Cheukting/mathqa huggingface dataset:
Question (physics): a walks at 10 kmph and 6 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 6 hours . x / 10 - x / 20 = 6 x = 120 km answer is d
Answer: d
Question (general): how many words , with or without meaning , can be formed using all letters of the word sharp using each letter exactly once ?
Options: a ) 90 , b ) 100 , c ) 110 , d ) 120 , e ) 130
Rationale: "the word sharp has exactly 5 letters which are all different . therefore the number of words that can be formed = number of permutations of 5 letters taken all at a time . = p ( 5 , 5 ) = 5 ! = 5 x 4 x 3 x 2 × 1 = 120 answer : d"
Answer: d
Question (gain): mary works in a restaurant a maximum of 80 hours . for the first 20 hours , she is paid $ 8 per hour . for each overtime hour , she is paid at a rate which is 25 % higher than her regular rate . how much mary can earn in a week ?
Options: a ) 600 , b ) 720 , c ) 760 , d ) 620 , e ) 700
Rationale: "mary receives $ 8 ( 20 ) = $ 160 for the first 20 hours . for the 60 overtime hours , she receives $ 8 ( 0.25 ) + $ 8 = $ 10 per hour , that is $ 10 ( 60 ) = $ 600 . the total amount is $ 160 + $ 600 = $ 760 answer c 360 ."
Answer: c
Question (general): if 2 x + y = 4 and x + 2 y = 5 , then ( x + y ) / 3 =
Options: a ) 1 , b ) 4 / 3 , c ) 17 / 5 , d ) 18 / 5 , e ) 4
Rationale: "we have two equations : 2 x + y = 4 x + 2 y = 5 notice that something nice happens when we add them . we get : 3 x + 3 y = 9 divide both sides by 3 to get : x + y = 3 so , ( x + y ) / 3 = 3 / 3 = 1 answer : a"
Answer: a
Question (general): the least number which when increased by 6 each divisible by each one of 24 , 32 , 36 and 54 is :
Options: a ) 858 , b ) 859 , c ) 869 , d ) 4320 , e ) none of these
Rationale: "solution required number = ( l . c . m . of 24 , 32 , 36 , 54 ) - 5 = 864 - 6 = 858 . answer a"
Answer: a
Question (general): find the mean proportional between 81 & 100 ?
Options: a ) a ) 59 , b ) b ) 61 , c ) c ) 63 , d ) d ) 65 , e ) e ) 90
Rationale: "formula = √ a × b a = 81 and b = 100 √ 81 × 100 = 9 × 10 = 90 e"
Answer: e
Question (general): if the sum of the first n positive integers is s , what is the sum of the first n positive integers divisible by 5 , in terms of s ?
Options: a ) s / 2 , b ) s , c ) 2 s , d ) 2 s + 2 , e ) 5 s
Rationale: "answer is e given sum of 1 2 3 . . . . . n = s sum of 5 , 10 , 15 . . . . 5 n = 5 [ sum ( 1 2 3 . . . . n ) ] = 5 s"
Answer: e
Question (physics): a man can row upstream at 30 kmph and downstream at 60 kmph , and then find the speed of the man in still water ?
Options: a ) 27 , b ) 29 , c ) 30 , d ) 20 , e ) 45
Rationale: "us = 30 ds = 60 m = ( 30 + 60 ) / 2 = 45 answer : e"
Answer: e
Question (general): if the average ( arithmetic mean ) of 2 a + 16 , 3 a - 8 is 94 , what is the value of a ?
Options: a ) 25 , b ) 30 , c ) 28 , d ) 36 , e ) 42
Rationale: "am of 2 a + 16 , 3 a - 8 = 2 a + 16 + 3 a - 8 / 2 = 5 a + 8 / 2 given that 5 a + 8 / 2 = 94 a = 36 answer is d"
Answer: d
Question (gain): a group of students was interviewed for that if it was asked whether or not they speak french and / or english . among those who speak french , 10 speak english well , while 40 of them do not speak english . if 75 % of students do not speak french , how many students were surveyed ?
Options: a ) 210 , b ) 225 , c ) 200 , d ) 250 , e ) 300
Rationale: "number of students who speak french are 40 + 10 = 50 of total students , the percentage of students who do not speak french was 75 % - - > percentage of who do is 25 % 50 - - - - - - - 25 % x - - - - - - - 100 % x = 50 * 100 / 25 = 200 = number of all students answer is c"
Answer: c
Question (physics): a train crosses a platform of 120 m in 15 sec , same train crosses another platform of length 250 m in 20 sec . then find the length of the train ?
Options: a ) a ) 150 m , b ) b ) 270 m , c ) c ) 180 m , d ) d ) 158 m , e ) e ) 350 m
Rationale: "length of the train be ‘ x ’ x + 120 / 15 = x + 250 / 20 4 x + 480 = 3 x + 750 x = 270 m answer : b"
Answer: b
Question (other): two numbers are in the ratio 3 : 4 . if their l . c . m . is 36 . what is sum of the numbers ?
Options: a ) 21 , b ) 56 , c ) 76 , d ) 84 , e ) 85
Rationale: "explanation : let the numbers be 3 x and 4 x lcm of 3 x and 4 x = 12 x ( since lcm of 3 and 4 is 12 . hence lcm of 3 x and 4 x is 12 x ) given that lcm of 3 x and 4 x is 36 = > 12 x = 36 = > x = 36 / 12 = 3 sum of the numbers = 3 x + 4 x = 7 x = 7 x 3 = 21 answer : option a"
Answer: a
Question (physics): in what time will a train 120 m long cross an electric pole , it its speed be 144 km / hr ?
Options: a ) 2.5 sec , b ) 3 sec , c ) 8.9 sec , d ) 6.9 sec , e ) 2.9 sec
Rationale: "speed = 144 * 5 / 18 = 40 m / sec time taken = 120 / 40 = 3 sec . answer : b"
Answer: b
Question (general): evaluate : 1234562 - 12 * 3 * 2 = ?
Options: a ) 32435453 , b ) 1234554 , c ) 76768786 , d ) 97979797 , e ) 75868656
Rationale: "according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 1234562 - 12 * 3 * 2 = 1234562 - 8 = 1234554 correct answer b"
Answer: b
Question (gain): 33 1 / 3 % of 360 ?
Options: a ) 80 , b ) 90 , c ) 110 , d ) 120 , e ) 130
Rationale: "33 1 / 3 % = 1 / 3 1 / 3 × 360 = 120 d )"
Answer: d
Question (geometry): what is the area of a square field whose sides have a length of 14 meters ?
Options: a ) 196 sq m , b ) 286 sq m , c ) 298 sq m , d ) 267 sq m , e ) 231 sq m
Rationale: "14 * 14 = 196 sq m the answer is a ."
Answer: a
Question (physics): x can do a piece of work in 40 days . he works at it for 8 days and then y finished it in 32 days . how long will y take to complete the work ?
Options: a ) 10 , b ) 40 , c ) 15 , d ) 18 , e ) 20
Rationale: "work done by x in 8 days = 8 * 1 / 40 = 1 / 5 remaining work = 1 - 1 / 5 = 4 / 5 4 / 5 work is done by y in 32 days whole work will be done by y in 32 * 5 / 4 = 40 days answer is b"
Answer: b
Question (physics): a man traveled a total distance of 1800 km . he traveled one - third of the whole trip by plane and the distance traveled by train is three - fifth of the distance traveled by bus . if he traveled by train , plane and bus , then find the distance traveled by bus ?
Options: a ) 239 , b ) 247 , c ) 277 , d ) 270 , e ) 898
Rationale: "explanation : total distance traveled = 1800 km . distance traveled by plane = 600 km . distance traveled by bus = x distance traveled by train = 3 x / 5 = > x + 3 x / 5 + 600 = 1800 = > 8 x / 5 = 1200 = > x = 750 km . answer : d"
Answer: d
Question (general): if k is a non - negative integer and 12 ^ k is a divisor of 856,736 then 3 ^ k - k ^ 3 =
Options: a ) 0 , b ) 1 , c ) 36 , d ) 120 , e ) 524
Rationale: "8 + 5 + 6 + 7 + 3 + 6 = 35 , so this number is not divisible by 3 and thus not divisible by 12 . therefore , k = 0 3 ^ k - k ^ 3 = 1 - 0 = 1 the answer is b ."
Answer: b
Question (geometry): the length of a rectangular plot is 10 mtr more than its width . the cost of fencing the plot along its perimeter at the rate of rs . 6.5 mtr is rs . 1950 . the perimeter of the plot is ?
Options: a ) 126
b ) 156
c ) 190
d ) 300
e ) 260
Rationale: sol . let width = x , length = ( 10 + x ) perimeter = 2 ( x + ( 10 + x ) ) = 2 ( 2 x = 10 ) & 2 ( 2 x + 10 ) * 6.5 = 1950 x = 70 required perimeter = 2 ( 70 + 80 ) = 300 d
Answer: d
Question (physics): a can do a piece of work in 8 days . b can do it in 6 days . with the assistance of c they completed the work in 2 days . find in how many days can c alone do it ?
Options: a ) 8.7 days , b ) 2.0 days , c ) 6.6 days , d ) 7.7 days , e ) 4.8 days
Rationale: "c = 1 / 2 - 1 / 8 - 1 / 8 = 5 / 24 = > 4.8 days answer : e"
Answer: e
Question (physics): a car started running at a speed of 30 km / hr and the speed of the car was increased by 2 km / hr at the end of every hour . find the total distance covered by the car in the first 10 hours of the journey .
Options: a ) 342 km , b ) 390 km , c ) 642 km , d ) 742 km , e ) 382 km
Rationale: "the total distance covered by the car in the first 10 hours = 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 + 48 = sum of 10 terms in ap whose first term is 30 and last term is 48 = 10 / 2 [ 30 + 48 ] = 390 km . answer : b"
Answer: b
Question (general): the maximum number of students among them 1230 pens and 920 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :
Options: a ) 91 , b ) 10 , c ) 1001 , d ) 1911 , e ) none of these
Rationale: "explanation : required number of students = h . c . f of 1230 and 920 = 10 . answer : b"
Answer: b
Question (physics): the length of a room is 7 m and width is 4.75 m . what is the cost of paying the floor by slabs at the rate of rs . 900 per sq . metre .
Options: a ) 25650 , b ) 25750 , c ) 26550 , d ) 26750 , e ) 29925
Rationale: "area = 7 × 4.75 sq . metre . cost for 1 sq . metre . = rs . 900 hence total cost = 7 × 4.75 × 900 = 7 × 4275 = rs . 29925 answer is e"
Answer: e
Question (physics): a train 110 m long is running with a speed of 27 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 7 sec , b ) 6 sec , c ) 8 sec , d ) 4 sec , e ) 12 sec
Rationale: "speed of train relative to man = 27 + 6 = 33 km / hr . = 33 * 5 / 18 = 9.1667 m / sec . time taken to pass the men = 110 / 9.1667 = 12 sec . answer : e"
Answer: e
Question (physics): a , b and c can do a piece of work in 24 days , 30 days and 60 days respectively . they began the work together but c left 4 days before the completion of the work . in how many days was the work completed ?
Options: a ) 10 days , b ) 11 days , c ) 13 days , d ) 21 days , e ) 31 days
Rationale: one day work of a , b and c = 1 / 24 + 1 / 30 + 1 / 60 = 11 / 120 work done by a and b together in the last 4 days = 4 * ( 1 / 24 + 1 / 30 ) = 3 / 10 remaining work = 7 / 10 the number of days required for this initial work = 7 days . the total number of days required = 4 + 7 = 11 days . answer : b
Answer: b
Question (gain): machine p and machine q are each used to manufacture 550 sprockets . it takes machine p 10 hours longer to produce 550 sprockets than machine q . machine q produces 10 % more sprockets per hour than machine a . how many sprockets per hour does machine a produce ?
Options: a ) 5 , b ) 15 , c ) 55 , d ) 95 , e ) 125
Rationale: "p makes x sprockets per hour . then q makes 1.1 x sprockets per hour . 550 / x = 550 / 1.1 x + 10 1.1 ( 550 ) = 550 + 11 x 11 x = 55 x = 5 the answer is a ."
Answer: a
Question (physics): what percent of a day is 7 hours ?
Options: a ) 29.2 % , b ) 12.5 % , c ) 13 % , d ) 11.3 % , e ) none of these
Rationale: explanation : solution : required percentage = ( 7 / 100 * 24 ) = 29.2 % answer : a
Answer: a
Question (general): if 4 xz + yw = 5 and xw + yz = 10 , what is the value of the expression ( 2 x + y ) ( 2 z + w ) ?
Options: a ) 9 . , b ) 12 . , c ) 15 . , d ) 16 . , e ) 25
Rationale: "( 2 x + y ) * ( 2 z + w ) = 5 + 2 ( 10 ) = 25 answer : e"
Answer: e
Question (geometry): rectangular tile each of size 70 cm by 30 cm must be laid horizontally on a rectangular floor of size 110 cm by 130 cm , such that the tiles do not overlap and they are placed with edges jutting against each other on all edges . a tile can be placed in any orientation so long as its edges are parallel to the edges of floor . no tile should overshoot any edge of the floor . the maximum number of tiles that can be accommodated on the floor is :
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "area of tile = 70 * 30 = 2100 area of floor = 130 * 110 = 14300 no of tiles = 14300 / 2100 = 6.8 so , the no of tile = 6 answer : b"
Answer: b
Question (general): 1394 x 1394 = ?
Options: a ) a ) 1951609 , b ) b ) 1951601 , c ) c ) 1951602 , d ) d ) 1943236 , e ) e ) 1951604
Rationale: "1394 x 1394 = ( 1394 ) 2 = ( 1400 - 6 ) 2 = ( 1400 ) 2 + ( 6 ) 2 - ( 2 x 1400 x 6 ) = 1960000 + 36 - 16800 = 1960036 - 16800 = 1943236 . answer : d"
Answer: d
Question (geometry): a circular ground whose diameter is 34 metres , has a 2 metre - broad garden around it . what is the area of the garden in square metres ?
Options: a ) 226.3
b ) 226.2
c ) 228.2
d ) 227
e ) 226
Rationale: req . area = ï € [ ( 19 ) 2 â € “ ( 17 ) 2 ] = 22 â  „ 7 ã — ( 36 ã — 2 ) [ since a 2 - b 2 = ( a + b ) ( a - b ) ] = ( 22 ã — 36 ã — 2 ) / 7 = 226.3 sq m answer a
Answer: a
Question (general): 3889 + 12.808 - ? = 3854.002
Options: a ) a ) 47.095 , b ) b ) 47.752 , c ) c ) 47.806 , d ) d ) 47.95 , e ) of the above
Rationale: let 3889 + 12.808 - x = 3854.002 . then x = ( 3889 + 12.808 ) - 3854.002 = 3901.808 - 3854.002 = 47.806 . answer = c
Answer: c
Question (general): a sum of money is sufficient to pay a ' s wages for 20 days and b ' s wages for 30 days . the same money is sufficient to pay the wages of both for ?
Options: a ) 12 days , b ) 15 days , c ) 20 days , d ) 18 days , e ) 22 days
Rationale: "let the total money be $ x a ' s 1 day work = $ x / 20 b ' s 1 day work = $ x / 30 a + b 1 day work = $ x / 12 money is sufficient to pay the wages of both for 12 days answer is a"
Answer: a
Question (physics): a river boat leaves silver town and travels upstream to gold town at an average speed of 6 kilometers per hour . it returns by the same route at an average speed of 8 kilometers per hour . what is the average speed for the round - trip in kilometers per hour ?
Options: a ) 6.8 , b ) 7.1 , c ) 7.2 , d ) 7.5 , e ) 8.0
Rationale: "pick a number which is lcm of 8 and 6 = 24 . upstream time = 24 / 6 = 4 hrs downstream time = 24 / 8 = 3 hrs total time = 7 hrs total distance = 48 average speed = 48 / 7 = 6.8 km / hr"
Answer: a
Question (geometry): the sides of a square region , measured to the nearest centimeter , are 7 centimeters long . the least possible value of the actual area of the square region is
Options: a ) 42.25 sq cm
b ) 45.25 sq cm
c ) 43.25 sq cm
d ) 50.25 sq cm
e ) 52.25 sq cm
Rationale: though there might be some technicalities concerning the termnearest ( as 6.5 is equidistant from both 6 and 7 ) the answer still should be a : 6.5 ^ 2 = 42.25 . answer : a
Answer: a
Question (other): a box contains 6 white , 5 red and 8 white marbles . 5 marbles are drawn from the box at random . what is the probability that both the marbles are of the same color ?
Options: a ) 19 / 11628 , b ) 36 / 11628 , c ) 613 / 11628 , d ) 6113 / 11628 , e ) 63 / 11628
Rationale: explanation : total marbles in a box = 6 black + 5 red + 8 green marbles = 19 marbles 5 marbles are drawn from 19 marbles at random . therefore , n ( s ) = 19 c 5 = 11628 ways let a be the event that 2 marbles drawn at random are of the same color . number of cases favorable to the event a is n ( a ) = 6 c 5 + 5 c 5 + 8 c 5 = 6 + 1 + 56 = 63 therefore , by definition of probability of event a , p ( a ) = n ( a ) / n ( s ) = 63 / 11628 answer : e
Answer: e
Question (general): 105 * 2
Options: a ) 11025 , b ) 23889 , c ) 29088 , d ) 1999 , e ) 17710
Rationale: "here d = 5 . 100 + 2 × × 5 / 25 = 11025 answer : a"
Answer: a
Question (general): what will be the reminder when ( 43 ^ 43 + 43 ) is divided by 44 ?
Options: a ) 32 , b ) 42 , c ) 83 , d ) 71 , e ) 92
Rationale: "( x ^ n + 1 ) will be divisible by ( x + 1 ) only when n is odd ; ( 43 ^ 43 + 1 ) will be divisible by ( 43 + 1 ) ; ( 43 ^ 43 + 1 ) + 42 when divided by 44 will give 42 as remainder . correct option : b"
Answer: b
Question (physics): maxwell leaves his home and walks toward brad ' s house at the same time that brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 40 kilometers , maxwell ' s walking speed is 4 km / h , and brad ' s running speed is 6 km / h , what is the distance traveled by brad ?
Options: a ) 16 , b ) 18 , c ) 20 , d ) 24 , e ) 30
Rationale: "time taken = total distance / relative speed total distance = 40 kms relative speed ( opposite side ) ( as they are moving towards each other speed would be added ) = 6 + 4 = 10 kms / hr time taken = 40 / 10 = 4 hrs distance traveled by brad = brad ' s speed * time taken = 6 * 4 = 24 kms . . . answer - d"
Answer: d
Question (general): the total of 342 of 20 paise and 25 paise make a sum of rs . 71 . the no of 20 paise coins is
Options: a ) 238 , b ) 290 , c ) 278 , d ) 200 , e ) 288
Rationale: "explanation : let the number of 20 paise coins be x . then the no of 25 paise coins = ( 342 - x ) . 0.20 * ( x ) + 0.25 ( 342 - x ) = 71 = > x = 290 . . answer : b ) 290"
Answer: b
Question (gain): a retailer buys a radio for rs 225 . his overhead expenses are rs 15 . he sellis the radio for rs 350 . the profit percent of the retailer is
Options: a ) 10 % , b ) 45.8 % , c ) 25 % , d ) 52 % , e ) none of these
Rationale: "explanation : cost price = ( 225 + 15 ) = 240 sell price = 350 gain = ( 110 / 240 ) * 100 = 45.8 % . answer : b"
Answer: b
Question (physics): a man can row upstream at 35 kmph and downstream at 45 kmph , and then find the speed of the man in still water ?
Options: a ) 32 kmph , b ) 34 kmph , c ) 40 kmph , d ) 45 kmph , e ) 65 kmph
Rationale: "us = 35 ds = 45 m = ( 35 + 45 ) / 2 = 40 answer : c"
Answer: c
Question (physics): a 220 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds . what is the length of the other train ?
Options: a ) 230 m , b ) 240 m , c ) 250 m , d ) 260 m , e ) 280 m
Rationale: speed = ( 120 + 80 ) km / h ( because direction is opposite hence relative velocity is added ) = 500 / 9 m / s time = 9 sec let the lenght of second train is x total distance covered = 220 + x therefore , d = speed * time thus 220 + x = 500 / 9 * 9 x = 500 - 220 = 280 m answer : e
Answer: e
Question (physics): if 80 lamps can be lighted 5 hours per day for 10 days for rs . 21.25 , then the number of lamps which can be lighted 4 hours daily for 30 days for rs . 76.50 , is ?
Options: a ) 100 , b ) 110 , c ) 120 , d ) 130 , e ) none of these
Rationale: explanation : ( hrs / day 4 : 5 ) : ( money 21.25 : 76.50 ) : ( days 30 : 10 ) : : 80 : x 4 * 21.25 * 30 * x = 5 * 76.50 * 10 * 80 so x = 120 answer : c
Answer: c
Question (general): in a group of ducks and cows , the total number of legs are 20 more than twice the no . of heads . find the total no . of buffaloes .
Options: a ) 10 , b ) 12 , c ) 13 , d ) 15 , e ) 16
Rationale: "let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 20 = > 2 x = 20 = > x = 10 a"
Answer: a
Question (general): the average weight of a , b and c is 45 kg . if the average weight of a and b be 40 kg and that of b and c be 41 kg , then the weight of b is :
Options: a ) 27 kg , b ) 20 kg , c ) 26 kg , d ) 31 kg , e ) 35 kg
Rationale: "let d sum of a , b , c is 3 * 45 = 135 and sum of a and b s 2 * 40 = 80 sum of b and c is 2 * 41 = 82 hence 80 + 82 - 135 = 27 ans = 27 answer : a"
Answer: a
Question (gain): i sold a book at a profit of 10 % . had i sold it for $ 100 more , 15 % would have been gained . find the cost price ?
Options: a ) $ 2000 , b ) $ 2500 , c ) $ 3000 , d ) $ 3120 , e ) $ 1540
Rationale: "115 % of cost - 110 % of cost = $ 100 5 % of cost = $ 100 cost = 100 * 100 / 5 = $ 2000 answer is a"
Answer: a
Question (gain): an inspector rejects 0.08 % of the meters as defective . how many will he examine to reject 2 ?
Options: a ) 1200 , b ) 1240 , c ) 1852 , d ) 3200 , e ) 2500
Rationale: "then , 0.08 % of x = 2 ( 8 / 100 ) * ( 1 / 100 ) x = 2 x = ( 2 * 100 * 100 ) / 8 = 2500 answer is e"
Answer: e
Question (general): the average age of a class is 15.8 years . the average age of the boys in the class is 16.4 years and that of the girls is 15.4 years . what is the ratio of boys to girls in the class ?
Options: a ) 1 : 2 , b ) 3 : 4 , c ) 2 : 3 , d ) 3 : 2 , e ) none of these
Rationale: "let number of boys = x ; let number of girls = y total numbers of students = x + y ( x + y ) × 15.8 = 16.4 x + 15.4 y 0.6 x = 0.4 y x / y = 0.4 / 0.6 = 2 / 3 answer : c"
Answer: c
Question (gain): in how many years will a sum of money doubles itself at 25 % per annum on simple interest ?
Options: a ) 4 % , b ) 8 % , c ) 10 % , d ) 12 % , e ) 15 %
Rationale: "p = ( p * 25 * r ) / 100 r = 4 % answer : a"
Answer: a
Question (other): log 3 n + log 7 n what is 3 digit number n that will be whole number
Options: a ) 343 , b ) 729 , c ) 829 , d ) 929 , e ) 727
Rationale: no of values n can take is 1 7 ^ 3 = 343 answer : a
Answer: a
Question (general): at the a - street fish market a vendor sells fresh caught fish . his store is filled with 2 / 7 bass , 1 / 5 tuna , 1 / 7 trout , and the rest are catfish . if a customer just bought 1 / 7 of all the tuna and 1 / 7 of all the catfish , and a fisherman arrived to restock the bass , doubling the number of bass , what proportion of fish now in the store are trout ?
Options: a ) 30 / 71 , b ) 4 / 7 , c ) 5 / 43 , d ) 1 / 2 , e ) 1 / 5
Rationale: bass = 2 / 7 = 10 / 35 tuna = 1 / 5 = 7 / 35 trout = 1 / 7 = 5 / 35 catfish = 1 - ( 10 / 35 + 7 / 35 + 5 / 35 ) = 13 / 35 purchased : tuna = 7 / 35 - ( 7 / 35 ) ( 1 / 7 ) = 6 / 35 , and catfish = 13 / 35 - ( 13 / 35 ) ( 1 / 7 ) = 12 / 35 stocked : doubling the number of bass ( 2 ) ( 10 / 35 ) = 20 / 35 now : 20 + 6 + 5 + 12 = 43 trout proportion is now 5 / 43 . answer : c
Answer: c
Question (gain): a and b started a business in partnership investing rs . 20000 and rs . 15000 respectively . after 6 months , c joined them with rs . 20000 . whatwill be b ' s share in total profit of rs . 20000 earned at the end of 2 years from the startingof the business ?
Options: a ) s . 5,000 , b ) s . 5,500 , c ) s . 5,700 , d ) s . 6,000 , e ) s . 7,500
Rationale: a : b : c = ( 20,000 x 24 ) : ( 15,000 x 24 ) : ( 20,000 x 18 ) = 4 : 3 : 3 . b ' s share = rs . 20000 x 3 / 10 = rs . 6,000 . d
Answer: d
Question (general): the product of two positive integers is 323 and their difference is 2 . what is the smaller number ?
Options: a ) 17 , b ) 18 , c ) 16 , d ) 19 , e ) 14
Rationale: let ' s use trial and error to find the two numbers . 20 * 18 = 360 ( too high ) 19 * 17 = 323 the answer is a .
Answer: a
Question (other): an alloy is to contain steel and iron in the ratio 5 : 2 . the iron required to be melted with 35 kg of steel is ?
Options: a ) 12 kg , b ) 14 kg , c ) 15 kg , d ) 20 kg , e ) 18 kg
Rationale: let the required quantity of steel be x kg 5 : 2 : : 35 : x 5 x = 2 * 35 x = 14 kg answer is b
Answer: b
Question (physics): a man complete a journey in 30 hours . he travels first half of the journey at the rate of 20 km / hr and second half at the rate of 10 km / hr . find the total journey in km .
Options: a ) 220 km , b ) 224 km , c ) 230 km , d ) 400 km , e ) 234 km
Rationale: 0.5 x / 20 + 0.5 x / 10 = 30 - - > x / 20 + x / 10 = 60 - - > 3 x = 20 x 60 - - > x = ( 60 x 20 ) / 3 = 400 km . answer : d
Answer: d
Question (physics): a man sitting in a train which is traveling at 60 kmph observes that a goods train , traveling in opposite direction , takes 9 seconds to pass him . if the goods train is 280 m long , find its speed . ?
Options: a ) 52 kmph , b ) 58 kmph , c ) 62 kmph , d ) 65 kmph , e ) 75 kmph
Rationale: "relative speed = 280 / 9 m / sec = ( ( 280 / 9 ) * ( 18 / 5 ) ) kmph = 112 kmph . speed of goods train = ( 112 - 60 ) kmph = 52 kmph . answer : a"
Answer: a
Question (general): 0.0006 ? = 0.03
Options: a ) 2 , b ) 20 , c ) 0.2 , d ) 0.02 , e ) none of these
Rationale: "explanation : required answer = 0.0006 / 0.03 = 0.06 / 3 = 0.02 . answer : option d"
Answer: d
Question (physics): a train 125 m long passes a man , running at 4 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is ?
Options: a ) 11 , b ) 49 , c ) 88 , d ) 65 , e ) 22
Rationale: "speed of the train relative to man = ( 125 / 10 ) m / sec = ( 25 / 2 ) m / sec . [ ( 25 / 2 ) * ( 18 / 5 ) ] km / hr = 45 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 4 ) km / hr . x - 4 = 45 = = > x = 49 km / hr . answer : b"
Answer: b