Cheukting/mathqa huggingface dataset:
Question (physics): 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
Question (physics): 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
Question (physics): 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
Question (geometry): 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
Question (general): 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
Question (physics): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (other): 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
Question (general): 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
Question (physics): 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
Question (general): 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
Question (gain): 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
Question (general): 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
Question (general): 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
Question (gain): 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
Question (gain): 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
Question (general): 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
Question (physics): 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
Question (gain): 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
Question (gain): 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
Question (physics): 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
Question (other): 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
Question (general): 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
Question (gain): 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
Question (physics): 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
Question (gain): 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
Question (gain): 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
Question (gain): 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
Question (general): 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
Question (other): 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
Question (general): 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
Question (other): 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
Question (physics): 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
Question (gain): 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
Question (general): 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
Question (probability): 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
Question (physics): 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
Question (physics): 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
Question (gain): 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
Question (other): 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
Question (physics): 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
Question (physics): 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
Question (physics): 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
Question (general): 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
Question (physics): 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
Question (gain): 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
Question (general): 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