is positive and - b is positive , so expression is totally positive ) = b - 4 + ab - b = ab - 4 answer - a
Answer: a
Problem: p software has coding line 5 % more than n , n software has coding line 1 / 3 more than m . m software has 90 lines of coding . find p lines .
Options: a ) 106 , b ) 107 , c ) 126 , d ) 109 , e ) 110
Rationale: m s / w has 90 line of code n s / w has = 90 + 90 * 1 / 3 = 120 line of code p s / w 5 % more n ' code 120 + 6 = 126 answer : c
Answer: c
Problem: the length of a rectangle is 4 times its width . if the width of the rectangle is 5 inches , what is the rectangle ' s area , in square inches ?
Options: a ) 30 square inches , b ) 75 square inches , c ) 100 square inches , d ) 89 square inches , e ) 92 square inches
Rationale: "if the width is 5 in and the length is 4 times the width , then the length is 4 * 5 = 20 in the area is given by 5 * 20 = 100 square inches correct answer c"
Answer: c
Problem: a and b go around a circular track of length 1800 m on a cycle at speeds of 36 kmph and 54 kmph . after how much time will they meet for the first time at the starting point ?
Options: a ) 120 sec , b ) 165 sec , c ) 186 sec , d ) 167 sec , e ) 360 sec
Rationale: time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 1800 / ( 36 * 5 / 18 ) , 1800 / ( 54 * 5 / 18 ) } = lcm ( 180 , 120 ) = 360 sec . answer : e
Answer: e
Problem: if f ( x ) = 3 x ^ 4 - 4 x ^ 3 - 3 x ^ 2 + 6 x , then f ( - 1 ) =
Options: a ) - 2 , b ) - 1 , c ) 0 , d ) 1 , e ) 2
Rationale: f ( - 1 ) = 3 ( - 1 ) ^ 4 - 4 ( - 1 ) ^ 3 - 3 ( - 1 ) ^ 2 + 6 ( - 1 ) = 3 + 4 - 3 - 6 = - 2 the answer is a .
Answer: a
Problem: the greatest common divisor of ( b - 2 ) ! , ( b + 1 ) ! , and ( b + 4 ) ! is 5040 . what is the value of b ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 9 , e ) 6
Rationale: gcd of ( b - 2 ) ! , ( b + 1 ) ! , and ( b + 4 ) ! is 5040 . find x . best way to find n is substitute each of the answer and find out the correct one . only option d gave the correct answer . option d : 9 and find gcd or 7 ! , 10 ! and 13 ! . 7 ! itself is 5040 and 7 ! which is contained in the other two factorials . this satisfies the condition , hence answer is 9 . answer is d .
Answer: d
Problem: the length of a side of a hexagon is 10 inches . what is the perimeter ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 60
Rationale: "hexagon . it means 6 equal sides . p = 6 ( 10 ) = 60 inches answer e"
Answer: e
Problem: in february wilson ’ s earnings were 40 percent of his family ’ s total income . in march wilson earned 25 percent less than in february . if the rest of his family ’ s income was the same in both months , then , in march , wilson ’ s earnings were approximately what percent s of his family ’ s total income ?
Options: a ) 15 % , b ) 17 % , c ) 24 % , d ) 30 % , e ) 33 %
Rationale: "lets suppose the total family income in feb = 100 x wilson ' s earning in feb = 40 % of 100 x = 40 x earnings of remaining family in feb = 100 x - 40 x = 60 x wilson ' s earning in march = 75 % of wilson ' s feb earnings = 75 % of 40 x = 30 x earnings of remaining family in march = earnings of remaining family in feb = 60 x thus wilson ' s earning as % of total family income in march s = 30 x / ( 30 + 60 ) x = 30 x / 90 x = 33.33 % thus answer is e"
Answer: e
Problem: if a : b = 1 : 4 , b : c = 13 : 9 , c : d = 5 : 13 , find a : d ?
Options: a ) 5 / 46 , b ) 7 / 36 , c ) 1 / 36 , d ) 5 / 36 , e ) 5 / 37
Rationale: a / d = ( 1 / 4 ) * ( 13 / 9 ) * ( 5 / 13 ) = > 5 / 36 answer : d
Answer: d
Problem: in a rectangular coordinate system , what is the area of a rectangle whose vertices have the coordinates ( - 5 , 1 ) , ( 1 , 1 ) , ( 1 , - 4 ) and ( - 5 , - 4 ) ?
Options: a ) 20
b ) 30
c ) 40
d ) 55
e ) 48
Rationale: length of side 1 = 5 + 1 = 6 length of side 2 = 4 + 1 = 5 area of rectangle = 6 * 5 = 30 b is the answer
Answer: b
Problem: population of a city in 20004 was 1000000 . if in 2005 there isan increment of 15 % , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 30 % , then find the population of city atthe end of the year 2007
Options: a ) 976374 , b ) 971750 , c ) 980241 , d ) 2356677 , e ) 1083875
Rationale: "required population = p ( 1 + r 1 / 100 ) ( 1 - r 2 / 100 ) ( 1 + r 3 / 100 ) = p ( 1 + 15 / 100 ) ( 1 - 35 / 100 ) ( 1 + 30 / 100 ) = 971750 b"
Answer: b
Problem: what is the greatest value of positive integer x such that 2 ^ x is a factor of 100 ^ 90 ?
Options: a ) 180 , b ) 160 , c ) 140 , d ) 150 , e ) 120
Rationale: "put in simple words , we need to find the highest power of 2 in 100 ^ 90 100 = 2 ^ 2 * 5 ^ 2 therefore 100 ^ 90 = ( 2 ^ 2 * 5 ^ 2 ) ^ 90 = 2 ^ 180 * 5 ^ 180 answer : a"
Answer: a
Problem: alex takes a loan of $ 9,000 to buy a used truck at the rate of 9 % simple interest . calculate the annual interest to be paid for the loan amount .
Options: a ) 680 , b ) 810 , c ) 800 , d ) 730 , e ) 750
Rationale: from the details given in the problem principle = p = $ 9,000 and r = 9 % or 0.09 expressed as a decimal . as the annual interest is to be calculated , the time period t = 1 . plugging these values in the simple interest formula , i = p x t x r = 9,000 x 1 x 0.09 = 810.00 annual interest to be paid = $ 810 answer : b
Answer: b
Problem: last month , john rejected 0.7 % of the products that he inspected and jane rejected 0.8 percent of the products that she inspected . if total of 0.75 percent of the products produced last month were rejected , what fraction of the products did jane inspect ?
Options: a ) 1 / 6 , b ) 1 / 2 , c ) 5 / 8 , d ) 5 / 6 , e ) 15 / 16
Rationale: "x - fraction of products jane inspected ( 1 - x ) - fraction of products john inspected 0.8 ( x ) + 0.7 ( 1 - x ) = 0.75 0.1 x = 0.75 - 0.7 x = 0.05 / 0.1 x = 1 / 2 therefore the answer is b : 1 / 2 ."
Answer: b
Problem: if the average ( arithmetic mean ) of x and y is 60 , and z – x = 80 , what is the average of y and z ?
Options: a ) 100 , b ) 120 , c ) 125 , d ) 115 , e ) 90
Rationale: "x + y / 2 = 60 = > x + y = 120 x = z - 80 . . . sub this value z - 80 + y = 120 = > z + y = 200 = > z + y / 2 = 100 answer : a"
Answer: a
Problem: what is the smallest integer z for which 27 ^ z > 3 ^ 24 ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 12
Rationale: "27 ^ z > 3 ^ 24 converting into the same bases : 27 ^ z > 27 ^ 8 therefore for the equation to hold true , z > 8 or z = 9 option c"
Answer: c
Problem: a is twice as good a work man as b and together they finish the work in 8 days . in how many days a alone can finish the work ?
Options: a ) 23 , b ) 12 , c ) 77 , d ) 92 , e ) 61
Rationale: "wc = 2 : 1 2 x + x = 1 / 8 = > x = 1 / 24 2 x = 1 / 12 a can do the work in 12 days . answer : b"
Answer: b
Problem: the sum of two numbers is 21 and the sum of their squares is 527 . find the product of the numbers .
Options: a ) 48 , b ) 41 , c ) 46 , d ) 43 , e ) 96
Rationale: let a and b be the two numbers ( a + b ) ^ 2 = a ^ 2 + 2 ab + b ^ 2 given ( a + b ) = 21 a ^ 2 + b ^ 2 = 527 so , 21 ^ 2 = 527 + 2 ab 2 ab = 527 - 441 2 ab = 86 ab = 43 ans d
Answer: d
Problem: thabo owns exactly 280 books , and each book is either paperback fiction , paperback nonfiction , or hardcover nonfiction . if he owns 20 more paperback nonfiction books than hardcover nonfiction books , and twice as many paperback fiction books as paperback nonfiction books , how many hardcover books nonfiction books does thabo own ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 55
Rationale: "i think we can use double - matrix method and solve using only one variable . our goal is to find the number of hardcover nonfiction books . let that number be x . we are given that all 140 books are either paperback fiction , paperback nonfiction , or hardcover nonfiction . this implies that number of hardcover fiction books is 0 . double - matrix : p = paperback ; h = hardcover ; f = fiction ; nf = nonfiction p h total f 2 x + 40 0 nf x + 20 x total 3 x + 60 x 280 3 x + 60 + x = 280 x = 55 answer ( e . )"
Answer: e
Problem: in the number 100 ab , a and b represent the tens and units digits , respectively . if 110 ab is divisible by 55 , what is the greatest possible value of b × a ?
Options: a ) 0 , b ) 5 , c ) 10 , d ) 15 , e ) 25
Rationale: you should notice that 55 * 2 = 110 so 11,000 is divisible by 55 : 55 * 200 = 11,000 ( or you can notice that 11,000 is obviously divisible by both 5 and 11 so by 55 ) - - > b * a = 0 * 0 = 0 . next number divisible by 55 is 11,000 + 55 = 11,055 : b * a = 5 * 5 = 15 ( next number wo n ' t have 110 as the first 3 digits so we have only two options 0 and 25 ) . answer : e . ! please post ps questions in the ps subforum : gmat - problem - solving - ps - 140 / please post ds questions in the ds subforum : gmat - data - sufficiency - ds - 141 / no posting of ps / ds questions is allowed in the mainmath forum . d
Answer: d
Problem: a train 350 m long , running with a speed of 63 km / hr will pass a tree in ?
Options: a ) 22 sec , b ) 16 sec , c ) 17 sec , d ) 88 sec , e ) 20 sec
Rationale: "speed = 63 * 5 / 18 = 35 / 2 m / sec time taken = 350 * 2 / 35 = 20 sec answer : e"
Answer: e
Problem: a car travelling with 5 / 7 km of its actual speed covers 42 km in 1 hr 40 min 48 sec find the actual speed of the car ?
Options: a ) 78 kmph , b ) 85 kmph , c ) 35 kmph , d ) 24 kmph , e ) 74 kmph
Rationale: time taken = 1 hr 40 min 48 sec = 126 / 75 hrs let the actual speed be x kmph then 5 / 7 x * 126 / 75 = 42 x = ( 42 * 7 * 75 ) / 5 * 126 = 35 kmph answer ( c )
Answer: c
Problem: compare the rates of two trains , one travelling at 90 km / hr and other is at 50 m / s ?
Options: a ) 2 : 1 , b ) 1 : 2 , c ) 1 : 3 , d ) 3 : 1 , e ) 2 : 3
Rationale: speed of the 1 st train = 90 km / hr speed of the 2 nd train = 50 m / s = 50 * 18 / 5 = 180 km / hr ratio of the speeds of the train = 90 : 180 = 1 : 2 answer is b
Answer: b
Problem: a computer manufacturer produces a certain electronic component at a cost of $ 100 per component . shipping costs for delivering the components are $ 2 per unit . further , the manufacturer has costs of $ 10,000 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 1000 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?
Options: a ) 122 , b ) 112 , c ) 134 , d ) 108 , e ) 101
Rationale: "$ 10000 is a fixed cost each component is $ 102 ( $ 100 to produce , $ 2 to ship ) manufacturer will be producing and selling 1000 components so therefore the equation to find price would be 1000 * p = 10000 + ( 1000 * 100 ) + ( 1000 * 2 ) p = ( 10000 + 100000 + 2000 ) / 1000 p = 112 answer : b"
Answer: b
Problem: sari and ken climb up a mountain . at night , they camp together . on the day they are supposed to reach the summit , sari wakes up at 08 : 00 and starts climbing at a constant pace . ken starts climbing only at 10 : 00 , when sari is already 700 meters ahead of him . nevertheless , ken climbs at a constant pace of 500 meters per hour , and reaches the summit before sari . if sari is 50 meters behind ken when he reaches the summit , at what time did ken reach the summit ?
Options: a ) 13 : 00 , b ) 13 : 30 , c ) 14 : 00 , d ) 15 : 00 , e ) 15 : 30
Rationale: "both sari and ken climb in the same direction . speed of sari = 700 / 2 = 350 meters / hr ( since she covers 700 meters in 2 hrs ) speed of ken = 500 meters / hr at 8 : 00 , distance between ken and sari is 700 meters . ken needs to cover this and another 50 meters . time he will take = total distance to be covered / relative speed = ( 700 + 50 ) / ( 500 - 350 ) = 5 hrs starting from 10 : 00 , in 5 hrs , the time will be 15 : 00 answer ( d )"
Answer: d
Problem: the average weight of a , b and c is 30 kg . if the average weight of a and b be 25 kg and that of b and c be 28 kg , then the weight of b is :
Options: a ) 14 kg , b ) 15 kg , c ) 18 kg , d ) 19 kg , e ) 16 kg
Rationale: explanation let a , b , c represent their respective weights . then , we have : a + b + c = ( 30 x 3 ) = 90 â € ¦ . ( i ) a + b = ( 25 x 2 ) = 50 â € ¦ . ( ii ) b + c = ( 28 x 2 ) = 56 â € ¦ . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 106 â € ¦ . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 16 . b â € ™ s weight = 16 kg . answer e
Answer: e
Problem: the cost of a one - family home was $ 120000 in 1980 . in 1988 , the price had increased to $ 192000 . what was the percent increase in the cost of the home ?
Options: a ) 60 % , b ) 50 % , c ) 55 % , d ) 40 % , e ) 33.3 %
Rationale: increase = 192000 - 120000 = 72000 % increase = 72000 * 100 / 120000 = 60 % answer : option a
Answer: a
Problem: one fourth of one third of two fifth of a number is 20 . what will be 40 % of that number
Options: a ) a ) 140 , b ) b ) 150 , c ) c ) 180 , d ) d ) 240 , e ) e ) 220
Rationale: explanation : ( 1 / 4 ) * ( 1 / 3 ) * ( 2 / 5 ) * x = 20 then x = 20 * 30 = 600 40 % of 600 = 240 answer : option d
Answer: d
Problem: a card board of 34 * 14 has to be attached to a wooden box and a total of 35 pins are to be used on the each side of the cardbox . find the total number of pins used .
Options: a ) 135 , b ) 136 , c ) 137 , d ) 138 , e ) 139
Rationale: ( 35 * 4 ) - 4 = 136 answer : b
Answer: b
Problem: a 200 meter long train crosses a platform in 50 seconds while it crosses a signal pole in 42 seconds . what is the length of the platform ?
Options: a ) 39.9 , b ) 37.88 , c ) 35 , d ) 38.88 , e ) 38.09
Rationale: "speed = [ 200 / 42 ] m / sec = 100 / 21 m / sec . let the length of the platform be x meters . then , x + 200 / 50 = 100 / 21 21 ( x + 200 ) = 5000 è x = 38.09 m . answer : e"
Answer: e
Problem: how much water should be added to 11 liters of a 20 % - solution of alcohol to reduce the concentration of alcohol in the solution by 75 % ?
Options: a ) 25 liters , b ) 29 liters , c ) 30 liters , d ) 32 liters , e ) 35 liters
Rationale: "let x ltr water to be added 2 ltr alcohol to be represented as ( 20 ( 1 - 3 / 4 ( new soln . = 11 + x ) ) ) 2 = 5 % * ( 11 + x ) - - - - - - - - > x = 29 ans b"
Answer: b
Problem: a van takes 5 hours to cover a distance of 600 km . what speed in kph should the van maintain to cover the same distance in 3 / 2 of the previous time ?
Options: a ) 80 , b ) 84 , c ) 88 , d ) 92 , e ) 96
Rationale: "( 3 / 2 ) * 5 = 7.5 hours 600 / 7.5 = 80 kph the answer is a ."
Answer: a
Problem: the ratio of ages of aman , bren , and charlie are in the ratio 5 : 8 : 7 respectively . if 8 years ago , the sum of their ages was 76 , what will be the age of bren 12 years from now ?
Options: a ) 17 , b ) 25 , c ) 27 , d ) 52 , e ) 60
Rationale: "let the present ages of aman , bren , and charlie be 5 x , 8 x and 7 x respectively . 5 x - 8 + 8 x - 8 + 7 x - 8 = 76 x = 5 present age of bren = 8 * 5 = 40 bren ' s age 12 years hence = 40 + 12 = 52 answer = e"
Answer: e
Problem: a and b undertake to do a piece of work for $ 500 . a alone can do it in 5 days while b alone can do it in 10 days . with the help of c , they finish it in 2 days . find the share of c ?
Options: a ) $ 200 , b ) $ 150 , c ) $ 300 , d ) $ 25 , e ) $ 100
Rationale: "c ' s 1 day work = ( 1 / 2 ) - ( 1 / 5 + 1 / 10 ) = 1 / 5 a : b : c = 1 / 5 : 1 / 10 : 1 / 5 = 2 : 1 : 2 b ' s share = 500 * 2 / 5 = $ 200 answer is a"
Answer: a
Problem: a clock store sold a certain clock to a collector for 15 percent more than the store had originally paid for the clock . when the collector tried to resell the clock to the store , the store bought it back at 45 percent of what the collector had paid . the shop then sold the clock again at a profit of 85 percent on its buy - back price . if the difference between the clock ' s original cost to the shop and the clock ' s buy - back price was $ 80 , for how much did the shop sell the clock the second time ?
Options: a ) $ 168.58 , b ) $ 187.54 , c ) $ 158.74 , d ) $ 120.56 , e ) $ 200.84
Rationale: "now , in the question above , lets say the original cost of the clock to store was c $ and then it sold the same to the collector at 15 % profit . this means the clocks ' selling price was c ( 1.15 ) and this becomes cost price for the collector . now , when the collector tries to sell the same clock to the store , the store buys it for 45 % the price at which the collector bought it . thus , you get = 1.15 * 0.45 * c = 0.5175 c furthermore , the store sells the clock for the second time for 85 % profit and thus the selling price of the clock becomes = cost price of the clock for the store at buy - back * 1.85 = 1.85 * 0.5175 c finally given that c - 0.5175 c = 80 - - - - > c = 165.80 $ thus , the cost of the clock the second time around = 1.85 * 0.5175 c = 1.85 * 0.5175 * 165.80 = 158.74 $ . hence c is the correct answer ."
Answer: c
Problem: angelina walked 100 meters from her home to the grocery at a constant speed . she then walked 180 meters to the gym at double the speed . she spent 40 seconds less on her way from the grocery to the gym than on her way from home to the grocery . what was angelina ' s speed , in meters per second , from the grocery to the gym ?
Options: a ) 2 , b ) 3 , c ) 0.5 , d ) 6 , e ) 12
Rationale: "let the speed be x . . . so time taken from home to grocery = 100 / x . . the speed to gym = 2 x . . so time taken = 180 / 2 x = 90 / x . . its given 100 / x - 90 / x = 40 . . 10 / x = 40 . . x = 0.25 m / secs . . so grocery to gym = 2 * 0.25 = 0.5 m / s . . . answer : c"
Answer: c
Problem: if 45 % of z is 39 % of y and y is 75 % of x , what percent of x is z ?
Options: a ) 200 , b ) 160 , c ) 100 , d ) 65 , e ) 50
Rationale: "( 45 / 100 ) z = ( 39 / 100 ) y and y = ( 75 / 100 ) x i . e . y = ( 3 / 4 ) x i . e . ( 45 / 100 ) z = ( 39 / 100 ) * ( 3 / 4 ) x i . e . z = ( 39 * 3 ) x / ( 45 * 4 ) i . e . z = ( 0.65 ) x = ( 65 / 100 ) x i . e . z is 65 % of x answer : option d"
Answer: d
Problem: 10 camels cost as much as 24 horses , 16 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants . if the cost of 10 elephants is rs . 130000 , find the cost of a camel ?
Options: a ) s . 9800 , b ) s . 3800 , c ) s . 9800 , d ) s . 5200 , e ) s . 6880
Rationale: "cost of the camel = p 10 camels = 24 horses 16 horses = 4 oxen 6 oxen = 4 elephants 10 elephants = rs . 130000 p = rs . [ ( 24 * 4 * 4 * 130000 ) / ( 10 * 16 * 6 * 10 ) ] p = rs . ( 49920000 / 9600 ) = > p = rs . 5200 answer : d"
Answer: d
Problem: a worker makes a toy in every 3 h . if he works for 150 h , then how many toys will he make ?
Options: a ) 40 , b ) 54 , c ) 45 , d ) 50 , e ) none
Rationale: no . of toys = 150 / 3 = 50 answer : d
Answer: d
Problem: in one hour , a boat goes 11 km along the stream and 5 km against the stream . the speed of the boat in still water in ( km / hr ) is
Options: a ) 3 , b ) 5 , c ) 8 , d ) 9 , e ) 7
Rationale: "solution speed in still water = 1 / 2 ( 11 + 5 ) km / hr = 8 km / hr . answer c"
Answer: c
Problem: 45 workers work 8 hours to dig a hole 30 meters deep . how many extra workers should be hired to dig another hole 40 meters deep by working for 6 hours ?
Options: a ) 75 , b ) 80 , c ) 50 , d ) 35 , e ) 40
Rationale: 45 workers * 8 hours / 30 meters = x * 6 / 40 x = 80 total workers 80 - 45 = 35 the answer is d .
Answer: d
Problem: if an amount of rs 42,900 is distributed equally amongst 22 persons , how much amount would each person get ?
Options: a ) rs 1950 , b ) rs 2000 , c ) rs 745 , d ) rs 765 , e ) none
Rationale: required amount = 42900 / 22 = rs 1950 answer a
Answer: a
Problem: what is the perimeter , in meters , of a rectangular garden 8 meters wide that has the same area as a rectangular playground 16 meters long and 12 meters wide ?
Options: a ) 48 , b ) 56 , c ) 64 , d ) 76 , e ) 192
Rationale: "say length of garden is l meters . then ( l * 8 ) = 16 * 12 [ given area is same . area = l * b ] therefore l works out to 24 meters . perimeter of garden = 2 * ( 24 + 8 ) = 64 meter . answer is c"
Answer: c
Problem: what is the value of : - 9 ^ 7 + 9 ^ 9 ?
Options: a ) 9 ^ 2 , b ) - 18 ^ 16 , c ) 63 ( 9 ^ 7 ) , d ) - 80 ( 9 ^ 7 ) , e ) 80 ( 9 ^ 7 )
Rationale: - 9 ^ 7 + 9 ^ 9 = 9 ^ 7 ( - 1 + 9 ^ 2 ) = 9 ^ 7 ( - 1 + 81 ) = 80 ( 9 ^ 7 ) , answer e .
Answer: e
Problem: let the sides of a rectangular prism are consecutive multiples of 5 . which among the following could be the base area
Options: a ) 360
b ) 450
c ) 560
d ) 670
e ) 780
Rationale: length = 5 * a breadth = 5 * ( a + 1 ) or 5 * ( a + 2 ) base area - > multiple of 25 450 = 25 * 18 answer : b
Answer: b
Problem: if teena is driving at 55 miles per hour and is currently 7.5 miles behind joe , who is driving at 40 miles per hour in the same direction then in how many minutes will teena be 45 miles ahead of joe ?
Options: a ) 15 , b ) 60 , c ) 75 , d ) 90 , e ) 210
Rationale: "this type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30 - 40 seconds for a difficult one . teena covers 55 miles in 60 mins . joe covers 40 miles in 60 mins so teena gains 15 miles every 60 mins teena need to cover 7.5 + 45 miles . teena can cover 7.5 miles in 30 mins teena will cover 45 miles in 180 mins so answer 30 + 180 = 210 mins . ( answer e )"
Answer: e
Problem: the sum of ages of 4 children born at the intervals of 10 years each is 80 years . what is the age of the youngest child ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 10 ) + ( x + 20 ) + ( x + 30 ) = 80 4 x = 20 x = 5 . age of the youngest child = x = 5 years . answer : b"
Answer: b
Problem: a bag contains 3 blue and 5 white marbles . one by one , marbles are drawn out randomly until only two are left in the bag . what is the probability x that out of the two , one is white and one is blue ?
Options: a ) 15 / 56 , b ) 41 / 56 , c ) 13 / 28 , d ) 15 / 28 , e ) 5 / 14
Rationale: "the required probability x = probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls . ways to select 6 out of total 8 = 8 c 6 ways to select 4 out of 5 white balls = 5 c 4 ways to select 2 out of 3 blue balls = 3 c 2 thus the required probability = ( 5 c 4 * 3 c 2 ) / 8 c 6 = 15 / 28 . d is thus the correct answer ."
Answer: d
Problem: one hour after yolanda started walking from x to y , a distance of 17 miles , bob started walking along the same road from y to x . if yolanda ' s walking rate was 3 miles per hour and bob т ' s was 4 miles per hour , how many miles had bob walked when they met ?
Options: a ) 24 , b ) 23 , c ) 22 , d ) 21 , e ) 8
Rationale: when b started walking y already has covered 3 miles out of 17 , hence the distance at that time between them was 17 - 3 = 14 miles . combined rate of b and y was 3 + 4 = 7 miles per hour , hence they would meet each other in 14 / 7 = 2 hours . in 6 hours b walked 2 * 4 = 8 miles . answer : e .
Answer: e
Problem: a dozen eggs and 10 pounds of oranges are currently at the same price . if the price of a dozen eggs rises by 9 percent and the price of oranges rises by 6 % . how much more will it cost to buy a dozen eggs and 10 pounds of oranges .
Options: a ) 5 % , b ) 10 % , c ) 15 % , d ) 20 % , e ) 25 %
Rationale: "say currently both a dozen eggs and 10 pounds of oranges cost $ 100 ( they are at the same price ) . so , to buy a dozen eggs and 10 pounds of oranges we need $ 100 . after the increase , the price of a dozen eggs will be $ 109 and the price of 10 pounds of oranges will be $ 106 . so after the increase , to buy a dozen eggs and 10 pounds of oranges we ' ll need $ 215 . increase = 15 % . answer : c ."
Answer: c
Problem: at what price must an article costing rs . 47.50 be marked in order that after deducting 5 % from the list price . it may be sold at a profit of 40 % on the cost price ?
Options: a ) 62.5 , b ) 69.5 , c ) 67.5 , d ) 62.5 , e ) 70
Rationale: "cp = 47.50 sp = 47.50 * ( 140 / 100 ) = 66.5 mp * ( 95 / 100 ) = 66.5 mp = 70 answer : e"
Answer: e
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 19 mph between the 2 friends until the friends meet . how many miles does the pigeon travel ?
Options: a ) 54 , b ) 57 , c ) 60 , d ) 36 , e ) 96
Rationale: "b 57 it takes 3 hours for the friends to meet ; so the pigeon flies for 3 hours at 19 mph = 57 miles"
Answer: b
Problem: in a river flowing at 2 km / hr , a boat travels 48 km upstream and then returns downstream to the starting point . if its speed in still water be 6 km / hr , find the total journey time .
Options: a ) 10 hours , b ) 12 hours , c ) 14 hours , d ) 18 hours , e ) none of these
Rationale: "explanation : speed of the boat = 6 km / hr speed downstream = ( 6 + 2 ) = 8 km / hr speed upstream = ( 6 - 2 ) = 4 km / hr distance traveled downstream = distance traveled upstream = 48 km total time taken = time taken downstream + time taken upstream = ( 48 / 8 ) + ( 48 / 4 ) = 18 hr . answer : option d"
Answer: d
Problem: in smithtown , the ratio of right - handed people to left - handed people is 3 to 1 and the ratio of men to women is 3 to 2 . if the number of right - handed men is maximized , then what x percent of all the people in smithtown are left - handed women ?
Options: a ) 50 % , b ) 40 % , c ) 25 % , d ) 20 % , e ) 10 %
Rationale: "looking at the ratio we can take total number of people = 20 . . ans 5 / 20 or 25 % c"
Answer: c
Problem: the number of degrees that the hour hand of a clock moves through between noon and 2.30 in the afternoon of the same day is ?
Options: a ) 38 , b ) 27 , c ) 75 , d ) 28 , e ) 21
Rationale: explanation : the hour hand moves from pointing to 12 to pointing to half way between 2 and 3 . the angle covered between each hour marking on the clock is 360 / 12 = 30 . since the hand has covered 2.5 of these divisions the angle moved through is 75 . answer : c
Answer: c
Problem: a rectangular tiled patio is composed of 30 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 30 tiles , and it will still be rectangular . how many rows are in the tile patio before the change in layout ?
Options: a ) 5 , b ) 6 , c ) 10 , d ) 13 , e ) 28
Rationale: "suppose there are c columns and there are r rows original situation so , number of tiles = c * r = 30 also . reach column has r tiles and each row has c tiles new situation number of tiles in each column is r - 2 and number of tiles in each row is c + 4 so , number of rows = r - 2 and number of columns is c + 4 so , number of tiles = ( r - 2 ) * ( c + 4 ) = 30 comparing both of them we get c * r = ( r - 2 ) * ( c + 4 ) = > 4 r - 2 c = 8 c = 2 r - 4 putting it in c * r = 30 ( 2 r - 4 ) * r = 30 2 r ^ 2 - 4 r - 30 = 0 r can not be negative so r = 5 and c = 6 so , answer will be a"
Answer: a
Problem: a row of ants comprised of 102 ants . a man walked upon it and all except 42 were crushed beneath his foot . how many ants are left alive ?
Options: a ) 41 , b ) 42 , c ) 43 , d ) 44 , e ) 45
Rationale: solution : all except 42 were crushed means that all the ants except 42 were crushed beneath the man ' s foot . hence , 42 ants are alive now answer b
Answer: b
Problem: at a certain food stand , the price of each apple is 40 ¢ and the price of each orange is 60 ¢ . mary selects a total of 10 apples and oranges from the food stand , and the average ( arithmetic mean ) price of the 10 pieces of fruit is 54 ¢ . how many oranges must mary put back so that the average price of the pieces of fruit that she keeps is 45 ¢ ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "if the average price is 54 , then mary has 7 oranges and 3 apples ( a ratio of 7 : 3 ) . for the average price to be 45 , the ratio should be 1 : 3 . mary must put back 6 oranges . the answer is e ."
Answer: e
Problem: what percent is 50 gm of 1 kg ?
Options: a ) 0.5 % , b ) 1 % , c ) 1.5 % , d ) 2 % , e ) 5 %
Rationale: "1 kg = 1000 gm 50 / 1000 × 100 = 5000 / 1000 = 5 % e )"
Answer: e