regisss/math_qa huggingface dataset:
Problem: the length of the bridge , which a train 160 meters long and travelling at 45 km / hr can cross in 30 seconds , is ?
Options: a ) 766 m , b ) 156 m , c ) 215 m , d ) 156 m , e ) 156 m
Rationale: "speed = ( 45 * 5 / 18 ) m / sec = ( 25 / 2 ) m / sec . time = 30 sec . let the length of bridge be x meters . then , ( 160 + x ) / 30 = 25 / 2 = = > 2 ( 160 + x ) = 750 = = > x = 215 m . answer : c"
Answer: c
Problem: a car that moves at an average speed of 60 kmph , reaches its destination on time . when its average speed becomes 50 kmph , then it reaches its destination 45 minutes late . find the length of journey .
Options: a ) 189 km , b ) 225 km , c ) 255 km , d ) 199 km , e ) none
Rationale: sol . difference between timings = 45 min = 3 / 4 hr . let the length of journey be x km . then , x / 50 - x / 60 = 1 / 4 â ‡ ” 6 x - 5 x = 225 â ‡ ” x = 225 km . answer b
Answer: b
Problem: one pipe can fill a tank in 15 hour . but because of hole in a tank , this tank fill in 20 hour . so in how much time this hole will empty the full tank ?
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70
Rationale: in 1 hour hole empty = [ 1 / 15 - 1 / 20 ] = 1 / 60 so total time taken to empty the full tank through hole = 60 hour . answer d
Answer: d
Problem: the ratio of the volumes of two cubes is 125 : 1728 . what is the ratio of their total surface areas ?
Options: a ) 81 : 121 , b ) 9 : 11 , c ) 25 : 144 , d ) 27 : 121 , e ) none of these
Rationale: "ratio of the sides = â ³ â ˆ š 125 : â ³ â ˆ š 1728 = 5 : 12 ratio of surface areas = 5 ^ 2 : 12 ^ 2 = 25 : 144 answer : c"
Answer: c
Problem: moli buys 3 ribbons , 7 clips and 1 soap for rs . 120 exactly . at the same place it would cost rs . 164 for 4 ribbons , 10 clips and one soap . how much would it cost for one ribbon , one clip and one soap ?
Options: a ) 36 , b ) 34 , c ) 38 , d ) 32 , e ) 31
Rationale: explanation : let us consider , ribbon is denoted by r clips is denoted by c soaps is denoted by s now according to the question , = > 3 r + 7 c + s = 120 - - - - - - - - ( 1 ) = > 4 r + 10 c + s = 164 - - - - - - - - ( 2 ) ( 1 ) - ( 2 ) = > ( 3 r - 4 r ) + ( 7 c - 10 c ) + ( s - s ) = 120 - 164 = > - r - 3 c = - 44 multily the equation by - 1 , it becomes = > r + 3 c = 44 - - - - - - - ( 3 ) now perform this operation 2 * ( 1 ) - ( 2 ) = > 2 r + 4 c + s = 76 - - - - - - - ( 4 ) finaly ( 4 ) - ( 3 ) = > r + c + s = 32 hence , the cost of 1 ribbon , 1 clip and 1 saop would be 32 rs . answer : d
Answer: d
Problem: the speed of a train is 90 kmph . what is the distance covered by it in 5 minutes ?
Options: a ) 7.5 , b ) 66 , c ) 77 , d ) 52 , e ) 42
Rationale: "90 * 5 / 60 = 7.5 kmph answer : a"
Answer: a
Problem: a rainstorm increased the amount of water stored in state j reservoirs from 124 billion gallons to 140 billion gallons . if the storm increased the amount of water in the reservoirs to 80 percent of total capacity , approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm ?
Options: a ) 51 , b ) 48 , c ) 55 , d ) 63 , e ) 65
Rationale: "let total capacity be x we know 140 = 0.80 x x = 140 / 0.80 = 175 prior to storm , we had 124 bn gallons 175 - 124 = 51 answer : a"
Answer: a
Problem: if ( m - 8 ) is a factor of m ^ 2 - km - 24 , then k =
Options: a ) 3 , b ) 5 , c ) 6 , d ) 11 , e ) 16
Rationale: "( m - 8 ) ( m - a ) = m ^ 2 - km - 24 a = - 3 k = 8 + a = 5 = b"
Answer: b
Problem: a box contains either blue or red flags . the total number of flags in the box is an even number . a group of children are asked to pick up two flags each . if all the flags are used up in the process such that 60 % of the children have blue flags , and 70 % have red flags , what percentage of children have flags of both the colors ?
Options: a ) 5 % , b ) 10 % , c ) 15 % , d ) 20 % , e ) 30 %
Rationale: solution : let the total number of flags be 100 ( even number ) let the total number of ' blue ' flags alone be ' a ' let the total number of ' red ' flags alone be ' b ' let the total number of ' both ' flags be ' c ' we have given , total number of blue flags = 60 % = 60 = a + c total number of red flags = 70 % = 70 = b + c total number of flags = a + b + c = 100 ( since all the flags have been utilized ) so , substituting for c in the third equation , we have , 60 - c + c + 70 - c = 100 c = 30 option e .
Answer: e
Problem: a dog breeder currently has 9 breeding dogs . 6 of the dogs have exactly 1 littermate , and 3 of the dogs have exactly 2 littermates . if 2 dogs are selected at random , what is the probability w that both selected dogs are not littermates ?
Options: a ) 1 / 6 , b ) 2 / 9 , c ) 5 / 6 , d ) 7 / 9 , e ) 8 / 9
Rationale: we have three pairs of dogs for the 6 with exactly one littermate , and one triplet , with each having exactly two littermates . so , in fact there are two types of dogs : those with one littermate - say a , and the others with two littermates - b . work with probabilities : choosing two dogs , we can have either one dog of type b or none ( we can not have two dogs both of type b ) . the probability of choosing one dog of type b and one of type a is 3 / 9 * 6 / 8 * 2 = 1 / 2 ( the factor of 2 for the two possibilities ba and ab ) . the probability of choosing two dogs of type a which are not littermates is 6 / 9 * 4 / 8 = 1 / 3 ( choose one a , then another a which is n ' t the previous one ' s littermate ) . the required probability is 1 / 2 + 1 / 3 = 5 / 6 . find the probability for the complementary event : choose aa or bb . probability of choosing two dogs of type a who are littermates is 6 / 9 * 1 / 8 = 1 / 12 . probability of choosing two dogs of type b ( who necessarily are littermates ) is 3 / 9 * 2 / 8 = 1 / 12 . again , we obtain 1 - ( 1 / 12 + 1 / 12 ) w = 5 / 6 . answer : c
Answer: c
Problem: how many 4 - digit positive integers are there , where each digit is positive , and no 4 adjacent digits are same ?
Options: a ) 1236 , b ) 3024 , c ) 4096 , d ) 4608 , e ) 6561
Rationale: "first digit . . 9 posibilities second digit , 8 possibilities third digit , 7 possibilities fourth digit , 6 possibilities . 9 * 8 * 7 * 6 = 3024 . b"
Answer: b
Problem: p can do a work in 15 days and q cando the same work in 20 days . if they can work together for 4 days , what is the fraction of work left ?
Options: a ) 6 / 15 , b ) 7 / 13 , c ) 8 / 15 , d ) 9 / 17 , e ) 2 / 13
Rationale: amount of work p can do in 1 day = 1 / 15 amount of work q can do in 1 day = 1 / 20 amount of work p and q can do in 1 day = 1 / 15 + 1 / 20 = 7 / 60 amount of work p and q can together do in 4 days = 4 × ( 7 / 60 ) = 7 / 15 fraction of work left = 1 – 7 / 15 = 8 / 15 c
Answer: c
Problem: how many of the integers between 25 and 95 are even ?
Options: a ) 35 , b ) 90 , c ) 11 , d ) 10 , e ) 9
Rationale: "number start between 25 to 95 is 70 numbers half of them is even . . which is 35 answer : a"
Answer: a
Problem: the sale price shirts listed for rs . 400 after successive discount is 10 % and 5 % is ?
Options: a ) 280 , b ) 290 , c ) 342 , d ) 250 , e ) 253
Rationale: 400 * ( 90 / 100 ) * ( 95 / 100 ) = 342 c
Answer: c
Problem: village x has a population of 78000 , which is decreasing at the rate of 1200 per year . village y has a population of 42000 , which is increasing at the rate of 800 per year . in how many years will the population of the two villages be equal ?
Options: a ) 15 , b ) 19 , c ) 11 , d ) 18 , e ) 13
Rationale: "let the population of two villages be equal after p years then , 78000 - 1200 p = 42000 + 800 p 2000 p = 36000 p = 18 answer is d ."
Answer: d
Problem: if a whole number n is divided by 4 , we will get 3 as remainder . what will be the remainder if 2 n is divided by 4 ?
Options: a ) 4 , b ) 3 , c ) 2 , d ) 1 , e ) 0
Rationale: explanation : let n ÷ 4 = p , remainder = 3 = > n = 4 p + 3 2 n = 2 ( 4 p + 3 ) = 8 p + 6 = 8 p + 4 + 2 = 4 ( 2 p + 1 ) + 2 hence , if 2 n is divided by 4 , we will get 2 as remainder . answer : c
Answer: c
Problem: in an election between two candidates , one got 55 % of the total valid votes , 20 % of the votes were invalid . if the total number of votes was 4000 , the number of valid votes that the other candidate got , was :
Options: a ) 3500 , b ) 1200 , c ) 1650 , d ) 3700 , e ) 1800
Rationale: "number of valid votes = 80 % of 4000 = 3200 . valid votes polled by other candidate = 45 % of 4000 = ( 45 / 100 ) x 4000 = 1800 answer = e"
Answer: e
Problem: a invested $ 300 in a business after 6 months b invested $ 200 in the business . end of the year if they got $ 100 as profit . find a shares ?
Options: a ) $ 100 , b ) $ 75 , c ) $ 20 , d ) $ 120 , e ) $ 50
Rationale: "a : b = 300 * 12 : 200 * 6 a : b = 3 : 1 a ' s share = 100 * 3 / 4 = $ 75 answer is b"
Answer: b
Problem: a hat company ships its hats , individually wrapped , in 8 - inch by 10 - inch by 12 - inch boxes . each hat is valued at $ 7.50 . if the company ’ s latest order required a truck with at least 336,000 cubic inches of storage space in which to ship the hats in their boxes , what was the minimum value of the order ?
Options: a ) $ 960 , b ) $ 1,350 , c ) $ 1,725 , d ) $ 2,625 , e ) $ 2,250
Rationale: "number of boxes = total volume / volume of one box = 336,000 / ( 8 * 10 * 12 ) = 350 one box costs 7.50 , so 350 box will cost = 350 * 7.5 = 2625 d is the answer"
Answer: d
Problem: the sum of 77 consecutive integers is 7777 . what is the greatest integer in the set ?
Options: a ) 139 , b ) 141 , c ) 143 , d ) 145 , e ) 147
Rationale: "let x be the first integer in the set . then x + 76 is the largest integer . the sum is : x + ( x + 1 ) + ( x + 2 ) + . . . + ( x + 76 ) = 77 x + 76 * 77 / 2 = 77 ( x + 38 ) then x + 38 = 101 x = 63 the largest integer in the set is 63 + 76 = 139 the answer is a ."
Answer: a
Problem: a group of boy scouts and girls scouts is going on a rafting trip . 80 % of the scouts arrived with signed permission slips . if 40 % of the scouts were boy scouts and 75 % of the boy scouts arrived with signed permission slips , then what percentage of the girl scouts arrived with signed permission slips ? round to the nearest percent .
Options: a ) 79 , b ) 81 , c ) 82 , d ) 83 , e ) 85
Rationale: "40 % were boy scouts so 60 % ( 100 - 40 = 60 ) were girl scouts . # of boy scouts with permission slips signed + # of girl scouts with permission slips signed = total # with permission slip signed ( 75 % of 40 % of the total going ) + ( ? % of 60 % of the total going ) = 80 % of the total going we can let the ` ` total going ' ' = 100 arbitrarily since we only care about the percent ( of girl scouts w / permission signed ) . 75 * . 40 * 100 + x * . 60 * 100 = . 80 * 100 30 + x * 60 = 80 60 x = 50 x = 50 / 60 x = . 833333 converting this to a percent , we have 83 % d"
Answer: d
Problem: a sum fetched a total simple interest of rs . 4016.25 at the rate of 1 % p . a . in 3 years . what is the sum ?
Options: a ) 122762 , b ) 132877 , c ) 122882 , d ) 133875 , e ) 132887
Rationale: "principal = ( 100 * 4016.25 ) / ( 1 * 3 ) = rs . 133875 . answer : d"
Answer: d
Problem: pipe a can fill a tank in 12 minutes and pipe b cam empty it in 24 minutes . if both the pipes are opened together after how many minutes should pipe b be closed , so that the tank is filled in 30 minutes ?
Options: a ) 18 , b ) 27 , c ) 98 , d ) 27 , e ) 36
Rationale: "let the pipe b be closed after x minutes . 30 / 12 - x / 24 = 1 = > x / 24 = 30 / 12 - 1 = 3 / 2 = > x = 3 / 2 * 24 = 36 . answer : e"
Answer: e
Problem: sandy is younger than molly by 18 years . if the ratio of their ages is 7 : 9 , how old is sandy ?
Options: a ) 42 , b ) 49 , c ) 56 , d ) 63 , e ) 70
Rationale: "let sandy ' s age be 7 x and let molly ' s age be 9 x . 9 x - 7 x = 18 x = 9 sandy is 63 years old . the answer is d ."
Answer: d
Problem: score interval - - - - - - - - - - - - - - - - number of scores 50 - 59 - - - - - - - - - - - - - - - - - - - - - - - - - - 2 60 - 69 - - - - - - - - - - - - - - - - - - - - - - - - - - 4 70 - 79 - - - - - - - - - - - - - - - - - - - - - - - - - - 10 80 - 89 - - - - - - - - - - - - - - - - - - - - - - - - - - 27 90 - 99 - - - - - - - - - - - - - - - - - - - - - - - - - - 18 the table above shows the distribution of test scores for a group of management trainees . which score interval contains the median of the 61 scores ?
Options: a ) 30 , b ) 32 , c ) 31 th ( 80 - 89 ) , d ) 34 , e ) 36
Rationale: total scores = 2 + 4 + 10 + 27 + 18 = 61 , which is odd , therefore the median is the floor ( 61 / 2 ) + 1 = 31 th score . and the 31 th score is in the 80 - 89 range , because 50 - 79 only reference 28 scores . c
Answer: c
Problem: a side of beef lost 20 percent of its weight in processing . if the side of beef weighed 640 pounds after processing , how many pounds did it weigh before processing ?
Options: a ) 191 , b ) 355 , c ) 800 , d ) 840 , e ) 900
Rationale: "let weight of side of beef before processing = x ( 80 / 100 ) * x = 640 = > x = ( 640 * 100 ) / 80 = 800 answer c"
Answer: c
Problem: two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds . the ratio of their speeds is ?
Options: a ) 3 / 7 , b ) 3 / 2 , c ) 3 / 5 , d ) 3 / 1 , e ) 3 / 3
Rationale: "let the speeds of the two trains be x m / sec and y m / sec respectively . then , length of the first train = 27 x meters , and length of the second train = 17 y meters . ( 27 x + 17 y ) / ( x + y ) = 23 = = > 27 x + 17 y = 23 x + 23 y = = > 4 x = 6 y = = > x / y = 3 / 2 . answer : b"
Answer: b
Problem: the cost price of 16 articles is the same as the selling price of 12 articles . find the loss / profit percentages .
Options: a ) 30 % , b ) 32.50 % , c ) 33 1 / 3 % , d ) 40 % , e ) 50 %
Rationale: "explanation : the gain is 4 out of 12 articles . therefore , gain percentage = 4 x 100 / 12 = 100 / 3 = 33 1 / 3 % answer : option c"
Answer: c
Problem: selling an kite for rs . 30 , a shop keeper gains 30 % . during a clearance sale , the shopkeeper allows a discount of 10 % on the marked price . his gain percent during the sale is ?
Options: a ) 8 % , b ) 10 % , c ) 11 % , d ) 17 % , e ) 20 %
Rationale: "explanation : marked price = rs . 30 c . p . = 100 / 130 * 30 = rs . 23.07 sale price = 90 % of rs . 30 = rs . 27 required gain % = 3.92 / 23.07 * 100 = 17 % . answer : d"
Answer: d
Problem: the manufacturing cost of a shoe is rs . 220 and the transportation lost is rs . 500 for 100 shoes . what will be the selling price if it is sold at 20 % gains
Options: a ) s 222 , b ) s 216 , c ) s 220 , d ) s 270 , e ) s 217
Rationale: "explanation : total cost of a watch = 220 + ( 500 / 100 ) = 225 . gain = 20 % = > sp = 1.2 cp = 1.2 x 225 = 270 answer : d"
Answer: d
Problem: a grocer has a sale of rs . 5124 , rs . 5366 , rs . 5808 , rs . 5399 and rs . 6124 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 5400 ?
Options: a ) 4079 , b ) 4579 , c ) 5579 , d ) 5679 , e ) 5779
Rationale: "total sale for 5 months = rs . ( 5124 + 5366 + 5808 + 5399 + 6124 ) = rs . 27821 . required sale = rs . [ ( 5400 x 6 ) - 27821 ] = rs . ( 32400 - 27821 ) = rs . 4579 . answer : b"
Answer: b
Problem: one bacterium splits into 8 bacteria of the next generation . but due to environment , only 50 % of one generation can produced the next generation . if the seventh generation number is 4096 million , what is the number in first generation ?
Options: a ) 1 million , b ) 2 million , c ) 4 million , d ) 8 million , e ) none of these
Rationale: solution : let the number of bacteria in the 1 st generation be x , then number of bacteria in 2 nd , 3 rd , 4 th . . . . . generation would be 8 ( x / 2 ) , 8 ( 4 x / 2 ) , 8 ( 16 x / 2 ) . . . . and so on . as x , 4 x , 16 x , 64 x . . . . . it is in gp with common ratio 4 . hence , 7 th term of gp , x ( 4 ) 6 = 4096 or , x = 1 or 1 million . answer : option a
Answer: a
Problem: xavier , yvonne , and zelda each try independently to solve a problem . if their individual probabilities for success are 1 / 4 , 1 / 3 and 5 / 8 , respectively , what is the probability that xavier and yvonne , but not zelda , will solve the problem ?
Options: a ) 1 / 32 , b ) 7 / 8 , c ) 9 / 64 , d ) 5 / 64 , e ) 3 / 64
Rationale: "p ( xavier will solve ) = 1 / 4 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 / 4 ) * ( 1 / 3 ) * ( 3 / 8 ) = 1 / 32 . ans . a ."
Answer: a
Problem: a class has a ratio of 3 : 6 : 7 of children with red hair , blonde hair and black hair respectively . if the class has 9 kids with red hair , how many kids are there with black hair ?
Options: a ) 7 , b ) 6 , c ) 9 , d ) 21 , e ) 63
Rationale: "since there is a 3 : 7 ratio between red haired children and black - haired children , if there are 9 children with red hair , then there must be 3 times the amount of black - haired children . therefore , are 21 children with black hair . answer : d )"
Answer: d
Problem: a walks at 10 kmph and 5 hours after his start , b cycles after him at 20 kmph . how far from the start does b catch up with a ?
Options: a ) 100 km , b ) 150 km , c ) 50 km , d ) 120 km , e ) 200 km
Rationale: "suppose after x km from the start b catches up with a . then , the difference in the time taken by a to cover x km and that taken by b to cover x km is 5 hours . x / 10 - x / 20 = 5 x = 100 km answer is a"
Answer: a
Problem: evaluate : 28 % of 400 + 45 % of 250
Options: a ) 220.3 , b ) 224.5 , c ) 190.3 , d ) 150 , e ) none of these
Rationale: explanation : 28 % of 400 + 45 % of 250 = ( 28 / 100 * 400 + 45 / 100 * 250 ) = ( 112 + 112.5 ) = 224.5 answer b
Answer: b
Problem: a rope of which a calf is tied is increased from 10 m to 20 m , how much additional grassy ground shall it graze ?
Options: a ) 540 , b ) 128 , c ) 100 , d ) 942 , e ) 942.86
Rationale: "π ( 202 – 102 ) = 942.86 answer : e"
Answer: e
Problem: a card is drawn from a pack of 52 cards . the probability of getting a queen of club or a king of heart is :
Options: a ) 1 / 26 , b ) 1 / 52 , c ) 2 / 62 , d ) 2 / 26 , e ) 3 / 26
Rationale: "here , n ( s ) = 52 . let e = event of getting a queen of club or a king of heart . then , n ( e ) = 2 . p ( e ) = n ( e ) / n ( s ) = 2 / 52 = 1 / 26 answer should be a"
Answer: a
Problem: a man can row 8 kmph in still water . when the river is running at 1.8 kmph , it takes him 2 hour to row to a place and back . what is the total distance traveled by the man ?
Options: a ) 8.2 km , b ) 6.7 km , c ) 7.6 km , d ) 7.4 km , e ) 6.3 km
Rationale: "m = 8 s = 1.8 ds = 9.8 us = 6.2 x / 9.8 + x / 6.2 = 1 x = 3.8 d = 2.88 * 2 = 7.6 answer : c"
Answer: c
Problem: a cube of side 5 cm is painted on all its side . if it is sliced into 1 cubic centimer cubes , how many 1 cubic centimeter cubes will have exactly one of their sides painted ?
Options: a ) 9
b ) 61
c ) 98
d ) 54
e ) 64
Rationale: explanatory answer when a 5 cc cube is sliced into 1 cc cubes , we will get 5 * 5 * 5 = 125 cubes of 1 cubic centimeter . in each side of the larger cube , the smaller cubes on the edges will have more than one of their sides painted . therefore , the cubes which are not on the edge of the larger cube and that lie on the facing sides of the larger cube will have exactly one side painted . in each face of the larger cube , there will be 5 * 5 = 25 cubes . of these , the cubes on the outer rows will be on the edge . 16 such cubes exist on each face . if we count out the two outer rows on either side of a face of the cube , we will be left with 3 * 3 = 9 cubes which are not on the edge in each face of the cube . therefore , there will be 9 cubes of 1 - cc volume per face that will have exactly one of their sides painted . in total , there will be 9 * 6 = 54 such cubes . choice d is the correct answer .
Answer: d
Problem: a person buys an article at $ 800 . at what price should he sell the article so as to make a profit of 12 % ?
Options: a ) 896 , b ) 890 , c ) 990 , d ) 789 , e ) 740
Rationale: "a 896 cost price = $ 800 profit = 12 % of 800 = $ 96 selling price = cost price + profit = 800 + 96 = 896"
Answer: c
Problem: if m = 3 ^ n , what is the greatest value of n for which m is a factor of 25 !
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "we should find the highest power of 3 in 25 ! : 25 / 3 + 25 / 3 ^ 2 = 8 + 2 = 10 ( take only the quotient into account ) . . so the highest power of 3 in 25 ! is 10 . answer : b ."
Answer: b
Problem: jane makes toy bears . when she works with an assistant , she makes 44 percent more bears per week and works 10 percent fewer hours each week . having an assistant increases jane ’ s output of toy bears per hour by what percent ?
Options: a ) 20 % , b ) 60 % , c ) 100 % , d ) 180 % , e ) 200 %
Rationale: "let ' s assume just jane 40 bears per 40 / hrs a week , so that is 1 bear / hr . with an assistant she makes 57.6 bears per 36 hours a week or 1.6 bears / hr ( [ 40 bears * 1.44 ] / [ 40 hrs * . 90 ] ) . [ ( 1.6 - 1 ) / 1 ] * 100 % = 60 % answer : b"
Answer: b
Problem: two trains are moving in the same direction at 108 kmph and 36 kmph . the faster train crosses the slower train in 17 seconds . find the length of the faster train in meters .
Options: a ) 270 m , b ) 340 m , c ) 310 m , d ) 350 m , e ) 327 m
Rationale: relative speed = ( 108 - 36 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in 17 sec = 17 * 20 = 340 m . the length of the faster train = 340 m . answer : b
Answer: b
Problem: how many seconds will a 500 metre long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
Options: a ) 25 , b ) 30 , c ) 40 , d ) 45 , e ) 55
Rationale: "solution speed of train relative to man = ( 63 - 3 ) km / hr = 60 km / hr = ( 60 x 5 / 18 ) m / sec = 50 / 3 m / sec time taken to pass the man = ( 500 x 3 / 50 ) sec = 30 sec answer b"
Answer: b
Problem: if 5 < x < 8 < y < 13 , then what is the greatest possible positive integer difference of x and y ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "let x = 5.1 and y = 12.1 greatest possible difference = 12.1 - 5.1 = 7 answer e"
Answer: e
Problem: in a garden , 26 trees are planted at equal distances along a yard 500 metres long , one tree being at each end of the yard . what is the distance between two consecutive trees ?
Options: a ) 20 , b ) 8 , c ) 12 , d ) 14 , e ) 16
Rationale: "26 trees have 25 gaps between them . length of each gap = 500 / 25 = 20 i . e . , distance between two consecutive trees = 20 answer is a ."
Answer: a
Problem: a lent rs . 5000 to b for 2 years and rs . 3000 to c for 4 years on simple interest at the same rate of interest and received rs . 2200 in all from both of them as interest . the rate of interest per annum is :
Options: a ) 5 % , b ) 10 % , c ) 7 % , d ) 8 % , e ) 9 %
Rationale: "explanation : let the rate of interest per annum be r % simple interest for rs . 5000 for 2 years at rate r % per annum + simple interest for rs . 3000 for 4 years at rate r % per annum = rs . 2200 ⇒ 5000 × r × 2 / 100 + 3000 × r × 4 / 100 = 2200 ⇒ 100 r + 120 r = 2200 ⇒ 220 r = 2200 ⇒ r = 10 i . e , rate = 10 % . answer : option b"
Answer: b
Problem: 12 + 6 = 792 10 + 2 = 110 1 + 9 = 9 2 + 7 = 16 11 + 4 = ? ? solve it ?
Options: a ) 100 , b ) 120 , c ) 190 , d ) 160 , e ) 154
Rationale: x + y = x [ y + ( x - 1 ) ] = x ^ 2 + xy - x 12 + 6 = 12 [ 6 + ( 12 - 1 ) ] = 792 10 + 2 = 10 [ 2 + ( 10 - 1 ) ] = 110 1 + 9 = 1 [ 9 + ( 1 - 1 ) ] = 9 2 + 7 = 2 [ 7 + ( 2 - 1 ) ] = 16 11 + 4 = 11 [ 4 + ( 11 - 1 ) ] = 154 answer : e
Answer: e
Problem: at a certain high school , the senior class is 3 times the size of the junior class . if 1 / 3 of the seniors and 3 / 4 of the juniors study japanese , what fraction of the students in both classes study japanese ?
Options: a ) 1 / 2 , b ) 3 / 8 , c ) 5 / 16 , d ) 1 / 4 , e ) 7 / 16
Rationale: start by deciding on a number of students to represent the number of students in the senior class . for this example i will choose 300 students . that would make the number of students in the junior class 100 . then we can find out how many students are taking japanese in each grade and add them together . ( 1 / 3 ) * 300 = 100 and ( 3 / 4 ) * 100 = 75 . 100 + 75 = 175 . there are a total of 400 students in the junior class and senior class combined ( 100 + 300 = 300 ) , and there are 175 total students in japanese , so 175 students in japanese / 400 total students equals 7 / 16 of the students in both classes that study japanese . answer : e
Answer: e
Problem: a squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 4 feet . how many feet does the squirrel travels if the post is 12 feet tall and 3 feet in circumference ?
Options: a ) 9 feet , b ) 12 feet , c ) 13 feet , d ) 15 feet , e ) 18 feet
Rationale: "total circuit = 12 / 4 = 3 total feet squirrel travels = 3 * 3 = 9 feet answer : a"
Answer: a
Problem: evaluate 2 + 22 + 222 + 2.22
Options: a ) 269.72 , b ) 268.22 , c ) 248.21 , d ) 248.22 , e ) 268.21
Rationale: "2 + 22 + 222 + 2.22 = 248.22 option d"
Answer: d
Problem: the least number which when increased by 7 each divisible by each one of 24 , 32 , 36 and 54 is :
Options: a ) 857 , b ) 859 , c ) 869 , d ) 4320 , e ) none of these
Rationale: "solution required number = ( l . c . m . of 24 , 32 , 36 , 54 ) - 7 = 864 - 7 = 857 . answer a"
Answer: a
Problem: what is the area of a square field whose diagonal of length 12 m ?
Options: a ) 288 , b ) 72 , c ) 200 , d ) 112 , e ) 178
Rationale: "d 2 / 2 = ( 12 * 12 ) / 2 = 72 answer : b"
Answer: b
Problem: at a contest with 3,500 participants , 1 / 2 of the people are aged 18 to 22 . next year , the number of people aged 18 to 22 will increase by 1 / 7 . after this change , what percentage of the total 3,500 people will the 18 - to 22 - year - olds represent ?
Options: a ) 33 % , b ) 40 % , c ) 55 % , d ) 57.14 % , e ) 66.14 %
Rationale: "i just wanted to mention a couple of things here : * this is a pure ratio question ; the number 3,500 is completely irrelevant , and you can ignore it if you like . when we increase something by 1 / 7 , we are multiplying it by 1 + 1 / 7 = 8 / 7 , so the answer here must be ( 1 / 2 ) * ( 8 / 7 ) = 4 / 7 = 57.14 % . answer : d"
Answer: d
Problem: a recipe requires 2 1 / 2 ( mixed number ) cups of flour 2 3 / 4 ( mixed number ) cups of sugar and 1 1 / 3 ( mixed number ) cups of milk to make one cake . victor has 15 cups if flour , 16 cups of sugar and 8 cups of milk . what is the greatest number of cakes jerry can make using this recipe ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "less work up front : go through each item and see what the greatest number of cakes you can make with each . the lowest of these will be the right answer . flour : 15 cups , we need 2.5 cups each . just keep going up the line to see how many cakes we can make : that means i can make 2 cakes with 5 cups , so 6 cakes overall with 15 cups . i ' ve already got the answer narrowed to either a or b . sugar : 16 cups , we need 2.75 cups each . same principle . i can make 2 cups with 5.5 cups , so to make 6 cakes i ' d need 16.5 cups . i do n ' t have that much sugar , so we ' re limited to 5 cakes . no need to even do milk because we ' re already at 5 . sugar will be the limiting factor . answer is a"
Answer: a
Problem: daniel went to a shop and bought things worth rs . 25 , out of which 30 paise went on sales tax on taxable purchases . if the tax rate was 6 % , then what was the cost of the tax free items ?
Options: a ) 19.7 , b ) 20 , c ) 21.3 , d ) 21.5 , e ) 22
Rationale: "total cost of the items he purchased = rs . 25 given that out of this rs . 25 , 30 paise is given as tax = > total tax incurred = 30 paise = rs . 30 / 100 let the cost of the tax free items = x given that tax rate = 6 % ∴ ( 25 − 30 / 100 − x ) 6 / 100 = 30 / 100 ⇒ 6 ( 25 − 0.3 − x ) = 30 ⇒ ( 25 − 0.3 − x ) = 5 ⇒ x = 25 − 0.3 − 5 = 19.7 a"
Answer: a
Problem: the sum of the present age of henry and jill is 40 . what is their present ages if 11 years ago henry was twice the age of jill ?
Options: a ) and 27 , b ) and 24 , c ) and 23 , d ) and 29 , e ) of these
Rationale: "let the age of jill 11 years ago be x , age of henry be 2 x x + 11 + 2 x + 11 = 40 x = 6 present ages will be 17 and 23 answer : c"
Answer: c
Problem: if log 2 = 0.3010 and log 3 = 0.4771 , the value of log 5 512 is :
Options: a ) 2.87 , b ) 2.965 , c ) 3.876 , d ) 3.9 , e ) 4.526
Rationale: "log 5 512 = log 512 / log 5 = log 2 ^ 9 / log ( 10 / 2 ) = 9 log 2 / log 10 - log 2 = ( 9 * 0.3010 ) / 1 - 0.3010 = 2.709 / 0.699 = 2709 / 699 = 3.876 answer c"
Answer: c
Problem: a is half good a work man as b and together they finish a job in 18 days . in how many days working alone b finish the job ?
Options: a ) 23 , b ) 22 , c ) 27 , d ) 36 , e ) 48
Rationale: "c 27 wc = 1 : 2 2 x + x = 1 / 18 = > x = 1 / 54 2 x = 1 / 27 = > 27 days"
Answer: c
Problem: the radius and height of a right circular cone are in the ratio 3 : 4 . if its volume is 96 ∏ cm ³ , what is its slant height ?
Options: a ) 8 cm
b ) 10 cm
c ) 12 cm
d ) 14 cm
e ) none
Rationale: sol . let the radius and the height of the cone be 3 x and 4 x respectively . then , 1 / 3 * ∏ * ( 3 x ) ² * 4 x = 96 ∏ ⇔ 36 x ³ = ( 96 * 3 ) ⇔ x ³ = [ 96 * 3 / 36 ] = 8 ⇔ x = 2 & ther 4 ; radius = 6 cm , height = 8 cm . slant height = √ 6 ² + 8 ² cm = √ 100 cm = 10 cm . answer b
Answer: b
Problem: rs . 1500 is divided into two parts such that if one part is invested at 6 % and the other at 5 % the whole annual interest from both the sum is rs . 84 . how much was lent at 5 % ?
Options: a ) 299 , b ) 466 , c ) 578 , d ) 600 , e ) 677
Rationale: "( x * 5 * 1 ) / 100 + [ ( 1500 - x ) * 6 * 1 ] / 100 = 84 5 x / 100 + 90 – 6 x / 100 = 84 x / 100 = 6 = > x = 600 answer : d"
Answer: d
Problem: an engine moves at the speed of 60 kmph without any coaches attached to it . speed of the train reduces at the rate that varies directly as the square root of the number of coaches attached . when 4 coaches are attached speed decreases to 48 kmph . what will be the speed of train when 36 coaches are attached .
Options: a ) 24 , b ) 28 , c ) 20 , d ) 32 , e ) 40
Rationale: "1 . no . of coaches = 4 sqr root = 2 speed decreases by 12 12 = k * 2 k = 6 no . of coaches = 36 swr root = 6 decrease = 6 * 6 = 36 new speed = 60 - 36 = 24 a"
Answer: a
Problem: you and your friend spent a total of $ 15 for lunch . your friend spent $ 5 more than you . how much did your friend spend on their lunch ?
Options: a ) $ 9 , b ) $ 3 , c ) $ 4 , d ) $ 6 , e ) $ 10
Rationale: "my lunch = l , my friends lunch = l + 5 ( l ) + ( l + 5 ) = 15 l + l + 5 - 5 = 15 - 5 2 l = 10 l = 5 my friends lunch l + 5 = 5 + 5 = $ 10 , the answer is e"
Answer: e
Problem: the rear – most end of a 66 foot truck exits a 330 foot tunnel exactly 6 seconds after the front – most end of the truck entered the tunnel . if the truck traveled the entire tunnel at a uniform speed , what is the speed of the truck in miles per hour ( 1 mile = 5,280 feet ) ?
Options: a ) 225 , b ) 90 , c ) 45 , d ) 37.5 , e ) 27
Rationale: total length will be 330 + 66 = 396 time = 6 secs speed = 396 / 6 = 66 feet / sec conversion to miles per hour = 66 * 3600 / 5280 = 45 . answer c
Answer: c
Problem: the length of a room is 5.5 m and width is 3.75 m . find the cost of paving the floor by slabs at the rate of rs . 800 per sq . metre .
Options: a ) rs . 15000 , b ) rs . 15550 , c ) rs . 15600 , d ) rs . 16500 , e ) none of these
Rationale: "solution area of the floor = ( 5.5 × 3.75 ) m 2 = 20.625 m 2 ∴ cost of paving = rs . ( 800 × 20.625 ) = 16500 . answer d"
Answer: d
Problem: 2 men and 2 women are lined up in a row . what is the number of cases where they stand with each other in turn ? ( the number of cases in which men ( or women ) do not stand next to each other )
Options: a ) 4 , b ) 15 , c ) 18 , d ) 21 , e ) 24
Rationale: the list should be wmwmw . hence , from women 2 ! and men 2 ! , we get ( 2 ! ) ( 2 ! ) = 4 . therefore , the correct answer is a .
Answer: a
Problem: a , b , k start from the same place and travel in the same direction at speeds of 30 km / hr , 40 km / hr , 60 km / hr respectively . b starts six hours after a . if b and k overtake a at the same instant , how many hours after a did k start ?
Options: a ) 3 , b ) 4.5 , c ) 4 , d ) d ) 12 , e ) e ) 5
Rationale: "the table you made does n ' t make sense to me . all three meet at the same point means the distance they cover is the same . we know their rates are 30 , 40 and 60 . say the time taken by b is t hrs . then a takes 6 + t hrs . and we need to find the time taken by k . distance covered by a = distance covered by b 30 * ( 6 + t ) = 40 * t t = 18 hrs distance covered by b = distance covered by k 40 * t = 60 * time taken by k time taken by k = 40 * 18 / 60 = 12 hrs time taken by a = 6 + t = 6 + 18 = 24 hrs time taken by k = 12 hrs so k starts 24 - 12 = 12 hrs after a . ( answer d )"
Answer: d
Problem: how many paying stones , each measuring 2 1 / 2 m * 2 m are required to pave a rectangular court yard 70 m long and 16 1 / 2 m board ?
Options: a ) 99 , b ) 18 , c ) 16 , d ) 10 , e ) 231
Rationale: "70 * 33 / 2 = 5 / 2 * 2 * x = > x = 231 answer : e"
Answer: e
Problem: what is the rate percent when the simple interest on rs . 1200 amount to rs . 160 in 4 years ?
Options: a ) 3.3 % , b ) 7 % , c ) 9 % , d ) 2 % , e ) 4 %
Rationale: "160 = ( 1200 * 4 * r ) / 100 r = 3.3 % answer : a"
Answer: a
Problem: the simple form of the ratio 2 / 3 : 2 / 5 is ?
Options: a ) 5 : 0 , b ) 5 : 3 , c ) 5 : 1 , d ) 5 : 2 , e ) 5 : 7
Rationale: "2 / 3 : 2 / 5 = 10 : 6 = 5 : 3 answer : d"
Answer: d
Problem: on a map , 1 inch represents 28 miles . how many inches would be necessary to represent a distance of 383.6 miles ?
Options: a ) 5.2 , b ) 7.4 , c ) 13.7 , d ) 21.2 , e ) 28.7
Rationale: "28 miles represented by 1 inch 1 mile represented by ( 1 / 28 ) inch 383.6 miles represented by ( 1 / 28 ) * 383.6 approximately = 14 we should use estimation here as the answer options are not close . ( 28 * 10 = 280 and 28 * 20 = 560 , hence we select the only option between 10 and 20 ) answer c"
Answer: c
Problem: the average age of students of a class is 15.8 years . the average age of boys in the class is 16.4 years and that of the girls is 15.5 years , the ratio of the number of boys to the number of girls in the class is
Options: a ) 1 : 2 , b ) 2 : 3 , c ) 9 : 3 , d ) 6 : 3 , e ) 2 : 5
Rationale: "explanation : let the ratio be k : 1 . then , k * 16.4 + 1 * 15.5 = ( k + 1 ) * 15.8 < = > ( 16.4 - 15.8 ) k = ( 15.8 - 15.5 ) < = > k = 0.3 / 0.6 = 1 / 2 . required ratio = 1 / 2 : 1 = 1 : 2 . answer : a"
Answer: a
Problem: a car traveled 462 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city . if the car traveled 3 fewer miles per gallon in the city than on the highway , how many miles per gallon did the car travel in the city ?
Options: a ) 8 , b ) 16 , c ) 21 , d ) 22 , e ) 27
Rationale: i treat such problems as work ones . work = rate * time mileage ( m ) = rate ( mpg ) * gallons ( g ) x gallons is a full tank { 462 = rx { 336 = ( r - 3 ) x solve for r , r = 11 11 - 3 = 8 mpg a
Answer: a
Problem: how many multiples of 5 are less than 5000 , and also multiples of 50 ?
Options: a ) 100 , b ) 208 , c ) 625 , d ) 832 , e ) 833
Rationale: the lcm of 5 and 50 is 50 . divide 5000 / 50 = 100 . xxx . so a is your answer .
Answer: a
Problem: solution for 3.15 + . 014 + . 458
Options: a ) 3.622 , b ) 3.911 , c ) 4.938 , d ) 2.986 , e ) 2.999
Rationale: "3.15 + . 014 + . 458 = 0 0 = 0 - 3.15 - 0.014 - 0.458 0 = - 3.622 answer : a"
Answer: a
Problem: a , b and c are entered into a partnership . a invested rs . 6500 for 6 months , b invested rs . 8400 for 5 months and c invested for rs . 10000 for 3 months . a is a working partner and gets 5 % of the total profit for the same . find the share of c in a total profit of rs . 7400 .
Options: a ) 2997 , b ) 1900 , c ) 2887 , d ) 2898 , e ) 27912
Rationale: "65 * 6 : 84 * 5 : 100 * 3 26 : 28 : 20 c share = 74000 * 95 / 100 = 7030 * 20 / 74 = > 1900 . answer : b"
Answer: b
Problem: 3 , 7,12 , 18,25 . . . . . . . . . . . . . . 9 th terms
Options: a ) 43 , b ) 53 , c ) 63 , d ) 65 , e ) 78
Rationale: "3 + 4 = 7 7 + 5 = 12 12 + 6 = 18 18 + 7 = 25 25 + 8 = 33 33 + 9 = 42 42 + 10 = 52 52 + 11 = 63 answer : c"
Answer: c
Problem: if 60 % of ( x - y ) = 30 % of ( x + y ) then what percent of x is y ?
Options: a ) 33 % , b ) 10 % , c ) 5 % , d ) 15 % , e ) 25 %
Rationale: "60 % of ( x - y ) = 30 % of ( x + y ) ( 60 / 100 ) ( x - y ) = ( 30 / 100 ) ( x + y ) 6 ( x - y ) = 3 ( x + y ) 3 x = 9 y x = 3 y therefore required percentage = ( ( y / x ) x 100 ) % = ( ( y / 3 y ) x 100 ) = 33 % answer is a ."
Answer: a
Problem: working alone at their respective constant rates , a can complete a task in ‘ a ’ days and b in ‘ b ’ days . they take turns in doing the task with each working 2 days at a time . if a starts they finish the task in exactly 10 days . if b starts , they take a day more . how long does it take to complete the task if they both work together ?
Options: a ) 5 , b ) 4.5 , c ) 6 , d ) 7 , e ) 8
Rationale: work done by a & b in a day = x & y respectively . when a starts : no . of days when a works = 6 no . of days when b works = 4 → 6 x + 4 y = 1 when b starts : no . of days when b works = 5 no . of days when a works = 5 → 5 x + 5 y = 1 solving the above two equations for xy x = 1 / 10 y = 1 / 10 → total work done by ab in a day = 1 / 10 + 1 / 10 = 2 / 10 = 1 / 5 → no . of days to complete the work when both work together = 5 answer : a
Answer: a
Problem: a multiple choice test consists of 4 questions , and each question has 5 answer choices . in how many q ways can the test be completed if every question is unanswered ?
Options: a ) 24 , b ) 120 , c ) 625 , d ) 720 , e ) 1024
Rationale: 5 choices for each of the 4 questions , thus total q of 5 * 5 * 5 * 5 = 5 ^ 4 = 625 ways to answer all of them . answer : c .
Answer: c
Problem: two numbers are in the ratio 3 : 5 . if 9 be subtracted from each , they are in the ratio of 3 : 2 . the first number is :
Options: a ) a ) 3 , b ) b ) 98 , c ) c ) 34 , d ) d ) 35 , e ) e ) 62
Rationale: "( 3 x - 9 ) : ( 5 x - 9 ) = 3 : 2 x = 1 = > 3 x = 3 answer : a"
Answer: a
Problem: at a speed of 60 miles per hour , a certain car uses 1 gallon of gasoline every 30 miles . if the car starts with a full 12 gallon tank of gasoline and travels for 5 hours at 60 miles per hour , the amount of gasoline used would be what fraction of a full tank ?
Options: a ) 3 / 25 , b ) 11 / 36 , c ) 7 / 12 , d ) 2 / 3 , e ) 5 / 6
Rationale: "gas used = ( 5 hours ) * ( 60 miles / hour ) * ( 1 gallon / 30 miles ) = 10 gallons portion used = ( 10 ) / 12 = 5 / 6 ans e"
Answer: e
Problem: on a map , 2 inches represent 30 miles . how many miles approximately is the distance if you measured 38 centimeters assuming that 1 - inch is 2.54 centimeters ?
Options: a ) 226 , b ) 228 , c ) 230 , d ) 224 , e ) 232
Rationale: "1 inch = 2.54 cm 2 inch = 2.54 * 2 cm 5.08 cm = 30 miles 38 cms = 30 / 5.08 * 38 = 224 miles answer : d"
Answer: d
Problem: a is an integer greater than 49 but less than 61 , b is an integer greater than 59 but less than 71 , what is the range of a / b ?
Options: a ) 2 / 7 , b ) 1 / 2 , c ) 3 / 4 , d ) 1 , e ) 5 / 4
Rationale: "min value of a / b will be when b is highest and a is lowest - - - > a = 50 and b = 70 so , a / b = 5 / 7 max value of a / b will be when b is lowest and a is highest - - - > a = 60 and b = 60 so , a / b = 1 range is 1 - ( 5 / 7 ) = 2 / 7 . answer should be a ."
Answer: a
Problem: find the value of x , y by solving the below equations x + y = 15 x - y = 5
Options: a ) 10 , 5 , b ) 8 , 7 , c ) 9 , 6 , d ) 11 , 4 , e ) 12 , 3
Rationale: x + y = 15 - - - ( i ) x - y = 5 - - - - - ( ii ) by adding ( i ) and ( ii ) - - - - - - - - - - - - 2 x = 20 = = > x = 20 / 2 = 10 by replacing the value of x in ( i ) we get 10 + y = 15 = = > y = 15 - 10 = 5 . so , x = 10 , y = 5 answer a ) 10 , 5
Answer: a
Problem: in a urban village of india named ` ` owlna ' ' , 90 % people have refrigerator , 86 % people have television , 80 % people got computers and 80 % got air - conditionor . how many people ( minimum ) got all these luxury .
Options: a ) 23 % , b ) 36 % , c ) 30 % , d ) 34 % , e ) 42 %
Rationale: "b 10 % 100 - [ ( 100 - 90 ) + ( 100 - 86 ) + ( 100 - 80 ) + ( 100 - 80 ) ] = 100 - ( 10 + 14 + 20 + 20 ) = 100 - 64"
Answer: b
Problem: the annual interest rate earned by an investment increased by 8 percent from last year to this year . if the annual interest rate earned by the investment this year was 27 percent , what was the annual interest rate last year ?
Options: a ) 22 % , b ) 20 % , c ) 25 % , d ) 23 % , e ) 21 %
Rationale: "let i = interest rate i ( this year ) = i ( last year ) + 0.08 i ( last year ) = 1.08 i ( last year ) 27 = 1.08 x i ( last year ) i ( last year ) = 27 / 1.08 = 2700 / 108 = 25 % answer : c"
Answer: c
Problem: if a and b are positive numbers , and a ^ 3 + b ^ 3 = 140 , then the greatest possible value of a is between :
Options: a ) 0 and 2 , b ) 2 and 3 , c ) 3 and 4 , d ) 4 and 5 , e ) 5 and 8
Rationale: if a = 5.1 and b is a bit less than 2 , then a ^ 3 + b ^ 3 can equal 140 . if a > 8 , then a ^ 3 + b ^ 3 > 140 . the answer is e .
Answer: e
Problem: a train 160 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 140 m long ?
Options: a ) 40 sec , b ) 50 sec , c ) 44 sec , d ) 24 sec , e ) 60 sec
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 160 + 140 = 300 m required time = 300 * 2 / 25 = 24 sec answer : d"
Answer: d
Problem: the proportion of water to alcohol in solution a is 4 : 1 and the proportion of water to alcohol in solution b is 2 : 3 . if an equal amount of each solution is mixed together , what is the concentration of alcohol in the new solution ?
Options: a ) 39 % , b ) 40 % , c ) 41 % , d ) 42 % , e ) 43 %
Rationale: let v be the total volume of the new solution . then a volume of v / 2 was added from each solution a and b . the amount of alcohol added to the new solution was : ( 1 / 5 ) ( v / 2 ) + ( 3 / 5 ) ( v / 2 ) = v / 10 + 3 v / 10 = 4 v / 10 = 2 v / 5 . the concentration of alcohol is 2 / 5 = 40 % the answer is b .
Answer: b
Problem: at what rate percent on simple interest will rs . 750 amount to rs . 900 in 4 years ?
Options: a ) 6 % , b ) 2 % , c ) 4 % , d ) 5 % , e ) 3 %
Rationale: "150 = ( 750 * 4 * r ) / 100 r = 5 % answer : d"
Answer: d
Problem: if m is not equal to zero , and m + 1 / m = 1 , then what is the value of m ^ 4 + ( 1 / m ) ^ 4 ?
Options: a ) - 5 , b ) - 4 , c ) - 3 , d ) - 2 , e ) - 1
Rationale: m + 1 / m = 1 we square both sides so we have m ^ 2 + 1 / m ^ 2 + 2 = 1 or m ^ 2 + 1 / m ^ 2 = - 1 squaring again we have m ^ 4 + 1 / m ^ 4 + 2 = 1 or m ^ 4 + 1 / m ^ 4 = - 1 answer = - 1 ( e )
Answer: e
Problem: the ratio of money with ram and gopal is 7 : 17 and that with gopal and krishan is 7 : 17 . if ram has rs . 539 , krishan has ?
Options: a ) s . 2890 , b ) s . 2330 , c ) s . 1190 , d ) s . 1620 , e ) s . 3179
Rationale: "ram : gopal = 7 : 17 = 49 : 119 gopal : krishan = 7 : 17 = 119 : 289 ram : gopal : krishan = 49 : 119 : 289 ram : krishan = 49 : 289 thus , 49 : 289 = 539 : n & there n = 289 x 539 / 49 = rs . 3179 answer : e"
Answer: e
Problem: the price of a cycle is reduced by 25 per cent . the new price is reduced by a further 20 per cent . the two reductions together are equal to a single reduction of
Options: a ) 33 , b ) 40 , c ) 99 , d ) 28 , e ) 72
Rationale: "explanation : let the original price of the cycle be 100 . after the first reduction the price will be 75 . this new price is then reduced by 20 % = 0.8 x 75 = 60 60 represents a reduction of 40 percent on the original . answer : b ) 40 %"
Answer: b
Problem: suresh started a business , investing rs . 18000 . after 3 months and 4 months respectively , rohan and sudhir joined him with capitals of 12000 and 9000 . at the end of the year the total profit was rs . 3960 . what is the difference between rohan ’ s and sudhir ’ s share in the profit ?
Options: a ) s . 345 , b ) s . 350 , c ) s . 352 , d ) s . 360 , e ) s . 368
Rationale: "suresh : rohan : sudhir ratio of their investments = 18000 × 12 : 12000 × 9 : 9000 × 8 = 6 : 3 : 2 the difference between rohan ’ s and sudhir ’ s share = 1 share : . i . e . = rs . 3960 × 1 / 11 = rs . 360 . d"
Answer: d
Problem: in a ratio which is equal to 7 : 9 , if the antecedent is 56 , then the consequent is ?
Options: a ) 72 , b ) 85 , c ) 64 , d ) 51 , e ) 45
Rationale: "we have 7 / 9 = 56 / x 7 x = 56 * 9 x = 72 consequent = 72 answer is a"
Answer: a
Problem: if 20 % of a certain number is 60 , then what is 80 % of that number ?
Options: a ) 220 , b ) 210 , c ) 240 , d ) 250 , e ) 260
Rationale: "explanation : 20 % = 20 * 3 = 60 80 % = 80 * 3 = 240 answer : option c"
Answer: c
Problem: if 2 men or 3 women can reap a field in 5 days how long will 5 men and 6 women take to reap it ?
Options: a ) 2 / 24 , b ) 6 / 18 , c ) 2 / 22 , d ) 5 / 12 , e ) 9 / 10
Rationale: "explanation : 2 men reap 2 / 5 field in 1 day 1 man reap 1 / ( 2 x 5 ) 3 women reap 1 / 43 field in 1 day 1 woman reap 1 / ( 5 x 3 ) 5 men and 6 women reap ( 5 / ( 2 x 5 ) + 6 / ( 3 x 5 ) ) = 9 / 10 in 1 day 5 men and 6 women will reap the field in 9 / 10 days answer : option e"
Answer: e
Problem: a customer went to a shop and paid a total of $ 30 , out of which $ 1.28 was for sales tax on taxable purchases . if the tax rate was 8 % , then what was the cost of the tax free items ?
Options: a ) $ 9.84 , b ) $ 10.68 , c ) $ 11.26 , d ) $ 12.72 , e ) $ 13.54
Rationale: the total cost was $ 30 . the tax was $ 1.28 let the original price of the taxable items = x given that tax rate = 8 % 0.08 x = 1.28 x = $ 16 the cost of the tax free items was $ 30 - $ 16 - $ 1.28 = $ 12.72 the answer is d .
Answer: d
Problem: 2 + 2 + 2 ² + 2 ³ . . . + 2 ^ 11
Options: a ) 2 ^ 9 , b ) 2 ^ 10 , c ) 2 ^ 16 , d ) 2 ^ 12 , e ) 2 ^ 37
Rationale: "2 + 2 = 2 ^ 2 2 ^ 2 + 2 ^ 2 = ( 2 ^ 2 ) * ( 1 + 1 ) = 2 ^ 3 2 ^ 3 + 2 ^ 3 = ( 2 ^ 3 ) * ( 1 + 1 ) = 2 ^ 4 so you can notice the pattern . . . in the end you will have 2 ^ 11 + 2 ^ 11 , which will give you 2 ^ 12 answer d"
Answer: d
Problem: if a number p is prime , and 2 p + 5 = q , where q is also prime , then the decimal expansion of 1 / q will produce a decimal with q - 1 digits . if this method produces a decimal with 166 digits , what is the units digit of the product of p and q ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: 1 / 7 = 014285 . . . ( a repeating pattern one digit long ) a
Answer: a
Problem: walking at 25 % of his usual speed a man takes 24 minutes more to cover a distance . what is his usual time to cover this distance ?
Options: a ) 8 , b ) 16 , c ) 42 , d ) 48 , e ) 54
Rationale: "speed is inversly proprtional to time walking at 25 % of speed meand 1 / 4 s takes 4 t . it takes 24 minutes extra to cover the distance . then 4 t = t + 24 3 t = 24 t = 8 . option a is correct"
Answer: a
Problem: the lowest number which should be added to 1277 so that the sum is exactly divisible by 3 , 2 , 5 , 4 and 7 is :
Options: a ) 303 , b ) 403 , c ) 203 , d ) 453 , e ) 203
Rationale: "l . c . m . of 5 , 6 , 4 and 3 = 420 . on dividing 1277 by 420 , the remainder is 17 . number to be added = ( 420 - 17 ) = 403 . answer : option ' b '"
Answer: b
Problem: father is aged 3 times more than his son ronit . after 8 years , he would be two and half times if ronit ' s age . after further 8 years , how many times would he be of ronit ' s age ?
Options: a ) 2 times , b ) 2.5 times , c ) 3 times , d ) 3.8 times , e ) 4 times
Rationale: ronit ' s present age be x years . then , father ' s present age = ( x + 3 x ) years = 4 x years therefore ( 4 x + 8 ) = 5 / 2 ( x + 8 ) 8 x + 16 = 5 x + 40 3 x = 24 , x = 8 , ratio = ( 4 x + 16 ) / ( x + 16 ) = 48 / 24 = 2 , correct answer ( a )
Answer: a
Problem: due to construction , the speed limit along an 12 - mile section of highway is reduced from 55 miles per hour to 35 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "12 / 35 - 12 / 55 = 12 / 5 * ( 11 - 7 ) / 77 = 12 / 5 * 4 / 77 * 60 min = 12 * 12 * 4 / 77 = 576 / 77 ~ 7.4 answer - d"
Answer: d
Problem: the area of sector of a circle whose radius is 12 metro and whose angle at the center is 54 â ° is ?
Options: a ) 52.6 , b ) 52.9 , c ) 67.9 , d ) 52.1 , e ) 52.2
Rationale: "54 / 360 * 22 / 7 * 12 * 12 = 67.9 m 2 answer : c"
Answer: c