Cheukting/mathqa huggingface dataset:
Question (physics): the lenght of a room is 5.5 m and width is 4 m . find the cost of paving the floor by slabs at the rate of rs . 750 per sq . metre .
Options: a ) s . 15,550 , b ) s . 15,600 , c ) s . 16,500 , d ) s . 17,600 , e ) s . 17,900
Rationale: "area of the floor = ( 5.5 ã — 4 ) m 2 = 22 m 2 . cost of paving = rs . ( 750 ã — 22 ) = rs . 16500 . answer : option c"
Answer: c
Question (gain): a dishonest dealer professes to sell goods at the cost price but uses a weight of 950 grams per kg , what is his percent ?
Options: a ) 22 % , b ) 25 % , c ) 77 % , d ) 5.26 % , e ) 12 %
Rationale: 950 - - - 50 100 - - - ? = > 5.26 % answer : d
Answer: d
Question (gain): find the compound interest on rs . 25000 in 2 years at 4 % per annum . the interest being compounded half yearly .
Options: a ) rs 2060.808 , b ) rs 2060.801 , c ) rs 2060.804 , d ) rs 2060.802 , e ) rs 2060.805
Rationale: "explanation : given : principal = rs . 25000 , rate = 4 % per half year , time = 2 years = 4 half years therefore , amount = p ( 1 + ( r / 2 ) / 100 ) 2 n amount = rs . [ 25000 * ( 1 + 2 / 100 ) 4 ] = rs . ( 25000 * 51 / 50 * 51 / 50 * 51 / 50 * 51 / 50 ) = rs . 27060.804 therefore , c . i . = rs . ( 27060.804 – 25000 ) = rs 2060.804 answer : c"
Answer: c
Question (physics): ravi covers a distance of 900 mtrs in 180 secs . find his speed in kmph ?
Options: a ) 10 kmph , b ) 18 kmph , c ) 20 kmph , d ) 26 kmph , e ) 28 kmph
Rationale: given distance d = 900 meters and time = 180 seconds speed = distance / time = 900 / 180 = 5 m / s . but speed is asked in kmph , to convert 5 mps to kmph , multiply it by 18 / 5 . speed in kmph = 5 x 18 / 5 = 18 kmph b
Answer: b
Question (general): find the value of x from the below equation ? : 3 x ^ 2 - 5 x + 2 = 0
Options: a ) 2 / 3 , b ) - 1 , c ) 0 , d ) - 2 / 3 , e ) 2
Rationale: "a = 3 , b = - 5 , c = 2 x 1,2 = ( 5 â ± â ˆ š ( ( - 5 ) ^ 2 - 4 ã — 3 ã — 2 ) ) / ( 2 ã — 3 ) = ( 5 â ± â ˆ š ( 25 - 24 ) ) / 6 = ( 5 â ± 1 ) / 6 x 1 = ( 5 + 1 ) / 6 = 6 / 6 = 1 x 2 = ( 5 - 1 ) / 6 = 4 / 6 = 2 / 3 a"
Answer: a
Question (general): n ^ ( n / 2 ) = 4 is true when n = 4 in the same way what is the value of n if n ^ ( n / 2 ) = 8 ?
Options: a ) 4 , b ) 8 , c ) 2 , d ) 6 , e ) 10
Rationale: n ^ ( n / 2 ) = 8 apply log n / 2 logn = log 8 nlogn = 2 log 8 = log 8 ^ 2 = log 64 logn = log 64 now apply antilog n = 64 / n now n = 8 . answer : b
Answer: b
Question (general): if n = 2 ^ 0.25 and n ^ b = 8 , b must equal
Options: a ) 3 / 80 , b ) 3 / 5 , c ) 12 , d ) 5 / 3 , e ) 80 / 3
Rationale: "25 / 100 = 1 / 4 n = 2 ^ 1 / 4 n ^ b = 2 ^ 3 ( 2 ^ 1 / 4 ) ^ b = 2 ^ 3 b = 12 answer : c"
Answer: c
Question (general): [ ( 3.242 x 15 ) / 100 ] = ?
Options: a ) 0.045388 , b ) 4.5388 , c ) 453.88 , d ) 473.88 , e ) 0.04863
Rationale: "answer multiplying 3.242 x 15 = 4.863 now divide 4.863 by 100 so , 4.863 ÷ 100 = 0.04863 ∴ shift the decimal two places to the left as 100 correct option : e"
Answer: e
Question (general): there are 41 students in a class , number of girls is one more than number of guys . we need to form a team of 4 students . all 4 in the team can not be from same gender . number of girls and guys in the team should not be equal . how many ways can such a team be made ?
Options: a ) 50540 ways , b ) 60540 ways , c ) 50840 ways , d ) 40540 ways , e ) 51540 ways
Rationale: boys = 20 and girls = 21 now the combinations are { girl , girl , girl , boy } or { boy , boy , boy , girl } so 21 c 3 * 20 c 1 + 20 c 3 * 21 c 1 = 50540 ways answer : a
Answer: a
Question (general): find the total number of prime factors in the expression ( 4 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 2
Options: a ) 26 , b ) 22 , c ) 25 , d ) 27 , e ) 29
Rationale: "( 4 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 2 = ( 2 x 2 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 2 = 2 ^ 11 x 2 ^ 11 x 7 ^ 5 x 11 ^ 2 = 2 ^ 22 x 7 ^ 5 x 11 ^ 2 total number of prime factors = ( 22 + 5 + 2 ) = 29 . answer is e ."
Answer: e
Question (physics): pipe p can drain the liquid from a tank in 3 / 4 the time that it takes pipe q to drain it and in 3 / 3 the time that it takes pipe r to do it . if all 3 pipes operating simultaneously but independently are used to drain liquid from the tank , then pipe q drains what portion of the liquid from the tank ?
Options: a ) 9 / 29 , b ) 8 / 23 , c ) 3 / 8 , d ) 3 / 11 , e ) 3 / 4
Rationale: suppose q can drain in 1 hr . so , rq = 1 / 1 = 1 so , rp = 1 / [ ( 3 / 4 ) rq ] = 4 / 3 also , rp = rr / ( 3 / 3 ) = > 4 / 3 = rr / ( 3 / 3 ) = > rr = 4 / 3 let h is the time it takes to drain by running all 3 pipes simultaneously so combined rate = rc = 1 / h = 1 + 4 / 3 + 4 / 3 = 11 / 3 = 1 / ( 3 / 11 ) thus running simultaneously , pipe q will drain 3 / 11 of the liquid . thus answer = d .
Answer: d
Question (physics): xavier starts from p towards q at a speed of 40 kmph and after every 12 mins increases his speed by 20 kmph . if the distance between p and q is 56 km , then how much time does he take to cover the distance ?
Options: a ) 40 , b ) 48 , c ) 44 , d ) 36 , e ) 30
Rationale: "first 12 min = 40 * 12 / 60 = 8 km 2 nd 12 min = 60 * 12 / 60 = 12 km 3 rd 12 min = 80 * 12 / 60 = 16 km 4 th 12 min = 100 * 12 / 60 = 20 km total time 12.4 = 48 min b"
Answer: b
Question (general): in the next cricket world cup t - 20 , team w has decided to score 200 runs only through 4 s and 6 s . in how many ways can the team w score these 200 runs ?
Options: a ) 13 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: team w can score a maximum of 50 fours and a minimum of 2 fours with an interval or spacing of 3 units to accommodate the 6 ' s . so the number of fours scored forms an ap 2 , 5 , 8 , . . . 50 with a common difference of 3 . number of ways of scoring 200 only through 4 ' s and 6 ' s = ( 50 - 2 ) / 3 + 1 = 17 answer : d alternate solution : 4 x + 6 y = 200 - - > 2 x + 3 y = 100 x = ( 100 - 3 y ) / 2 - - > 100 - 3 y should be even . this is possible when 3 y is even . there are 17 even multiples of 3 between 0 and 100 . answer : d
Answer: d
Question (other): in a class of 50 students , 12 enrolled for both english and german . 22 enrolled for german . if the students of the class enrolled for at least one of the two subjects , then how many students enrolled for only english and not german ?
Options: a ) 30 , b ) 10 , c ) 18 , d ) 28 , e ) 32
Rationale: "total = english + german - both + neither - - > 50 = english + 22 - 12 + 0 - - > english = 40 - - > only english = english - both = 40 - 12 = 28 . answer : d ."
Answer: d
Question (geometry): the perimeter of a triangle is 20 cm and the inradius of the triangle is 3 cm . what is the area of the triangle ?
Options: a ) 22 , b ) 30 , c ) 77 , d ) 54 , e ) 23
Rationale: "area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 3 * 20 / 2 = 30 cm 2 answer : b"
Answer: b
Question (physics): a train 130 m long passes a man , running at 6 kmph in the direction opposite to that of the train , in 6 seconds . the speed of the train is
Options: a ) 54 kmph , b ) 60 kmph , c ) 66 kmph , d ) 72 kmph , e ) 82 kmph
Rationale: "speed of train relative to man : 130 / 6 * 18 / 5 km / hr = 78 km / hr let speed of train = x therefore x + 6 = 78 x = 78 - 6 x = 72 km / hr answer : d"
Answer: d
Question (physics): two pipes can fill a tank in 30 minutes and 20 minutes . an outlet pipe can empty the tank in 15 minutes . if all the pipes are opened when the tank is empty , then how many minutes will it take to fill the tank ?
Options: a ) 48 , b ) 54 , c ) 60 , d ) 66 , e ) 72
Rationale: "let v be the volume of the tank . the rate per minute at which the tank is filled is : v / 30 + v / 20 - v / 15 = v / 60 per minute the tank will be filled in 60 minutes . the answer is c ."
Answer: c
Question (physics): a barrel full of beer has 2 taps one midway , , which draw a litre in 6 minutes and the other at the bottom , which draws a litre in 4 minutes . the lower tap is lower normally used after the level of beer in the barrel is lower than midway . the capacity of the barrel is 36 litres . a new assistant opens the lower tap when the barrel is full and draws out some beer . as a result the lower tap has been used 24 minutes before the usual time . for how long was the beer drawn out by the new assistant ?
Options: a ) 15 minutes , b ) 16 minutes , c ) 17 minutes , d ) 18 minutes , e ) none of these
Rationale: sol . the top tab is operational till 18 litres is drawn out . ∴ time after which the lower tap is usually open = 18 × 6 = 108 minutes ∴ time after which it is open now = 108 – 24 = 84 minutes ∴ litres drawn = 84 / 6 = 14 litres ∴ 18 – 14 = 4 litres were drawn by the new assistant . ∴ time = 4 × 4 = 16 minutes answer b
Answer: b
Question (geometry): if a cube has a volume of 125 , what is the surface area of one side ?
Options: a ) 5
b ) 25
c ) 50
d ) 150
e ) 625
Rationale: volume of a cube = side ^ 3 125 = side ^ 3 so side = 5 area of one side of the cube = side ^ 2 = 5 ^ 2 = 25 correct answer - b
Answer: b
Question (general): xy = 1 then what is ( 6 ^ ( x + y ) ^ 2 ) / ( 6 ^ ( x - y ) ^ 2 )
Options: a ) 1296 , b ) 4 , c ) 8 , d ) 16 , e ) 32
Rationale: "( x + y ) ^ 2 - ( x - y ) ^ 2 ( x + y + x - y ) ( x + y - x + y ) ( 2 x ) ( 2 y ) 4 xy 4 6 ^ 4 = 1296 answer a"
Answer: a
Question (gain): reena took a loan of $ . 1200 with simple interest for as many years as the rate of interest . if she paid $ 192 as interest at the end of the loan period , what was the rate of interest ?
Options: a ) 3.6 , b ) 6 , c ) 4 , d ) can not be determined , e ) none of these
Rationale: "let rate = r % and time = r years . then , 1200 x r x r / 100 = 192 12 r 2 = 192 r 2 = 16 r = 4 . answer : c"
Answer: c
Question (general): √ ( 25 ) ^ 2
Options: a ) 5 , b ) 14 , c ) 25 , d ) 21 , e ) none of these
Rationale: "explanation √ ( 25 ) ^ 2 = ? or , ? = 25 answer c"
Answer: c
Question (physics): x can finish a work in 15 days . y can finish the same work in 20 days . y worked for 12 days and left the job . how many days does x alone need to finish the remaining work ?
Options: a ) 5 , b ) 3 , c ) 4 , d ) 7 , e ) 8
Rationale: "work done by x in 1 day = 1 / 15 work done by y in 1 day = 1 / 20 work done by y in 12 days = 12 / 20 = 3 / 5 remaining work = 1 – 3 / 5 = 2 / 5 number of days in which x can finish the remaining work = ( 1 / 3 ) / ( 1 / 15 ) = 5 a"
Answer: a
Question (general): the average of first 18 natural numbers is ?
Options: a ) 5.6 , b ) 9.5 , c ) 9.1 , d ) 9.8 , e ) 5.2
Rationale: "sum of 18 natural no . = 342 / 2 = 171 average = 171 / 18 = 9.5 answer : b"
Answer: b
Question (general): what is the sum of 20 consecutive integers from - 9 inclusive , in a increasing order ?
Options: a ) - 9 , b ) 9 , c ) - 10 , d ) 10 , e ) 20
Rationale: "from - 9 to - 1 - - > 9 nos . zero - - > 1 number from + 1 to + 9 - - > 9 nos . when we add up nos . from - 9 to + 9 sum will be zero . total 19 nos will be added . 20 th number will be 10 . sum of these 20 nos . = 10 . d is the answer ."
Answer: d
Question (other): if log 1087.5 = 2.9421 , then the number of digits in ( 875 ) 10 is ?
Options: a ) 30 , b ) 28 , c ) 27 , d ) 26 , e ) 40
Rationale: "x = ( 875 ) 10 = ( 87.5 x 10 ) 10 therefore , log 10 x = 10 ( log 2087.5 + 1 ) = 10 ( 2.9421 + 1 ) = 10 ( 3.9421 ) = 39.421 x = antilog ( 39.421 ) therefore , number of digits in x = 40 . answer : e"
Answer: e
Question (physics): annie and sam set out together on bicycles traveling at 15 and 12 km per hour respectively . after 40 minutes , annie stops to fix a flat tire . if it takes annie 20 minutes to fix the flat tire and sam continues to ride during this time , how many minutes will it take annie to catch up with sam assuming that annie resumes riding at 15 km per hour ?
Options: a ) 20 , b ) 40 , c ) 60 , d ) 80 , e ) 100
Rationale: "annie gains 3 km per hour ( or 1 km every 20 minutes ) on sam . after 40 minutes annie is 2 km ahead . sam rides 1 km every 5 minutes . in the next 20 minutes , sam rides 4 km so sam will be 2 km ahead . it will take annie 40 minutes to catch sam . the answer is b ."
Answer: b
Question (gain): last year the range of the annual yield on equal amount of investments in 100 mutual funds was $ 10000 . if the annual yield this year for each of the 100 mutual funds has improved by 15 percent this year than it was last year , what is the range of the annual yield on mutual funds this year ?
Options: a ) $ 12700 , b ) $ 13000 , c ) $ 23000 , d ) $ 11500 , e ) $ 33000
Rationale: let the lowest yield be x . therefore , highest yield is x + 10000 . now yield of each mutual fund investment is improved by 10 % . therefore the yields will remain arranged in the same order as before . or lowest yield = 1.15 x and highest = 1.15 * ( x + 10000 ) or range = highest - lowest = 1.15 * ( x + 10000 ) - 1.15 x = 11500 , hence , d
Answer: d
Question (general): a customer purchased a package of ground beef at a cost of $ 1.80 per pound . for the same amount of money , the customer could have purchased a piece of steak that weighed 25 percent less than the package of ground beef . what was the cost per pound of the steak ?
Options: a ) $ 2.00 , b ) $ 2.15 , c ) $ 2.30 , d ) $ 2.40 , e ) $ 2.65
Rationale: "for simplicity , let ' s assume the customer bought 1 pound of ground beef for $ 1.80 . let x be the price per pound for the steak . then 0.75 x = 180 x = 180 / 0.75 = $ 2.40 the answer is d ."
Answer: d
Question (physics): two trains a and b starting from two points and travelling in opposite directions , reach their destinations 9 hours and 4 hours respectively after meeting each other . if the train a travels at 100 kmph , find the rate at which the train b runs .
Options: a ) 40 , b ) 60 , c ) 150 , d ) 80 , e ) 100
Rationale: "if two objects a and b start simultaneously from opposite points and , after meeting , reach their destinations in ‘ a ’ and ‘ b ’ hours respectively ( i . e . a takes ‘ a hrs ’ to travel from the meeting point to his destination and b takes ‘ b hrs ’ to travel from the meeting point to his destination ) , then the ratio of their speeds is given by : sa / sb = √ ( b / a ) i . e . ratio of speeds is given by the square root of the inverse ratio of time taken . sa / sb = √ ( 4 / 9 ) = 2 / 3 this gives us that the ratio of the speed of a : speed of b as 2 : 3 . since speed of a is 100 kmph , speed of b must be 100 * ( 3 / 2 ) = 150 kmph answer c"
Answer: c
Question (general): a soft drink company had 6000 small and 15000 big bottles in storage . if 12 % of small 14 % of big bottles have been sold , then the total bottles remaining in storage is
Options: a ) 15360 , b ) 16010 , c ) 18180 , d ) 14930 , e ) 16075
Rationale: "6000 + 15000 - ( 0.12 * 6000 + 0.14 * 15000 ) = 18180 . answer : c ."
Answer: c
Question (general): in a box of 10 pencils , a total of 2 are defective . if a customer buys 3 pencils selected at random from the box , what is the probability that neither pencils will be defective ?
Options: a ) 1 / 12 , b ) 7 / 15 , c ) 2 / 13 , d ) 2 / 15 , e ) 1 / 17
Rationale: "first , there are 8 c 3 ways you can select 3 good pencils from 4 good ones . second , there are 10 c 3 ways you select 3 pencils from 6 ones in the box . then , the probability that neither pen will be defective is : 8 c 3 / 10 c 3 = 56 / 120 = 7 / 15 answer is b"
Answer: b
Question (general): company workers decided to raise rs . 3 lakhs by equal contribution from each . had they contributed rs . 50 each extra , the contribution would have been rs . 3.25 lakhs . how many workers were they ?
Options: a ) 300 , b ) 400 , c ) 500 , d ) 600 , e ) 700
Rationale: explanation : n * 50 = ( 325000 - 300000 ) = 25000 n = 25000 / 50 = 500 option c
Answer: c
Question (general): the average of 7 numbers is 20 . if each number be multiplied by 5 . find the average of new set of numbers ?
Options: a ) a ) 100 , b ) b ) 122 , c ) c ) 120 , d ) d ) 125 , e ) e ) 145
Rationale: "explanation : average of new numbers = 20 * 5 = 100 answer : option a"
Answer: a
Question (geometry): right triangle pqr is the base of the prism in the figure above . if pq = pr = â ˆ š 5 and the height of the prism is 10 , what is the volume of the prism ?
Options: a ) 5
b ) 10
c ) 15
d ) 20
e ) 25
Rationale: volume of prism = area of base * height = 1 / 2 * ( square root of 5 ) * ( square root of 5 ) * 10 = 25 answer : e
Answer: e
Question (general): each of the positive integers a and c is a 4 - digit integer . if each of the digits 0 through 9 appears in one of these 3 integers , what is the maximum possible value of the sum of a and c ?
Options: a ) 18695 , b ) 18325 , c ) 18365 , d ) 18395 , e ) 18485
Rationale: according to the stem we should use the digits 0 through 9 to construct 2 four - digit integers , so that their sum is as big as possible . to maximize the sum , maximize the thousands digits of a and c , so make them 9 and 8 . next , maximize hundreds digits . make them 7 and 6 . next maximize 10 ' s digit place by 5 and 4 use the remaining digits ( 3 , and 2 ) for units digits . so , a would be 9753 , and c would be 8642 . 9753 + 8642 = 18395 answer : d .
Answer: d
Question (geometry): the length of a rectangle is doubled while its width is doubled . what is the % change in area ?
Options: a ) 250 % , b ) 300 % , c ) 500 % , d ) 650 % , e ) 700 %
Rationale: "the original area is l * w the new area is 2 l * 2 w = 4 * l * w = l * w + 3 * l * w the area increased by 300 % . the answer is b ."
Answer: b
Question (physics): riya and priya set on a journey . riya moves eastward at a speed of 18 kmph and priya moves westward at a speed of 24 kmph . how far will be priya from riya after 15 minutes
Options: a ) 25 kms , b ) 11 kms , c ) 50 kms , d ) 30 kms , e ) 40 kms
Rationale: total eastward distance = 18 kmph * 1 / 4 hr = 4.5 km total westward distance = 24 kmph * 1 / 4 hr = 6 km total distn betn them = 4.5 + 6 = 10.5 m ans 11 km answer : b
Answer: b
Question (physics): 36 persons can repair a road in 12 days , working 5 hours a day . in how many days will 30 persons , working 6 hours a day , complete the work ?
Options: a ) 12 , b ) 16 , c ) 13 , d ) 18 , e ) 19
Rationale: "let the required number of days be x . less persons , more days ( indirect proportion ) more working hours per day , less days ( indirect proportion ) persons 30 : 36 : : 12 : x working hours / day 6 : 5 30 x 6 x x = 36 x 5 x 12 x = ( 36 x 5 x 12 ) / ( 30 x 6 ) x = 12 answer a"
Answer: a
Question (gain): a shopkeeper buys two articles for rs . 1000 each and then sells them , making 10 % profit on the first article and 10 % loss on second article . find the net profit or loss percent ?
Options: a ) 200 , b ) 278 , c ) 100 , d ) 202 , e ) 270
Rationale: profit on first article = 10 % of 1000 = 100 . this is equal to the loss he makes on the second article . that , is he makes neither profit nor loss . answer : c
Answer: c
Question (physics): a can run 4 times as fast as b and gives b a start of 63 m . how long should the race course be so that a and b might reach in the same time ?
Options: a ) 70 m , b ) 60 m , c ) 80 m , d ) 65 m , e ) 84 m
Rationale: "speed of a : speed of b = 4 : 1 means in a race of 4 m a gains 3 m . then in a race of 63 m he gains 63 * ( 4 / 3 ) i . e 84 m answer : e"
Answer: e
Question (gain): if c is 25 % of a and 10 % of b , what percent of a is b ?
Options: a ) 2.5 % , b ) 15 % , c ) 25 % , d ) 35 % , e ) 250 %
Rationale: "c is 25 % of a - - > c = a / 4 ; c is 10 % of b - - > c = b / 10 ; thus a / 4 = b / 10 - - > b = 5 / 2 * a = 2.5 a . therefore , b is 250 % of a . answer : e"
Answer: e
Question (physics): car x began traveling at an average speed of 35 miles per hour . after 72 minutes , car y began traveling at an average speed of 40 miles per hour . when both cars had traveled the same distance , both cars stopped . how many miles did car x travel from the time car y began traveling until both cars stopped ?
Options: a ) 205 , b ) 220 , c ) 240 , d ) 247 , e ) 294
Rationale: "car y began travelling after 72 minutes or 1.2 hours . let t be the time for which car y travelled before it stopped . both cars stop when they have travelled the same distance . so , 35 ( t + 1.2 ) = 40 t t = 8.4 distance traveled by car x from the time car y began traveling until both cars stopped is 35 x 8.4 = 294 miles answer : - e"
Answer: e
Question (geometry): what is the ratio between perimeters of two squares one having 2.5 times the diagonal then the other ?
Options: a ) 4 : 5 , b ) 1 : 3 , c ) 2.5 : 1 , d ) 3.5 : 1 , e ) 3 : 2
Rationale: "d = 2.5 d d = d a √ 2 = 2.5 d a √ 2 = d a = 2.5 d / √ 2 a = d / √ 2 = > 2.5 : 1 answer : c"
Answer: c
Question (general): a number when divided by 899 gives a remainder 63 . what remainder will be obtained by dividing the same number by 29
Options: a ) 8 , b ) 5 , c ) 7 , d ) 6 , e ) 9
Rationale: 63 / 29 , thereforerequired number is : 5 , correct answer ( b )
Answer: b
Question (physics): a and b can do a piece of work in 10 days , while b and c can do the same work in 15 days and c and a in 25 days . they started working together , after 4 days a left . after another 4 days b left . in how many days c can finish the remaining work ?
Options: a ) 16 , b ) 32 , c ) 64 , d ) 96 , e ) none of these
Rationale: "let the rates of a , b and c be a , b , and c respectively . a and b can do a piece of work in 10 days : a + b = 1 / 10 ; b and c can do the same work in 15 days : b + c = 1 / 15 ; c and a can do the same work in 25 days : c + a = 1 / 25 . sum the above 3 equations : 2 ( a + b + c ) = 31 / 150 - - > a + b + c = 31 / 300 subtract a + b = 1 / 10 from above to get c = 1 / 300 . for 4 days all 3 worked and completed 4 * ( a + b + a ) = 124 / 300 of the work . for the next 4 days b and c worked and they completed 4 ( b + c ) = 4 / 15 = 80 / 300 of the work . so , by the time c is left alone 1 - ( 124 / 300 + 80 / 300 ) = 96 / 300 of the work is left to be completed by c alone . time = job / rate = ( 96 / 300 ) / ( 1 / 300 ) = 96 days . answer : d"
Answer: d
Question (physics): 17 men take 21 days of 8 hours each to do a piece of work . how many days of 6 hours each would 21 women take to do the same . if 3 women do as much work as 2 men ?
Options: a ) 34 , b ) 87 , c ) 30 , d ) 99 , e ) 77
Rationale: "3 w = 2 m 17 m - - - - - - 21 * 8 hours 21 w - - - - - - x * 6 hours 14 m - - - - - - x * 6 17 * 21 * 8 = 14 * x * 6 x = 34 answer : a"
Answer: a
Question (general): if xy = 9 , x / y = 36 , for positive numbers x and y , y = ?
Options: a ) 1 / 2 , b ) 2 , c ) 1 / 3 , d ) 3 , e ) 1 / 6
Rationale: very easy question . 2 variables and 2 easy equations . xy = 9 - - - > x = 9 / y - ( i ) x / y = 36 - - - > replacing ( i ) here - - - > 9 / ( y ^ 2 ) = 36 - - - > y ^ 2 = 9 / 36 = 1 / 4 - - - > y = 1 / 2 or - 1 / 2 the question states that x and y are positive integers . therefore , y = 1 / 2 is the answer . answer a .
Answer: a
Question (general): in one year , the population , of a village increased by 20 % and in the next year , it decreased by 20 % . if at the end of 2 nd year , the population was 9600 , what was it in the beginning ?
Options: a ) 10000 , b ) 8000 , c ) 1988 , d ) 1277 , e ) 2081
Rationale: x * 120 / 100 * 80 / 100 = 9600 x * 0.96 = 9600 x = 9600 / 0.96 = > 10000 answer : a
Answer: a
Question (other): two numbers are in the ratio of 15 : 11 . if their h . c . f . is 13 , find the numbers .
Options: a ) 195,143 , b ) 185,133 , c ) 175,123 , d ) 165,113 , e ) none of them
Rationale: let the required numbers be 15 . x and llx . then , their h . c . f . is x . so , x = 13 . the numbers are ( 15 x 13 and 11 x 13 ) i . e . , 195 and 143 . answer is a .
Answer: a
Question (other): a bag contains 7 red , 5 blue and 4 green balls . if 2 ballsare picked at random , what is the probability that both are red ?
Options: a ) 2 / 15 , b ) 2 / 21 , c ) 7 / 40 , d ) 3 / 29 , e ) 4 / 27
Rationale: "p ( both are red ) , = 7 c 216 c 2 = 7 c 216 c 2 = 21 / 120 = 7 / 40 c"
Answer: c
Question (physics): a boat can travel with a speed of 22 km / hr in still water . if the speed of the stream is 5 km / hr , find the time taken by the boat to go 216 km downstream
Options: a ) 5 hours , b ) 4 hours , c ) 3 hours , d ) 2 hours , e ) 8 hours
Rationale: "explanation : speed of the boat in still water = 22 km / hr speed of the stream = 5 km / hr speed downstream = ( 22 + 5 ) = 27 km / hr distance travelled downstream = 216 km time taken = distance / speed = 216 / 27 = 8 hours . answer : option e"
Answer: e