Cheukting/mathqa huggingface dataset:
Question (general): a sum of rs . 1360 has been divided among a , b and c such that a gets 2 / 3 of what b gets and b gets 1 / 4 of what c gets . b ' s share is :
Options: a ) rs . 120 , b ) rs . 160 , c ) rs . 240 , d ) rs . 300 , e ) rs . 500
Rationale: "let c ' s share = rs . x then , b ' s share = rs . x / 4 ; a ' s share = rs . 2 / 3 * x / 4 = rs . x / 6 therefore x / 6 + x / 4 + x = 1360 17 x / 12 = 1360 x = 1360 * 12 / 17 = rs . 960 hence , b ' s share = rs . 960 / 4 = rs . 240 answer : c"
Answer: c
Question (physics): how many cuboids of length 5 m , width 3 m and height 2 m can be farmed from a cuboid of 18 m length , 15 m width and 2 m height .
Options: a ) 106 , b ) 109 , c ) 108 , d ) 101 , e ) 104
Rationale: "( 18 × 15 × 12 ) / ( 5 × 3 × 2 ) = 108 answer is c ."
Answer: c
Question (general): two - third of a positive number and 16 / 216 of its reciprocal are equal . find the positive number .
Options: a ) 4 / 12 , b ) 4 / 17 , c ) 4 / 15 , d ) 4 / 11 , e ) 4 / 03
Rationale: "explanation : let the positive number be x . then , 2 / 3 x = 16 / 216 * 1 / x x 2 = 16 / 216 * 3 / 2 = 16 / 144 x = √ 16 / 144 = 4 / 12 . answer : a"
Answer: a
Question (general): find large number from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder
Options: a ) 1235 , b ) 1346 , c ) 1378 , d ) 1635 , e ) 1489
Rationale: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 15 5 x = 1350 x = 270 large number = 270 + 1365 = 1635 d"
Answer: d
Question (general): the average of first three prime numbers greater than 5 is ?
Options: a ) 12.6 , b ) 12.9 , c ) 22.3 , d ) 10.3 , e ) 12.7
Rationale: "7 + 11 + 13 = 31 / 3 = 10.3 answer : d"
Answer: d
Question (general): in a recent election , james received 0.5 percent of the 2,000 votes cast . to win the election , a candidate needed to receive more than 50 percent of the vote . how many additional votes would james have needed to win the election ?
Options: a ) 901 , b ) 989 , c ) 990 , d ) 991 , e ) 1,001
Rationale: james = ( 0.5 / 100 ) * 2000 = 10 votes to win = ( 50 / 100 ) * total votes + 1 = ( 50 / 100 ) * 2000 + 1 = 1001 remaining voted needed to win election = 1001 - 10 = 991 answer : option d
Answer: d
Question (general): if 12 : 8 : : x : 16 , then find the value of x
Options: a ) 18 , b ) 24 , c ) 28 , d ) 16 , e ) 20
Rationale: explanation : treat 12 : 8 as 12 / 8 and x : 16 as x / 16 , treat : : as = so we get 12 / 8 = x / 16 = > 8 x = 192 = > x = 24 option b
Answer: b
Question (general): what least number must be subtracted from 3832 so that the remaining number is divisible by 5 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "on dividing 3832 by 5 , we get remainder = 2 . required number be subtracted = 2 answer : b"
Answer: b
Question (physics): find the length of the wire required to go 14 times round a square field containing 5625 m 2 .
Options: a ) 15840 , b ) 3388 , c ) 4200 , d ) 8766 , e ) 66711
Rationale: "a 2 = 5625 = > a = 75 4 a = 300 300 * 14 = 4200 answer : c"
Answer: c
Question (physics): how many bricks , each measuring 25 cm x 11.25 cm x 6 cm , will be needed to build a wall of 1 m x 2 m x 20 cm ?
Options: a ) 5600 , b ) 6000 , c ) 237 , d ) 7200 , e ) 8600
Rationale: "number of bricks = volume of the wall / volume of 1 brick = ( 100 x 200 x 20 ) / ( 25 x 11.25 x 6 ) = 237 . answer : option c"
Answer: c
Question (physics): spanish language broadcast records last 90 min on each of two sides . if it takes 3 hours to translate one hour of broadcast , how long will it take to translate 16 full records ?
Options: a ) 144 hours , b ) 124 hours , c ) 134 hours , d ) 154 hours , e ) 164 hours
Rationale: records last 90 min on each of 2 sides , = = > record last 90 * 2 = 180 min = 3 hours 16 full records - - > 16 * 3 = 48 hour broadcast given , 3 hours to translate 1 hour of broadcast let x be the time required to translate 48 hour broadcast ( 16 full records ) x = 48 * 3 = 144 hours answer : a
Answer: a
Question (other): a began business with rs . 45000 and was joined afterwards by b with rs . 5400 . when did b join if the profits at the end of the year were divided in the ratio of 2 : 1 ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 6 , e ) 5
Rationale: "45 * 12 : 54 * x = 2 : 1 x = 5 12 - 5 = 7 . answer : a"
Answer: a
Question (physics): a can do a piece of work in 4 hours ; b and c together can do it in 3 hours , which a and c together can do it in 2 hours . how long will b alone take to do it ?
Options: a ) 15 hours , b ) 14 hours , c ) 12 hours , d ) 74 hours , e ) 79 hours
Rationale: "a ' s 1 hour work = 1 / 4 ; ( b + c ) ' s 1 hour work = 1 / 3 ; ( a + c ) ' s 1 hour work = 1 / 2 ( a + b + c ) ' s 1 hour work = ( 1 / 4 + 1 / 3 ) = 7 / 12 b ' s 1 hour work = ( 7 / 12 + 1 / 2 ) = 1 / 12 b alone will take 12 hours to do the work . answer : c"
Answer: c
Question (physics): how many seconds will a 650 meter long train moving with a speed of 63 km / hr take to cross a man walking with a speed of 3 km / hr in the direction of the train ?
Options: a ) 48 , b ) 36 , c ) 26 , d ) 39 , e ) 18
Rationale: "explanation : here distance d = 650 mts speed s = 63 - 3 = 60 kmph = 60 x 5 / 18 m / s time t = = 39 sec . answer : d"
Answer: d
Question (physics): today is thursday . i came home from a trip 3 days before the day after last monday . how many days have i been home ?
Options: a ) 1 day , b ) 2 days , c ) 7 days , d ) 6 days , e ) 10 days
Rationale: d 6 days the day after last monday was tuesday . if i came home 3 days before that , i came home on saturday , sunday , monday , tuesday , wednesday , and thursday = 6 days .
Answer: d
Question (gain): an article is bought for rs . 675 and sold for rs . 1100 , find the gain percent ?
Options: a ) 65 % , b ) 64 % , c ) 63 % , d ) 62 % , e ) 61 %
Rationale: "675 - - - - 425 100 - - - - ? = > = 63 % answer : c"
Answer: c
Question (physics): in one hour , a boat goes 19 km along the stream and 5 km against the stream . the speed of the boat in still water ( in km / hr ) is :
Options: a ) 2 , b ) 4 , c ) 7 , d ) 12 , e ) 15
Rationale: "sol . speed in still water = 1 / 2 ( 19 + 5 ) kmph = 12 kmph . answer d"
Answer: d
Question (gain): a salesperson received a commission of 3 percent of the sale price for each of the first 100 machines that she sold and 4 percent of the sale price for each machine that she sold after the first 100 . if the sale price of each machine was $ 10,000 and the salesperson received a $ 45,000 commission , how many machines did she sell ?
Options: a ) 140 , b ) 103 , c ) 105 , d ) 115 , e ) 120
Rationale: "first 100 machines = 3 % commission = 0.03 * 100 * 10000 = 30000 commission from sale of next machines = 46000 - 30000 = 16000 so 40 more machines . . total = 140 machines imo a . ."
Answer: a
Question (general): solve the equation for x : 6 x - 27 + 3 x = 4 + 9 - x
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "d 4 9 x + x = 13 + 27 10 x = 40 = > x = 4"
Answer: d
Question (general): a profit of rs . 900 is divided between x and y in the ratio of 1 / 2 : 1 / 3 . what is the difference between their profit shares ?
Options: a ) s . 280 , b ) s . 180 , c ) s . 380 , d ) s . 50 , e ) s . 90
Rationale: a profit of rs . 900 is divided between x and y in the ratio of 1 / 2 : 1 / 3 or 3 : 2 . so profits are 540 and 360 . difference in profit share = 540 - 360 = 180 answer : b
Answer: b
Question (general): a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 27 , the how old is b ?
Options: a ) 7 , b ) 9 , c ) 8 , d ) 11 , e ) 10
Rationale: "explanation : let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 27 ⇒ 5 x = 25 ⇒ x = 5 . hence , b ' s age = 2 x = 10 years . answer : e"
Answer: e
Question (general): calculate the share of y , if rs . 2880 is divided among x , y and z in the ratio 3 : 5 : 8 ?
Options: a ) 540 , b ) 520 , c ) 140 , d ) 560 , e ) 240
Rationale: 3 + 5 + 8 = 16 2880 / 16 = 180 so y ' s share = 3 * 180 = 540 answer : a
Answer: a
Question (general): 3 years ago , paula was 3 times as old as karl . in 9 years , paula will be twice as old as karl . what is the sum of their ages now ?
Options: a ) 42 , b ) 46 , c ) 50 , d ) 54 , e ) 58
Rationale: "p - 3 = 3 ( k - 3 ) and so p = 3 k - 6 p + 9 = 2 ( k + 9 ) ( 3 k - 6 ) + 9 = 2 k + 18 k = 15 p = 39 p + k = 54 the answer is d ."
Answer: d
Question (physics): a train running at the speed of 50 km / hr crosses a post in 4 seconds . what is the length of the train ?
Options: a ) 90 , b ) 120 , c ) 60 , d ) 95 , e ) 75
Rationale: "speed = ( 54 x 5 / 18 ) = 15 m / sec . length of the train = ( speed x time ) . length of the train = 15 x 4 m = 60 m . answer : c"
Answer: c
Question (physics): if soundharya rows 49 km upstream and 77 km down steam taking 7 hours each , then the speed of the stream
Options: a ) 6 kmph , b ) 5 kmph , c ) 2 kmph , d ) 3 kmph , e ) 4 kmph
Rationale: speed upstream = 49 / 7 = 7 kmph speed down stream = 77 / 7 = 11 kmph speed of stream = ½ ( 11 - 7 ) = 2 kmph answer : c
Answer: c
Question (general): the digital sum of a number is the sum of its digits . for how many of the positive integers 24 - 140 inclusive is the digital sum a multiple of 7 ?
Options: a ) 7 , b ) 8 , c ) 14 , d ) 15 , e ) 20
Rationale: is there other way than just listing ? 25 34 43 52 59 61 68 70 77 86 95 106 115 124 133 15 ways . . d
Answer: d
Question (other): the ratio of 2 numbers is 2 : 5 and their h . c . f . is 6 . their l . c . m . is ?
Options: a ) 20 , b ) 24 , c ) 52 , d ) 36 , e ) 60
Rationale: "let the numbers be 2 x and 5 x their h . c . f . = 6 so the numbers are 2 * 6 , 5 * 6 = 12,30 l . c . m . = 60 answer is e"
Answer: e
Question (physics): 20 beavers , working together in a constant pace , can build a dam in 6 hours . how many hours will it take 12 beavers that work at the same pace , to build the same dam ?
Options: a ) 10 . , b ) 4 . , c ) 5 . , d ) 6 , e ) 8 .
Rationale: "total work = 20 * 6 = 120 beaver hours 12 beaver * x = 120 beaver hours x = 120 / 12 = 10 answer : a"
Answer: a
Question (other): if a student loses 6 kilograms , he will weigh twice as much as his sister . together they now weigh 126 kilograms . what is the student ' s present weight in kilograms ?
Options: a ) 82 , b ) 84 , c ) 86 , d ) 88 , e ) 90
Rationale: "let x be the weight of the sister . then the student ' s weight is 2 x + 6 . x + ( 2 x + 6 ) = 126 3 x = 120 x = 40 kg then the student ' s weight is 86 kg . the answer is c ."
Answer: c
Question (gain): a person buys an article at rs . 575 . at what price should he sell the article so as to make a profit of 15 % ?
Options: a ) 600 , b ) 277 , c ) 269 , d ) 661.25 , e ) 281
Rationale: "cost price = rs . 575 profit = 15 % of 575 = rs . 86.25 selling price = cost price + profit = 575 + 86.25 = 661.25 answer : d"
Answer: d
Question (physics): two consultants can type up a report in 12.5 hours and edit it in 7.5 hours . if mary needs 30 hours to type the report and jim needs 12 hours to edit it alone , how many t hours will it take if jim types the report and mary edits it immediately after he is done ?
Options: a ) 41.4 , b ) 34.1 , c ) 13.4 , d ) 12.4 , e ) 10.8
Rationale: "break down the problem into two pieces : typing and editing . mary needs 30 hours to type the report - - > mary ' s typing rate = 1 / 30 ( rate reciprocal of time ) ( point 1 in theory below ) ; mary and jim can type up a report in 12.5 and - - > 1 / 30 + 1 / x = 1 / 12.5 = 2 / 25 ( where x is the time needed for jim to type the report alone ) ( point 23 in theory below ) - - > x = 150 / 7 ; jim needs 12 hours to edit the report - - > jim ' s editing rate = 1 / 12 ; mary and jim can edit a report in 7.5 and - - > 1 / y + 1 / 12 = 1 / 7.5 = 2 / 15 ( where y is the time needed for mary to edit the report alone ) - - > y = 20 ; how many t hours will it take if jim types the report and mary edits it immediately after he is done - - > x + y = 150 / 7 + 20 = ~ 41.4 answer : a ."
Answer: a
Question (general): an amount of rs . 1638 was divided among a , b and c , in the ratio 1 / 2 : 1 / 3 : 1 / 4 . find the share of a ?
Options: a ) 656 , b ) 456 , c ) 756 , d ) 745 , e ) 720
Rationale: let the shares of a , b and c be a , b and c respectively . a : b : c = 1 / 2 : 1 / 3 : 1 / 4 let us express each term with a common denominator which is the last number divisible by the denominators of each term i . e . , 12 . a : b : c = 6 / 12 : 4 / 12 : 3 / 12 = 6 : 4 : 3 . share of a = 6 / 13 * 1638 = rs . 756 answer : c
Answer: c
Question (general): what least value should be replaced by * in 2551112 * so the number become divisible by 6
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "explanation : trick : number is divisible by 6 , if sum of all digits is divisible by 3 and 2 , so ( 2 + 5 + 5 + 1 + 1 + 1 + 2 + * ) = 17 + * should be divisible by , 17 + 1 will be divisible by 3 , but we ca n ' t take this number because 1 is not dividable by 2 ( 2 only dividable by those numbers who contain even number at last position ) so that least number is 4 . answer : option b"
Answer: b
Question (general): what number is obtained by adding the units digits of 734 ^ 100 and 347 ^ 83 ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "the units digit of 734 ^ 100 is 6 because 4 raised to the power of an even integer ends in 6 . the units digit of 347 ^ 83 is 3 because powers of 7 end in 7 , 9 , 3 , or 1 cyclically . since 83 is in the form 4 n + 3 , the units digit is 3 . then 6 + 3 = 9 . the answer is c ."
Answer: c
Question (geometry): in two triangles , the ratio of the areas is 4 : 3 and the ratio of their heights is 3 : 4 . find the ratio of their bases .
Options: a ) 2 : 3
b ) 4 : 5
c ) 16 : 9
d ) 7 : 9
e ) 8 : 5
Rationale: sol . let the bases of the two triangles be x and y and their heights be 3 h and 4 h respectively . then , ( ( 1 / 2 ) x xx 3 h ) / ( 1 / 2 ) x y x 4 h ) = 4 / 3  x / y = ( 4 / 3 x 4 / 3 ) = 16 / 9 required ratio = 16 : 9 . ans : c
Answer: c
Question (gain): a trader sells 40 metres of cloth for rs . 8200 at a profit of rs . 15 per metre of cloth . how much profit will the trder earn on 40 metres of cloth ?
Options: a ) rs . 950 , b ) rs . 1500 , c ) rs . 600 , d ) rs . 1200 , e ) none of these
Rationale: "explanation : sp of 1 metre cloth = 8200 / 40 = rs . 205 . cp of 1 metre cloth = rs . 205 – 15 = rs . 190 cp on 40 metres = 190 x 40 = rs . 7600 profit earned on 40 metres cloth = rs . 8200 – rs . 7600 = rs . 600 . answer : option c"
Answer: c
Question (probability): what is the probability of drawing a queen from a deck of 52 cards ?
Options: a ) 4 / 13 , b ) 1 / 13 , c ) 4 , d ) 1 , e ) 2 / 13
Rationale: "total number of cards , n ( s ) = 52 total number of queen cards , n ( e ) = 4 p ( e ) = n ( e ) / n ( s ) = 4 / 52 = 1 / 13 option b is answer"
Answer: b
Question (physics): a thief goes away with a santro car at a speed of 50 kmph . the theft has been discovered after half an hour and the owner sets off in a bike at 60 kmph when will the owner over take the thief from the start ?
Options: a ) a ) 2 , b ) b ) 5 , c ) c ) 7 , d ) d ) 5 , e ) e ) 8
Rationale: "explanation : | - - - - - - - - - - - 20 - - - - - - - - - - - - - - - - - - - - | 60 50 d = 20 rs = 60 – 50 = 10 t = 20 / 10 = 2 hours answer : option a"
Answer: a
Question (general): the average weight of 18 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg . find the average weights of all the boys in the class .
Options: a ) 48.68077 , b ) 42.25983 , c ) 50 , d ) 51.25388 , e ) 52.25
Rationale: "explanation : average weight of 18 boys = 50.25 total weight of 18 boys = 50.25 × 18 average weight of remaining 8 boys = 45.15 total weight of remaining 8 boys = 45.15 × 8 total weight of all boys in the class = ( 50.25 × 18 ) + ( 45.15 × 8 ) total boys = 18 + 8 = 26 average weight of all the boys = ( 50.25 × 18 ) + ( 45.15 × 8 ) / 26 = 48.68077 answer : option a"
Answer: a
Question (general): how many words , with or without meaning , can be formed using all letters of the word good using each letter exactly once ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 23 , e ) 24
Rationale: "the word good has exactly 4 letters which are all different . therefore the number of words that can be formed = number of permutations of 4 letters taken all at a time . = p ( 4 , 4 ) = 4 ! = 4 x 3 x 2 × 1 = 24 answer : e"
Answer: e
Question (geometry): in right triangle abc , ac is the hypotenuse . if ac is 40 and ab + bc = 60 , what is the area of the triangle abc ?
Options: a ) 225 , b ) 450 , c ) 25 √ 2 , d ) 500 , e ) 200 √ 2
Rationale: "square ab + bc = 60 : ( ab ) ^ 2 + 2 * ab * bc + ( bc ) ^ 2 = 3600 . since ( ac ) ^ 2 = ( ab ) ^ 2 + ( bc ) ^ 2 = 40 ^ 2 = 1600 , then ( ab ) ^ 2 + 2 * ab * bc + ( bc ) ^ 2 = 1600 + 2 * ab * bc = 3600 . 1600 + 2 * ab * bc = 3600 . ab * bc = 1000 . the area = 1 / 2 * ab * bc = 500 . answer : d ."
Answer: d
Question (geometry): the ratio of the area of a square to that of the square drawn on its diagonal is
Options: a ) 1 : 2 , b ) 1 : 0 , c ) 1 : 7 , d ) 1 : 5 , e ) 1 : 6
Rationale: answer : a ) 1 : 2
Answer: a
Question (general): a 4 digit number divisible by 7 becomes divisible by 3 when 19 is added to it . the largest such number is :
Options: a ) 4461 , b ) 4473 , c ) 4479 , d ) 4487 , e ) 4491
Rationale: out of all the 5 options , only 4487 is not divisible by 3 . all others are divisible so answer = d ( no further calculation required ) addition of any two non - divisible numbers by 3 gives the resultant divisible by 3 19 is non - divisible by 3 ; we are adding a number to that so that the resultant becomes divisible by 3 applying the above rule , it means that the number which we are going to add should be non - divisible by 3 so comes the answer = 4487 answer : d
Answer: d
Question (general): what is the probability for a family with 3 children to have a girl and two boys ( assuming the probability of having a boy or a girl is equal ) ?
Options: a ) 1 / 8 , b ) 1 / 4 , c ) 1 / 2 , d ) 3 / 8 , e ) 5 / 8
Rationale: one possible case is : girl - boy - boy the probability of this is 1 / 2 * 1 / 2 * 1 / 2 = 1 / 8 there are 3 c 2 = 3 such cases so we should multiply by 3 . p ( one girl and two boys ) = 3 / 8 the answer is d .
Answer: d
Question (general): a manufacturer produces a certain men ' s athletic shoe in integer sizes from 8 to 17 . for this particular shoe , each unit increase in size corresponds to a 1 / 5 - inch increase in the length of the shoe . if the largest size of this shoe is 30 % longer than the smallest size , how long , in inches , is the shoe in size 15 ?
Options: a ) 6.8 , b ) 7.4 , c ) 7.7 , d ) 8.2 , e ) 8.6
Rationale: "let x be the length of the size 8 shoe . then 0.3 x = 9 / 5 x = 90 / 15 = 6 inches the size 15 shoe has a length of 6 + 7 / 5 = 7.4 inches the answer is b ."
Answer: b
Question (general): if x + | x | + y = 7 and x + | y | - y = 5 what is x + y = ?
Options: a ) 1 , b ) - 1 , c ) 3 , d ) 5 , e ) 13
Rationale: "if x < 0 and y < 0 , then we ' ll have x - x + y = 7 and x - y - y = 6 . from the first equation y = 7 , so we can discard this case since y is not less than 0 . if x > = 0 and y < 0 , then we ' ll have x + x + y = 7 and x - y - y = 6 . solving gives x = 4 > 0 and y = - 1 < 0 - - > x + y = 3 . since in ps questions only one answer choice can be correct , then the answer is c ( so , we can stop here and not even consider other two cases ) . answer : c . adding both eqn we get 2 x + ixi + iyi = 13 now considering x < 0 and y > 0 2 x - x + y = 13 we get x + y = 5 hence answer should be d"
Answer: d
Question (physics): a 240 m long train running at the speed of 120 km / hr crosses another train running in opposite direction at the speed of 80 km / hr in 9 sec . what is the length of the other train ?
Options: a ) 260 , b ) 250 , c ) 240 , d ) 230 , e ) 220
Rationale: "relative speed = 120 + 80 = 200 km / hr . = 200 * 5 / 18 = 500 / 9 m / sec . let the length of the other train be x m . then , ( x + 240 ) / 9 = 500 / 9 = > x = 260 . answer : option a"
Answer: a
Question (geometry): 34 . the side surface of a cylinder is rolled with a rectangular plate . if the perimeter of the circular base is 9 feet , and the diagonal of the rectangular plate was 15 ft . what is height of the of the cylinder ?
Options: a ) 12
b ) 15
c ) 10
d ) 8
e ) 14
Rationale: think of a pringles can . if you took off the bottom and top and cut a slit down the length , it would flatten to a rectangle . the dimensions of the rectangle are the height of the can and the circumference of the circle . since you know both , one side and thehypothenuse use pythagoreans theorem or properties of 3 - 4 - 5 triangles to solve for the other side , 12 . correct answer a
Answer: a
Question (gain): what quantity of water should be added to reduce 9 liters of 50 % acidic liquid to 30 % acidic liquid ?
Options: a ) 6 liters , b ) 8 liters , c ) 10 liters , d ) 12 liters , e ) 15 liters
Rationale: acid in 9 liters = 50 % of 9 = 4.5 liters suppose x liters of water be added . then 4.5 liters of acid in 9 + x liters of diluted solution 30 % of 9 + x = 4.5 27 + 3 x = 45 x = 6 liters answer is a
Answer: a
Question (gain): a man gains 20 % by selling an article for a certain price . if the sells it at double the price , the percentage of profit will be :
Options: a ) 327 , b ) 140 , c ) 277 , d ) 178 , e ) 112
Rationale: "let c . p . = rs . x . then , s . p . = rs . ( 12 % of x ) = rs . 6 x / 5 new s . p . = 2 * 6 x / 5 = rs . 12 x / 5 profit = 12 x / 5 - x = rs . 7 x / 5 profit = 7 x / 5 * 1 / x * 100 = 140 % . \ answer : d"
Answer: d
Question (general): the average weight of 20 persons sitting in a boat had some value . a new person added to them whose weight was 46 kg only . due to his arrival , the average weight of all the persons decreased by 5 kg . find the average weight of first 20 persons ?
Options: a ) 55 , b ) 56 , c ) 57 , d ) 58 , e ) 59
Rationale: "20 x + 46 = 21 ( x – 5 ) x = 59 answer : e"
Answer: e
Question (physics): a and b can together finish a work in 40 days . they worked together for 10 days and then b left . after another 18 days , a finished the remaining work . in how many days a alone can finish the job ?
Options: a ) 10 , b ) 24 , c ) 60 , d ) 30 , e ) 20
Rationale: a + b 10 days work = 10 * 1 / 40 = 1 / 4 remaining work = 1 - 1 / 4 = 3 / 4 3 / 4 work is done by a in 18 days whole work will be done by a in 18 * 4 / 3 = 24 days answer is b
Answer: b
Question (gain): a student gets 55 % in one subject , 65 % in the other . to get an overall of 55 % how much should get in third subject .
Options: a ) 75 % , b ) 25 % , c ) 45 % , d ) 55 % , e ) 65 %
Rationale: "let the 3 rd subject % = x 55 + 65 + x = 3 * 55 120 + x = 165 x = 165 - 120 = 45 answer : c"
Answer: c
Question (gain): in an election between two candidates , the winner has a margin of 10 % of the votes polled . if 4000 people change their mind and vote for the loser , the loser would have won by a margin of 10 % of the votes polled . find the total number of votes polled in the election ?
Options: a ) 16000 , b ) 10000 , c ) 40000 , d ) 12000 , e ) 5000
Rationale: "winner - looser 55 % - 45 % if 4000 people change their mind and vote for the loser : winner - looser 45 % - 55 % thus 4,000 people compose 25 % of all voters , which means that the total number of votes is 40,000 answer : c"
Answer: c
Question (physics): there are 28 stations between ernakulam and chennai . how many second class tickets have to be printed , so that a passenger can travel from one station to any other station ?
Options: a ) 800 , b ) 820 , c ) 850 , d ) 870 , e ) 900
Rationale: "the total number of stations = 30 from 30 stations we have to choose any two stations and the direction of travel ( ernakulam to chennai is different from chennai to ernakulam ) in 30 p 2 ways . 30 p 2 = 30 * 29 = 870 answer : d"
Answer: d
Question (gain): what percent is 7 gm of 1 kg ?
Options: a ) 0.7 % , b ) 0.5 % , c ) 2.5 % , d ) 3.5 % , e ) 4 %
Rationale: "1 kg = 1000 gm 7 / 1000 × 100 = 700 / 1000 = 7 / 10 = 0.7 % a )"
Answer: a