Cheukting/mathqa huggingface dataset:
Question (other): in a certain state , the ratio of registered republicans to registered democrats is 3 to 2 , and every registered voter is either a republican or a democrat . if 80 percent of the republicans and 20 percent of the democrats are expected to vote for candidate x , and everyone else is expected to vote for candidate y , by what percent is candidate x expected to win the election ?
Options: a ) 2 % , b ) 5 % , c ) 8 % , d ) 10 % , e ) 12 %
Rationale: "since we were expected to find a percentage figure - it thought that it might be easier to pick a ' smart number ' to represent the total number of voters ( republicans and democrats ) . therefore , i picked 100 ( as the total number of voters ) and thus 30 : 20 represents the number ratio of republicans : democrats . if 80 % of republicans ( which is ( 60 * 0.8 ) = 48 ) and 20 % of democrats ( 40 * 0.2 = 8 ) voted for candidate x , means that out of total of 100 voters ; 56 ( 48 + 8 ) voters voted for candidate x and 44 voted for candidate y . thus we can infer that candidate x is expected to win the election by 12 ( 56 - 44 ) votes . therefore candidate x is expected to win the election by ( 12 / 100 ) votes which is equivalent to 12 % . i think the answer is e ."
Answer: e
Question (general): a school has received 50 % of the amount it needs for a new building by receiving a donation of $ 400 each from people already solicited . people already solicited represent 40 % of the people from whom the school will solicit donations . how much average contribution is requited from the remaining targeted people to complete the fund raising exercise ?
Options: a ) $ 400 , b ) $ 177.78 , c ) $ 320 , d ) $ 277 , e ) $ 200
Rationale: "let us suppose there are 100 people . 40 % of them donated $ 16000 ( 400 * 40 ) $ 16000 is 50 % of total amount . so total amount = 16000 * 100 / 50 remaining amount is 50 % of total amount . 50 % of total amount = 16000 * ( 100 / 50 ) * ( 50 / 100 ) = 16000 this amount has to be divided by 50 ( remaining people are 50 ) so per head amount is 16000 / 50 = 320 answer : c"
Answer: c
Question (geometry): the sides of a square region , measured to the nearest centimeter , are 10 centimeters long . the least possible value of the actual area of the square region is
Options: a ) 96.25 sq cm , b ) 98.25 sq cm , c ) 92.25 sq cm , d ) 100.25 sq cm , e ) 90.25 sq cm
Rationale: "though there might be some technicalities concerning the termnearest ( as 9.5 is equidistant from both 9 and 10 ) the answer still should be : 9.5 ^ 2 = 90.25 . answer : e"
Answer: e
Question (general): p software has coding line 5 % more than n , n software has coding line 1 / 2 more than m . m software has 100 lines of coding . find p lines .
Options: a ) 106 , b ) 107 , c ) 108 , d ) 109 , e ) 158
Rationale: "m s / w has 100 line of code n s / w has = 100 + 100 * 1 / 2 = 150 line of code p s / w 5 % more n ' code 150 + 7.5 = 157.5 or 158 line of code answer : e"
Answer: e
Question (physics): in a garden , there are 10 rows and 15 columns of mango trees . the distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden . the length of the garden is
Options: a ) 20 m , b ) 30 m , c ) 24 m , d ) 26 m , e ) 28 m
Rationale: "explanation : each row contains 15 plants . there are 14 gapes between the two corner trees ( 14 x 2 ) metres and 1 metre on each side is left . therefore length = ( 28 + 2 ) m = 30 m . answer : b"
Answer: b
Question (gain): if tim had lunch at $ 50.50 and he gave 10 % tip , how much did he spend ?
Options: a ) $ 30.60 , b ) $ 60.60 , c ) $ 70.60 , d ) $ 55.55 , e ) $ 50.60
Rationale: "the tip is 20 % of what he paid for lunch . hence tip = 20 % of 50.50 = ( 10 / 100 ) * 50.50 = $ 5.05 total spent 50.50 + 5.05 = $ 55.55 correct answer d"
Answer: d
Question (physics): a 240 meter long train running at the speed of 120 kmph crosses another train running in the opposite direction at the speed of 80 kmph in 9 seconds . what is the lenght of other train .
Options: a ) 260 m , b ) 220 m , c ) 230 m , d ) 240 m , e ) 250 m
Rationale: "relative speeds = ( 120 + 80 ) km / hr = 200 km / hr = ( 200 * 5 / 18 ) m / s = ( 500 / 9 ) m / s let length of train be xm x + 240 / 9 = 500 / 9 x = 260 ans is 260 m answer : a"
Answer: a
Question (gain): company a imported 12,000 widgets made of either brass or aluminum . the widgets are painted blue , red or green . if 10 percent of the widgets are made of brass and of those 20 percent are painted green and 40 percent are painted red how many brass widgets painted blue were imported ?
Options: a ) 420 , b ) 480 , c ) 1050 , d ) 1680 , e ) 2100
Rationale: answer a . we are told that 10 % of all imported widgets are made of brass and of those , 20 % are green and 40 % are red . since we know that there are only three colors , the remaining 40 % must be blue . 40 % blue of 10 % brass widgets leads to 4 % blue brass widgets out of the total 10,550 widgets . 12,000 / 100 * 4 = 480 . answer b .
Answer: b
Question (physics): mr . das decided to walk down the escalator of a mall . he found that if he walks down 26 steps , he requires 30 seconds to reach the bottom . however , if he steps down 34 stair she would only require 18 seconds to get to the bottom . if the time is measured from the moment the top step begins to descend to the time he steps off the last step at the bottom , find out the height of the stair way insteps ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: here when he step down 26 steps he has 30 seconds for remaining steps . if he step down 34 stairs he has only 18 sec . 30 - 18 = 12 12 secs for 8 steps . . 18 secs for 12 steps . 12 + 34 = 46 so ans is 46 . . answer : b
Answer: b
Question (gain): solution x is 30 % chemical a and 70 % chemical b by volume . solution y is 40 % chemical a and 60 % chemical b by volume . if a mixture of x and y is 36 % chemical a , what percent of the mixture is solution x ?
Options: a ) 30 % , b ) 35 % , c ) 40 % , d ) 45 % , e ) 50 %
Rationale: "the volume of the mixture be x + y . 0.3 x + 0.4 y = 0.36 ( x + y ) x = 2 y / 3 x / ( x + y ) = ( 2 y / 3 ) / ( 5 y / 3 ) = 2 / 5 = 40 % . the answer is c ."
Answer: c
Question (general): jim ’ s taxi service charges an initial fee of $ 2.45 at the beginning of a trip and an additional charge of $ 0.35 for each 2 / 5 of a mile traveled . what is the total charge for a trip of 3.6 miles ?
Options: a ) $ 3.15 , b ) $ 4.45 , c ) $ 4.80 , d ) $ 5.05 , e ) $ 5.6
Rationale: "let the fixed charge of jim ’ s taxi service = 2.45 $ and charge per 2 / 5 mile ( . 4 mile ) = . 35 $ total charge for a trip of 3.6 miles = 2.45 + ( 3.6 / . 4 ) * . 35 = 2.45 + 9 * . 35 = 5.6 $ answer e"
Answer: e
Question (general): a bowl contains equal numbers of red , orange , green , blue , and yellow candies . kaz eats all of the green candies and half of the orange ones . next , he eats half of the remaining pieces of each color . finally , he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 24 % of the original number . what percent of the red candies remain ?
Options: a ) 12.5 % , b ) 16.7 % , c ) 22.5 % , d ) 27.5 % , e ) 33.3 %
Rationale: let x be the original number of each color so there are a total of 5 x candies . kaz eats all of the green candies and half of the orange ones . there are 0 green candies and 0.5 x orange candies remaining . he eats half of the remaining pieces of each color . there are 0.25 x orange candies , and 0.5 x each of red , yellow , and blue candies . he eats red and yellow candies in equal proportions . orange + blue + red + yellow = 0.75 x + red + yellow = 1.2 x red + yellow = 0.45 x red = 0.225 x , since red = yellow . the answer is c .
Answer: c
Question (gain): on selling 9 balls at rs . 720 , there is a loss equal to the cost price of 5 balls . the cost price of a ball is :
Options: a ) s . 145 , b ) s . 150 , c ) s . 155 , d ) s . 160 , e ) s . 180
Rationale: "( c . p . of 9 balls ) - ( s . p . of 9 balls ) = ( c . p . of 5 balls ) c . p . of 4 balls = s . p . of 9 balls = rs . 720 . c . p . of 1 ball = rs . 720 / 4 = rs . 180 . answer : option e"
Answer: e
Question (gain): boy sells a book for rs . 630 he gets a loss of 10 % , to gain 10 % , what should be the sp ?
Options: a ) 430 , b ) 450 , c ) 550 , d ) 770 , e ) 660
Rationale: "cost price = 630 / 90 x 100 = 700 to gain 10 % = 700 x 10 / 100 = 70 sp = cp + gain = 700 + 70 = 770 answer : d"
Answer: d
Question (physics): a and b can do a piece of work in 11 days . with the help of c they finish the work in 5 days . c alone can do that piece of work in ?
Options: a ) 15.5 days , b ) 19.5 days , c ) 17.5 days , d ) 9.2 days , e ) 18.5 days
Rationale: "c = 1 / 5 – 1 / 11 = 6 / 55 = > 9.2 days answer : d"
Answer: d
Question (physics): a train 310 meters long is running with a speed of 60 kmph . in what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ?
Options: a ) 4 , b ) 6 , c ) 5 , d ) 17 , e ) 13
Rationale: "speed of train relative to man = ( 60 + 6 ) km / hr = 66 km / hr [ 66 * 5 / 18 ] m / sec = [ 55 / 3 ] m / sec . time taken to pass the man = [ 310 * 3 / 55 ] sec = 17 sec answer : d"
Answer: d
Question (other): how many odd factors does 210 have ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: start with the prime factorization : 210 = 2 * 3 * 5 * 7 for odd factors , we put aside the factor of two , and look at the other prime factors . set of exponents = { 1 , 1 , 1 } plus 1 to each = { 2 , 2 , 2 } product = 2 * 2 * 2 = 8 therefore , there are 8 odd factors of 210 . in case you are curious , they are { 1 , 3 , 5 , 7 , 15 , 21 , 35 , and 105 } answer : e .
Answer: e
Question (gain): sarah operated her lemonade stand monday through friday over a two week period and made a total profit of 350 dollars . on hot days she sold cups of lemonade for a price that was 25 percent higher than the regular days . each cup she sold had a total cost of 75 cents and sarah did not incur any other costs . if every day she sold exactly 32 cups and 3 of the days were hot , then what was the price of 1 cup on a hot day ?
Options: a ) $ 1.50 , b ) $ 1.88 , c ) $ 2.14 , d ) $ 2.50 , e ) $ 3.25
Rationale: "7 regular days - - > sales = 7 * 32 * x = 224 x ; 3 hot days - - > sales = 3 * 32 * ( 1.25 x ) = 120 x ; total sales = 224 x + 120 x = 344 x . total cost = 10 * 32 * 0.75 = 240 . profit = 344 x - 240 = 350 - - > x = 1.715 . 1.25 x = ~ 2.14 . answer : c ."
Answer: c
Question (general): what is the greatest prime factor of 2 ^ 8 - 1 ?
Options: a ) 11 , b ) 13 , c ) 17 , d ) 19 , e ) 23
Rationale: "2 ^ 8 - 1 = ( 2 ^ 4 - 1 ) ( 2 ^ 4 + 1 ) = 15 * 17 the answer is c ."
Answer: c
Question (general): if x , y , and z are positive integers and 2 x = 3 y = 4 z , then the least possible value of x + y + z is
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 31
Rationale: "given 2 x = 3 y = 5 z x + y + z in terms of x = x + ( 2 x / 3 ) + ( 2 x / 5 ) = 31 x / 15 now checking with each of the answers and see which value gives a minimum integer value . a x = 15 / 31 * 40 , not an integer b , c , d can be ruled out similarly . e is minimum value as x = 15 * 31 / 31 = 15 answer is e"
Answer: e
Question (geometry): right triangle abc is to be drawn in the xy - plane so that the right angle is at a and ab is parallel to the y - axis . if the x - and y - coordinates of a , b , and c are to be integers that are consistent with the inequalities - 7 ≤ x ≤ 1 and 4 ≤ y ≤ 9 , then how many different triangles can be drawn that will meet these conditions ?
Options: a ) 54 , b ) 432 , c ) 2,160 , d ) 3024 , e ) 148,824
Rationale: "we have the rectangle with dimensions 9 * 7 ( 9 horizontal dots and 7 vertical ) . ab is parallel to y - axis and ac is parallel to x - axis . choose the ( x , y ) coordinates for vertex a : 9 c 1 * 7 c 1 ; choose the x coordinate for vertex c ( as y coordinate is fixed by a ) : 8 c 1 , ( 9 - 1 = 8 as 1 horizontal dot is already occupied by a ) ; choose the y coordinate for vertex b ( as x coordinate is fixed by a ) : 6 c 1 , ( 7 - 1 = 6 as 1 vertical dot is already occupied by a ) . 9 c 1 * 7 c 1 * 8 c 1 * 6 c 1 = 3024 answer : d ."
Answer: d
Question (general): a man has $ 480 in the denominations of one - dollar , 5 - dollar notes and 10 - dollar . the number of dollars of each denomination is equal . what is the total number of dollar that he has ?
Options: a ) 50 , b ) 60 , c ) 90 , d ) 48 , e ) 67
Rationale: c $ 90 let number of notes of each denomination be x . then x + 5 x + 10 x = 480 16 x = 480 x = 30 . hence , total number of notes = 3 x = 90 .
Answer: c
Question (general): when n is divided by 48 , the remainder is 6 . what is the remainder when 4 n is divided by 8 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "let n = 6 ( leaves a remainder of 6 when divided by 48 ) 4 n = 4 ( 6 ) = 24 , which leaves a remainder of 0 when divided by 8 . answer a"
Answer: a
Question (general): find how many positive integers less than 10000 are there such thatthe sum of the digits of the no . is divisible by 3 ?
Options: a ) 2468 , b ) 2789 , c ) 2987 , d ) 3334 , e ) 3568
Rationale: if sum of the digits is divisible by 3 , the number is divisible by 3 . therefore , required number of non - negative integers is equal to count of numbers less than 10000 which are divisible by 3 . such numbers are ( 3 , 6 , 9 , . . . , 9999 ) ( arithmetic progression with first term = 3 , last term = 9999 , common difference = 3 ) . count of such numbers = 9999 3 = 3333 99993 = 3333 but zero is also divisible by 3 . this makes our total count 3334 d
Answer: d
Question (physics): a , b and c can do a work in 7 , 14 and 21 days respectively . they completed the work and got rs . 242 . what is the share of c ?
Options: a ) 33 , b ) 44 , c ) 55 , d ) 77 , e ) 99
Rationale: "the ratio of their working rates = 1 / 7 : 1 / 14 : 1 / 21 = 6 : 3 : 2 . since , they work together , the share of c = 2 / 11 * 242 = rs . 44 \ answer : b"
Answer: b
Question (gain): the present population of a town is 4320 . population increase rate is 20 % p . a . find the population of town before 2 years ?
Options: a ) 2500 , b ) 2100 , c ) 3500 , d ) 3000 , e ) 2050
Rationale: "p = 4320 r = 20 % required population of town = p / ( 1 + r / 100 ) ^ t = 4320 / ( 1 + 20 / 100 ) ^ 2 = 4320 / ( 6 / 5 ) ^ 2 = 3000 ( approximately ) answer is d"
Answer: d
Question (physics): if 12 men and 16 boys can do a piece of work in 7 days and 13 men together will 24 boys can do it in 4 days . compare the daily work done by a man with that of a boy .
Options: a ) 1 : 4 , b ) 1 : 2 , c ) 1 : 3 , d ) 2 : 1 , e ) 4 : 1
Rationale: "12 m + 16 b - - - - - 7 days 13 m + 24 b - - - - - - - 4 days 84 m + 112 b = 52 m + 96 b 32 m = 16 b = > 2 m = b m : b = 1 : 2 answer : b"
Answer: b
Question (physics): two persons a and b can complete a piece of work in 30 days and 45 days respectively . if they work together , what part of the work will be completed in 6 days ?
Options: a ) 2 / 5 , b ) 1 / 6 , c ) 1 / 3 , d ) 1 / 9 , e ) 2 / 6
Rationale: "a ' s one day ' s work = 1 / 30 b ' s one day ' s work = 1 / 45 ( a + b ) ' s one day ' s work = 1 / 30 + 1 / 45 = 1 / 18 the part of the work completed in 6 days = 6 ( 1 / 18 ) = 1 / 3 . answer c"
Answer: c
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 432,000 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 ) $ 2,050 , e ) $ 3,375
Rationale: "number of boxes = total volume / volume of one box = 432,000 / ( 8 * 10 * 12 ) = 450 one box costs 7.50 , so 450 box will cost = 450 * 7.5 = 3375 e is the answer"
Answer: e
Question (probability): in how many ways 4 boys and 4 girls can be seated in a row so that they are alternate .
Options: a ) 144 , b ) 288 , c ) 12 , d ) 576 , e ) none
Rationale: "solution : let the arrangement be , b g b g b g b g 4 boys can be seated in 4 ! ways . girl can be seated in 4 ! ways . required number of ways , = 4 ! * 4 ! = 576 . answer : option d"
Answer: d
Question (physics): two men a and b start from place x walking at 4 ½ kmph and 5 ¾ kmph respectively . how many km apart they are at the end of 4 ½ hours if they are walking in the same direction ?
Options: a ) 7 km , b ) 6 km , c ) 5 5 / 8 km , d ) 9 km , e ) 5 km
Rationale: "rs = 5 ¾ - 4 ½ = 1 ¼ t = 4 ½ h . d = 5 / 4 * 9 / 2 = 45 / 8 = 5 5 / 8 km answer : c"
Answer: c
Question (gain): kavi spends 50 % of his monthly salary on food and saves 80 % of the remaining amount . if his monthly salary is rs . 19000 , how much money does he save every month ?
Options: a ) rs . 2000 , b ) rs . 600 , c ) rs . 8000 , d ) rs . 3800 , e ) rs . 1200
Rationale: explanation : kavi ' s monthly income = rs . 19,000 he spends 50 % on food . the total money spent on food = 50 / 100 * 19000 = rs . 9500 now , his monthly remaining income = rs . 19000 – rs . 9500 = rs . 9500 out of rs . 9500 , he saves 40 % . amount saved = 40 / 100 * 9500 = rs . 3800 answer : d
Answer: d
Question (physics): a man can row upstream at 40 kmph and downstream at 52 kmph , and then find the speed of the man in still water ?
Options: a ) 27 , b ) 40 , c ) 42 , d ) 46 , e ) 24
Rationale: "us = 40 ds = 52 m = ( 40 + 52 ) / 2 = 46 answer : d"
Answer: d
Question (physics): a can do a piece of work in 10 days and b alone can do it in 20 days . how much time will both take to finish the work ?
Options: a ) a ) 5.333 , b ) b ) 6 , c ) c ) 6.666 , d ) d ) 8.333 , e ) e ) 9
Rationale: "this question can be solved by different methods . we need to conserve time in exams so solving this problem using equations is the good idea . time taken to finish the job = xy / ( x + y ) = 10 x 20 / ( 10 + 20 ) = 200 / 30 = 6.666 days answer : c"
Answer: c
Question (general): a ferry can transport 100 tons of vehicles . automobiles range in weight from 1,600 to 3,000 pounds . what is the greatest number of automobiles that can be loaded onto the ferry ?
Options: a ) 110 , b ) 128 , c ) 115 , d ) 130 , e ) 120
Rationale: "to get maximum vehicles we must take into consideration the minimum weight i . e 1600 pounds here since , 1 ton = 2000 pounds 100 tons will be 200,000 pounds from the answer choices : let max number of vehicles be 120 total weight will be = 120 * 1600 = 192000 pounds , which is lesser than the maximum weight allowed . ans : e"
Answer: e
Question (gain): the simple interest on rs . 10 for 4 months at the rate of 3 paise per rupeeper month is
Options: a ) 1.2 , b ) 1.4 , c ) 2.25 , d ) 3.21 , e ) none
Rationale: "sol . s . i . = rs . [ 10 * 3 / 100 * 4 ] = rs . 1.20 answer a"
Answer: a
Question (physics): two trains are moving in the same direction at 72 kmph and 36 kmph . the faster train crosses a man in the slower train in 48 seconds . find the length of the faster train ?
Options: a ) 270 , b ) 288 , c ) 266 , d ) 299 , e ) 480
Rationale: "relative speed = ( 72 - 36 ) * 5 / 18 = 2 * 5 = 10 mps . distance covered in 27 sec = 48 * 10 = 480 m . the length of the faster train = 480 m . answer : e"
Answer: e
Question (general): a bowl contains equal numbers of red , orange , green , blue , and yellow candies . kaz eats all of the green candies and half of the orange ones . next , he eats half of the remaining pieces of each color . finally , he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 25 % of the original number . what percent of the red candies remain ?
Options: a ) 10 % , b ) 15 % , c ) 25 % , d ) 35 % , e ) 40 %
Rationale: "let x be the original number of each color . kaz eats all of the green candies and half of the orange ones . there are 0 green candies and 0.5 x orange candies remaining . he eats half of the remaining pieces of each color . there are 0.25 x orange candies , and 0.5 x each of red , yellow , and blue candies . he eats red and yellow candies in equal proportions . orange + blue + red + yellow = 0.75 x + red + yellow = 1.25 x red + yellow = 0.5 x red = 0.25 x , since red = yellow . the answer is c ."
Answer: c
Question (general): what is the units digit of ( 63 ^ 4 ) ( 41 ^ 7 ) ( 99 ^ 9 ) ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "the units digit of 63 ^ 4 is the units digit of 3 ^ 4 which is 1 . the units digit of 41 ^ 7 is the units digit of 1 ^ 7 which is 1 . the units digit of 99 ^ 9 is the units digit of 9 ^ 9 which is 9 . note the pattern : 9 ^ 1 = 9 , 9 ^ 2 = 81 , 9 ^ 3 = 729 , . . . the units digit alternates between 9 and 1 . the units digit of 1 * 1 * 9 is 9 . the answer is e ."
Answer: e
Question (general): if - 4 and - 8 are negative integers , then - 4 * - 8 + 2 is
Options: a ) - 32 , b ) - 30 , c ) 34 , d ) - 24 , e ) - 10
Rationale: answer : c
Answer: c
Question (general): the maximum number of students among them 1234 pens and 874 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 ) 2 , c ) 1001 , d ) 1911 , e ) none of these
Rationale: "explanation : required number of students = h . c . f of 1234 and 874 = 2 . answer : b"
Answer: b
Question (physics): a boatman selling a boat along river flow . if he sell boat in steal water at 3 m / sec and flow of river is 2 m / sec . how much time he will take to sell 100 m .
Options: a ) 30 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: net speed = 3 + 2 = 5 m / sec distance = 100 m time = 100 / 5 = 20 sec answer d
Answer: d
Question (gain): a man can row his boat with the stream at 12 km / h and against the stream in 8 km / h . the man ' s rate is ?
Options: a ) 2 kmph , b ) 6 kmph , c ) 7 kmph , d ) 4 kmph , e ) 9 kmph
Rationale: explanation : ds = 12 us = 8 s = ? s = ( 12 - 8 ) / 2 = 2 kmph answer : a
Answer: a
Question (gain): jayant opened a shop investing rs . 30,000 . madhu joined him 2 months later , investing rs . 45,000 . they earned a profit of rs . 60,000 after completion of one year . what will be madhu ' s share of profit ?
Options: a ) rs . 27,000 , b ) rs . 24,000 , c ) rs . 30,000 , d ) rs . 36,000 , e ) none of these
Rationale: "30,000 * 12 = 45,000 * 8 1 : 1 madhu ' s share = 1 / 2 * 60,000 i . e . rs . 30,000 answer : c"
Answer: c
Question (general): if the average ( arithmetic mean ) of a and b is 120 , and the average of b and c is 150 , what is the value of a − c ?
Options: a ) − 60 , b ) − 100 , c ) 100 , d ) 135 , e ) it can not be determined from the information given
Rationale: "a + b = 240 b + c = 300 a - c = - 60 . imo option a ."
Answer: a
Question (general): a vessel of capacity 2 litre has 25 % of alcohol and another vessel of capacity 6 litre had 30 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ?
Options: a ) 23 % . , b ) 71 % . , c ) 49 % . , d ) 29 % . , e ) 51 % .
Rationale: "25 % of 2 litres = 0.5 litres 30 % of 6 litres = 1.8 litres therefore , total quantity of alcohol is 2.3 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 23 % answer : a"
Answer: a
Question (general): if x / 4 years ago roger was 14 years old and x / 4 years from now he will be 4 x years old , how old will he be 3 x years from now ?
Options: a ) 32 , b ) 35 , c ) 30 , d ) 40 , e ) 27
Rationale: "assume the current age = a a - x / 4 = 14 ( i ) a + x / 4 = 4 x or a = 15 x / 4 ( ii ) putting the value of a from ( ii ) in ( i ) 15 x / 4 - x / 4 = 14 or 14 x / 4 = 14 therefore x = 4 and a = 15 3 x years from now , age will be 15 + 3 * 4 = 27 option e"
Answer: e
Question (physics): jack and jill work at a hospital with 4 other workers . for an internal review , 2 of the 6 workers will be randomly chosen to be interviewed . what is the probability that jack and jill will both be chosen ?
Options: a ) 1 / 3 , b ) 1 / 4 , c ) 1 / 15 , d ) 3 / 8 , e ) 2 / 3
Rationale: "total number of ways to choose 2 out of 6 workers = 6 ! / 2 ! 4 ! = 15 number of ways to choose both jack and jill = 1 probability = 1 / 15 c should be the answer"
Answer: c