Cheukting/mathqa huggingface dataset:
Question (general): the average ( arithmetic mean ) of the 5 positive integers k , m , r , s , and t is 10 , and k < m < r < s < t . if t is 20 , what is the greatest possible value of the median of the 5 integers ?
Options: a ) 16 , b ) 18 , c ) 13 , d ) 20 , e ) 22
Rationale: "we need to find the median which is the third value when the numbers are in increasing order . since k < m < r < s < t , the median would be r . the average of the positive integers is 10 which means that in effect , all numbers are equal to 10 . if the largest number is 20 , it is 10 more than 20 . we need r to be maximum so k and m should be as small as possible to get the average of 10 . since all the numbers are positive integers , k and m can not be less than 1 and 2 respectively . 1 is 9 less than 10 and 2 is 8 less than 10 which means k and m combined are 17 less than the average . 20 is already 10 more than 10 and hence we only have 17 - 10 = 7 extra to distribute between r and s . since s must be greater than r , r can be 10 + 3 = 13 and s can be 10 + 4 = 14 . so r is 13 . answer ( c )"
Answer: c
Question (general): if a person walks at 15 km / hr instead of 10 km / hr , he would have walked 15 km more . the actual distance traveled by him is ?
Options: a ) 30 , b ) 50 , c ) 15 , d ) 12 , e ) 20
Rationale: "let the actual distance traveled be x km . then , x / 10 = ( x + 15 ) / 15 x - 30 = > x = 30 km . answer : a"
Answer: a
Question (general): the population of a bacteria culture doubles every 1 minutes . approximately how many minutes will it take for the population to grow from 1,000 to 500,000 bacteria
Options: a ) 9 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "this one ' s easy . 1000 * 2 ^ t = 500,000 2 ^ t = 500 now gauging , since 2 ^ 8 = 256 , then 2 ^ 9 = 512 so t = 9 but be careful , ' t ' is in time intervals of 1 minutes so answer is 9 * 1 = 9 minutes answer ( a )"
Answer: a
Question (geometry): a rectangular tiled patio is composed of 48 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 48 tiles , and it will still be rectangular . how many rows are in the tile patio before the change in layout ?
Options: a ) 5 , b ) 6 , c ) 10 , d ) 13 , e ) 28
Rationale: "suppose there are c columns and there are r rows original situation so , number of tiles = c * r = 48 also . reach column has r tiles and each row has c tiles new situation number of tiles in each column is r - 2 and number of tiles in each row is c + 4 so , number of rows = r - 2 and number of columns is c + 4 so , number of tiles = ( r - 2 ) * ( c + 4 ) = 48 comparing both of them we get c * r = ( r - 2 ) * ( c + 4 ) = > 4 r - 2 c = 8 c = 2 r - 4 putting it in c * r = 48 ( 2 r - 4 ) * r = 48 2 r ^ 2 - 4 r - 48 = 0 r can not be negative so r = 6 and c = 8 so , answer will be b"
Answer: b
Question (other): what is the units digit of 28 ! + 50 ! + 3 ! + 4 ! ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "for all n greater than 4 , the units digit of n ! is 0 . the sum of the four units digits is 0 + 0 + 6 + 4 = 10 the units digit is 0 . the answer is a ."
Answer: a
Question (gain): a shopkeeper loses 15 % , if an article is sold for rs . 119 . what should be the selling price of the article to gain 20 % ?
Options: a ) s . 177 , b ) s . 168 , c ) s . 144 , d ) s . 129 , e ) s . 112
Rationale: "given that sp = rs . 119 and loss = 15 % cp = [ 100 ( sp ) ] / ( 100 - l % ) = ( 100 * 119 ) / 85 = rs . 140 . to get 20 % profit , new sp = [ ( 100 + p % ) cp ] / 100 = ( 140 * 120 ) / 100 = rs . 168 answer : b"
Answer: b
Question (physics): eight women can do a work in 10 days . ten men can complete the same work in 6 days . what is the ratio between the capacity of a man and a woman ?
Options: a ) 1 : 2 , b ) 2 : 1 , c ) 2 : 3 , d ) 4 : 3 , e ) none of these
Rationale: "explanation : ( 8 ã — 10 ) women can complete the work in 1 day . â ˆ ´ 1 woman ' s 1 day ' s work = 1 / 80 ( 10 ã — 6 ) men can complete the work in 1 day . â ˆ ´ 1 man ' s 1 day ' s work = 1 / 60 so , required ratio = 1 / 80 : 1 / 60 = 4 : 3 answer : d"
Answer: d
Question (physics): x , y and z , each working alone can complete a job in 6 , 8 and 12 days respectively . if all three of them work together to complete a job and earn $ 2350 , what will be z ' s share of the earnings ?
Options: a ) $ 525 , b ) $ 550.50 , c ) $ 1080.02 , d ) $ 522.3 , e ) $ 1020.2
Rationale: "the dollars earned will be in the same ratio as amount of work done 1 day work of z is 1 / 12 ( or 2 / 24 ) 1 day work of the combined workforce is ( 1 / 6 + 1 / 8 + 1 / 12 ) = 9 / 24 z ' s contribution is 2 / 9 of the combined effort translating effort to $ = 2 / 9 * 2350 = $ 522.3 hence : d"
Answer: d
Question (geometry): the sides of a cube measures 6.5 cm . if the surface area of the cube is the same as a ball , what is the radius of the ball ? round to the nearest whole number .
Options: a ) 9
b ) 7
c ) 4
d ) 8
e ) 6
Rationale: first calculate the surface area of the cube . the cube is made of 6 squares with the sides measuring 6.5 cm each . the surface area of 1 side of the cube is 42.25 cm . multiply the surface area of the 1 side by 6 will give you the cube ' s total surface area . the cubes surface area is 253.5 cm . now we know that the surface area of the ball is 253.5 cm . to find out the surface area of a sphere you need to square the radius , then multiply by pi , and multiply by the number 4 . going backwards to find the radius - you will need to dived the surface area by 4 . then divide by pi . then determine the square root of the answer . the radius is 4.460 . rounding to the nearest whole number the radius is 4 . the correct answer is ( c ) .
Answer: c
Question (general): ratio of two numbers x and y is 5 : 7 . if x is increased by 20 % and y is increased by 2 then the new ratio becomes 2 : 3 . what is the ratio 3 y : ( x + 6 )
Options: a ) 7 : 8 , b ) 8 : 7 , c ) 6 : 7 , d ) 7 : 6 , e ) 2 : 7
Rationale: "let : x = 5 n y = 7 n 6 n / ( 7 n + 2 ) = 2 / 3 18 n = 2 * ( 7 n + 2 ) n = 1 so , x = 5 ; y = 7 y / ( x + 3 ) = 7 / 8 answer = a"
Answer: a
Question (general): if a = { 9 , 17 , 25 , 28 , 29 , 30 } , how much less is the mean of the numbers in a than the median of the numbers in s ?
Options: a ) 1.0 , b ) 9.6 , c ) 3.5 , d ) 3.2 , e ) 5.1
Rationale: "this is a good question to understand the difference between mean and median . mean : average of all the numbers . ( sum of all the elements divided by the number of elements ) median : arrange the elements of the set in increasing order . if the number of terms is odd , the middle term is the median . if the number of terms is even , the average of middle two terms is the median coming to this question , mean = ( 9 + 17 + 25 + 28 + 29 + 30 ) / 6 = 23 median = ( 25 + 28 ) / 2 = 26.5 difference = 3.5 option c"
Answer: c
Question (general): a , b and c have rs . 1000 between them , a and c together have rs . 700 and b and c rs . 600 . how much does c have ?
Options: a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) 500
Rationale: "a + b + c = 1000 a + c = 700 b + c = 600 - - - - - - - - - - - - - - a + b + 2 c = 1300 a + b + c = 1000 - - - - - - - - - - - - - - - - c = 300 answer : c"
Answer: c
Question (general): sam ’ s car was fined when he gave joe and peter a ride , so they decided to help sam pay the fine . joe paid $ 10 more than 1 / 4 of the fine and peter paid $ 10 less than 1 / 3 of the fine , leaving pay $ 25 less than 1 / 2 the fine to complete the payment . what fraction of the fine did sam pay ?
Options: a ) $ 120 , b ) $ 125 , c ) $ 130 , d ) $ 135 , e ) $ 140
Rationale: "call the fine f . joe paid ( 1 / 4 ) f + 4 and peter paid ( 1 / 3 ) f – 4 , leaving ( 1 / 2 ) f – 5 left . if we add those three up , they should add up to f . f = [ ( 1 / 4 ) f + 10 ] + [ ( 1 / 3 ) f – 10 ] + [ ( 1 / 2 ) f – 25 ] f = ( 1 / 4 ) f + ( 1 / 3 ) f + ( 1 / 2 ) f – 25 multiply all terms by 12 to clear the fractions . 12 f = 3 f + 4 f + 6 f – 300 12 f = 13 f – 300 – f = – 300 f = 300 well , if the fine cost $ 300 , then sam paid the part not covered by joe or peter . half the fine is $ 150 , and sam paid $ 25 less than this : $ 125 answer = b"
Answer: b
Question (probability): from a pack of 52 cards , 1 card is drawn at random . what is the probability that a king is drawn ?
Options: a ) 1 / 4 , b ) 4 / 13 , c ) 1 / 13 , d ) 3 / 26 , e ) 7 / 52
Rationale: "the total number of cards is 52 . the number of kings is 4 . p ( king ) = 4 / 52 = 1 / 13 the answer is c ."
Answer: c
Question (general): if ( 1 / 2 ) ^ 18 ( 1 / 81 ) ^ k = 1 / 18 ^ 18 , then k =
Options: a ) 9 , b ) 12 , c ) 16 , d ) 24 , e ) 36
Rationale: "i ' m going to focus on denominator only . . ( 2 ^ 18 ) . ( ( 3 ^ 4 ) ^ k = 18 ^ 18 ( 2 ^ 18 ) . ( ( 3 ^ 4 k ) = ( 2 . 3 ^ 2 ) ^ 18 ( 2 ^ 18 ) . ( ( 3 ^ 4 k ) = ( 2 ^ 24 ) . ( 3 ^ 2 ) ^ 18 hence 4 k = 36 k = 9 answer a i hope it ' s quite clear"
Answer: a
Question (other): in a college , the ratio of the number of boys to girls is 8 : 5 . if there are 300 girls , the total number of students in the college is
Options: a ) 420 , b ) 520 , c ) 620 , d ) 780 , e ) 820
Rationale: "explanation : let the boy are 8 x and girls are 5 x = > 5 x = 300 = > x = 60 total students = 8 x + 5 x = 13 x = 13 ( 60 ) = 780 option d"
Answer: d
Question (gain): the sale price sarees listed for rs . 390 after successive discount is 15 % and 25 % is ?
Options: a ) 298 , b ) 237 , c ) 248 , d ) 876 , e ) 291
Rationale: "390 * ( 85 / 100 ) * ( 75 / 100 ) = 248 answer : c"
Answer: c
Question (general): a student finds the average of 9 positive integers . each integer contains two digits . by mistake , the boy interchanges the digits of one number say pq for qp . due to this , the average becomes 1 less than the previous one . what was the difference of the two digits p and q ?
Options: a ) 8 , b ) 6 , c ) 1 , d ) 4 , e ) 2
Rationale: explanation : let the original number be pq i . e . , ( 10 p + q ) . after interchanging the digits , the new number becomes qp i . e . , ( 10 q + p ) . the question states that the average of 9 numbers has become 1 less than the original average . therefore , the sum of the original 9 numbers will be 9 * 1 more than the sum of the 9 numbers with the digits interchanged . i . e . , 10 p + q = 10 q + p + 9 = > 9 a - 9 b = 9 = > a - b = 1 . answer : c
Answer: c
Question (physics): a man can row a distance of 5 km in 60 min with the help of the tide . the direction of the tide reverses with the same speed . now he travels a further 25 km in 10 hours . how much time he would have saved if the direction of tide has not changed ?
Options: a ) 2 , b ) 5 , c ) 1 , d ) 6 , e ) 7
Rationale: "explanation : he covered 5 km in 1 hour , so he might cover 25 km in 5 hours . but he took 10 hours . he would have saved 10 â € “ 5 = 5 hours . answer : b"
Answer: b
Question (general): a grocer has a sale of rs . 6435 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 7000 ?
Options: a ) s . 4991 , b ) s . 5991 , c ) s . 6001 , d ) s . 6991 , e ) s . 7991
Rationale: "total fr 5 mnths = ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs 34009 . reqd . sale = rs . [ ( 7000 * 6 ) - 34009 ] = rs . ( 42000 - 34009 ) = rs . 7991 . answer : e"
Answer: e
Question (general): during the first two weeks of january , the total rainfall in springdale was 30 inches . if the rainfall during the second week was 1.5 times the rainfall during the first week , what was the rainfall during the second week of january ?
Options: a ) 5 inches , b ) 6 inches , c ) 9 inches , d ) 10 inches , e ) 18 inches
Rationale: "total rainfall in 2 weeks = 18 inches . assume the rainfall in second week = 1 . x rainfall in first week = x total rainfall = 2.5 x = 18 inches x = 12 and 1.5 x = 18 rainfall during second week = 18 inches option e"
Answer: e
Question (general): let f ( x , y ) be defined as the remainder when ( x – y ) ! is divided by x . if x = 45 , what is the maximum value of y for which f ( x , y ) = 0 ?
Options: a ) 32 , b ) 35 , c ) 39 , d ) 40 , e ) 42
Rationale: "the question is finding y such that ( 45 - y ) ! is a multiple of 45 . that means we need to have 5 * 3 ^ 2 in ( 45 - y ) ! 6 ! is the smallest factorial number with 5 * 3 ^ 2 as a factor . 45 - y = 6 y = 39 the answer is c ."
Answer: c
Question (general): what is the minimum value of | x - 4 | + | x + 2 | + | x - 5 | ?
Options: a ) - 3 , b ) 3 , c ) 5 , d ) 7 , e ) 8
Rationale: "a can not be the answer as all the three terms are in modulus and hence the answer will be non negative . | x - 4 | > = 0 - - > minimum occurs at x = 4 | x + 2 | > = 0 - - > minimum occurs at x = - 2 | x - 5 | > = 0 - - > minimum occurs at x = 5 x = - 2 - - > result = 6 + 0 + 7 = 13 . also any negative value will push the combined value of | x - 4 | + | x - 5 | to a value > 9 . x = 4 - - > result = 0 + 6 + 1 = 7 x = 5 - - > result = 1 + 7 + 0 = 8 x = 2 - - > result = 2 + 4 + 3 = 9 so minimum value of the expression occurs at x = 4 and the resultant value = 7 answer : d"
Answer: d
Question (general): the average weight of 8 persons increases by 4 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?
Options: a ) 75 kg , b ) 65 kg , c ) 55 kg , d ) 97 kg , e ) 25 kg
Rationale: "total weight increased = ( 8 x 4 ) kg = 32 kg . weight of new person = ( 65 + 32 ) kg = 97 kg . answer : d"
Answer: d
Question (physics): a train 120 m in length crosses a telegraph post in 16 seconds . the speed of the train is ?
Options: a ) 16 kmph , b ) 88 kmph , c ) 54 kmph , d ) 18 kmph , e ) 27 kmph
Rationale: "s = 120 / 16 * 18 / 5 = 27 kmph answer : e"
Answer: e
Question (general): subash can copy 50 pages in 10 hrs . subash and prakash together can copy 300 pages in 40 hours . in how much time prakash can copy 25 pages .
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "subhas ' s 1 hr copy page = 50 / 10 = 5 page ( subhas + prakash ) ' s 1 hr copy page = 300 / 40 = 7.5 page from above prakash ' s 1 hr copy page = 2.5 page so time taken in 30 page ' s copy = ( 25 / 2.5 ) = 10 hrs answer : b"
Answer: b
Question (general): if p and q are positive integers each greater than 1 , and 17 ( p + 1 ) = 25 ( q + 1 ) , what is the least possible value of p + q ?
Options: a ) 36 , b ) 42 , c ) 40 , d ) 46 , e ) none
Rationale: "17 ( p + 1 ) = 29 ( q + 1 ) - - > ( p + 1 ) / ( q + 1 ) = 29 / 17 - - > the least positive value of p + 1 is 25 , so the least value of p is 24 and the least positive value of q + 1 is 17 , so the least value of q is 16 - - > the least value of p + q is 24 + 16 = 40 . answer : c ."
Answer: c
Question (geometry): what will be the cost of building a fence around a square plot with area equal to 289 sq ft , if the price per foot of building the fence is rs . 54 ?
Options: a ) 3672 , b ) 920 , c ) 7290 , d ) 6928 , e ) 3729
Rationale: "explanation : let the side of the square plot be a ft . a 2 = 289 = > a = 17 length of the fence = perimeter of the plot = 4 a = 68 ft . cost of building the fence = 68 * 54 = rs . 3672 . answer : option a"
Answer: a
Question (physics): excluding stoppages , the speed of a train is 45 kmph and including stoppages it is 33 kmph . of how many minutes does the train stop per hour ?
Options: a ) 73 , b ) 83 , c ) 16 , d ) 83 , e ) 28
Rationale: "explanation : t = 12 / 45 * 60 = 16 answer : option c"
Answer: c
Question (physics): worker a takes 8 hours to do a job . worker b takes 10 hours to do the same job . how long should it take both a and b , working together but independently , to do the same job ?
Options: a ) 70 hours , b ) 40 / 9 hours , c ) 9 hours , d ) 16 hours , e ) 20 hours
Rationale: "a ’ s 1 hour ' s work = 1 / 8 b ' s 1 hour ' s work = 1 / 10 ( a + b ) ' s 1 hour ' s work = ( 1 / 8 ) + ( 1 / 10 ) = 9 / 40 both a and b will finish the work in 40 / 9 days . answer b 40 / 9 hours"
Answer: b
Question (physics): rectangle dimensions were given , 2 doors dimensions given , 2 windows dimensions given . 70 cm wide wallpaper to be covered on the walls of this room . cost of wallpaper is 60 per meter . . calculate total cost
Options: a ) 20 , b ) 25 , c ) 30 , d ) 60 , e ) 70
Rationale: area of room = ( l * b ) m ^ 2 area of door + window = ( d + w ) m ^ 2 remaining area = ( ( l * b ) - ( d + w ) ) m ^ 2 so length = remaining area / 0.70 m total cost = length * 60 - - - ans and total cost = 60 answer : d
Answer: d
Question (general): set s consists of integers { 12 , 34 } . if two numbers are chosen from set s at random , what is the probability that the sum of 2 numbers is more than 6 ?
Options: a ) 1 / 3 , b ) 1 / 6 , c ) 2 / 3 , d ) 2 / 5 , e ) 3 / 7
Rationale: number of ways you can choose 2 from 4 = 4 c 2 = 6 e = event of getting the 2 numbers is more than 6 = ( 3,4 ) = 1 probability = 1 / 6 answer is b
Answer: b
Question (gain): in a sample of 800 high school students in which all students are either freshmen , sophomores , juniors , or seniors , 23 percent are juniors and 75 percent are not sophomores . if there are 160 seniors , how many more freshmen than sophomores are there among the sample of students ?
Options: a ) 42 , b ) 48 , c ) 56 , d ) 64 , e ) 72
Rationale: 200 are sophomores . the number of freshmen is 600 - 160 - 0.23 ( 800 ) = 256 the answer is c .
Answer: c
Question (gain): the manager of a produce market purchased a quantity of tomatoes for $ 0.80 per pound . due to improper handling , 10 percent of the tomatoes , by weight , were ruined and discarded . at what price per pound should the manager sell the remaining tomatoes if she wishes to make a profit on the sale of the tomatoes equal to 9 percent of the cost of the tomatoes .
Options: a ) $ 0.94 , b ) $ 0.97 , c ) $ 0.98 , d ) $ 1.00 , e ) $ 1.20
Rationale: "assume the manager bought 100 tomatoes . cost price = 80 given : 10 % are damaged - - > available tomatoes to sell = 90 90 * x - 80 = 0.09 * 80 90 x - 80 = 7.2 90 x = 87.2 x = 87.2 / 90 = 0.968 x is slightly under 0.9688 = 0.97 answer : b"
Answer: b
Question (probability): if a coin has an equal probability of landing heads up or tails up each time it is flipped , what is the probability that the coin will land heads up exactly once in 3 consecutive flips ?
Options: a ) 0.125 , b ) 0.25 , c ) 0.75 , d ) 0.375 , e ) 0.666
Rationale: "total number of ways in which h or t can appear in 3 tosses of coin is = 2 * 2 * 2 = 8 ways for 2 t and 1 h thus probability is = p ( htt ) + p ( tth ) + p ( tht ) = 1 / 8 + 1 / 8 + 1 / 8 = 3 / 8 = . 375 answer : d"
Answer: d
Question (general): the average weight of 10 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 50 kg . what might be the weight of the new person ?
Options: a ) 76 kg , b ) 76.5 kg , c ) 75 kg , d ) data inadequate , e ) none of these
Rationale: "explanation : total weight increased = ( 10 x 2.5 ) kg = 25 kg . weight of new person = ( 50 + 25 ) kg = 75 kg . answer : c"
Answer: c
Question (physics): the speed of a boat in still water is 15 km / hr and the rate of current is 3 km / hourr . the distance travelled downstream in 24 mins is ?
Options: a ) 6 km , b ) 7 km , c ) 7.2 km , d ) 8 km , e ) 8.4 km
Rationale: "speed of a boat in still water = 15 km / hr speed of the current = 3 km / hr speed downstream = ( 15 + 3 ) = 18 km / hr distance travelled downstream in 24 minutes = 2460 × 18 = 2 × 185 = 7.2 km c"
Answer: c
Question (other): if 1 tic equals 4 tacs and 5 tacs equal 8 tocs , what is the ratio of one tic to one toc ?
Options: a ) 15 / 2 , b ) 6 / 5 , c ) 5 / 6 , d ) 32 / 5 , e ) 1 / 15
Rationale: "tic = 4 * tac and 5 * tac = 8 * toc ; 5 * tic = 20 * tac and 20 * tac = 32 * toc - - > 5 * tic = 32 * toc - - > tic / toc = 32 / 5 . answer : d ."
Answer: d
Question (physics): a man can row upstream at 22 kmph and downstream at 42 kmph , and then find the speed of the man in still water ?
Options: a ) 29 , b ) 92 , c ) 30 , d ) 32 , e ) 23
Rationale: "us = 22 ds = 42 m = ( 42 + 22 ) / 2 = 32 answer : d"
Answer: d
Question (geometry): if the side length of square b is five times that of square a , the area of square b is how many times the area of square a ?
Options: a ) 5 , b ) 15 , c ) 25 , d ) 35 , e ) 45
Rationale: "let x be the side length of square a . then the area of square a is x ^ 2 . the area of square b is ( 5 x ) ^ 2 = 25 x ^ 2 . the answer is c ."
Answer: c
Question (general): the average weight of 20 oarsmen in a boat is increased by 2 kg when one of the crew , who weight 40 kg is replaced by a new man . find the weight of the new man .
Options: a ) 60 kg , b ) 50 kg , c ) 92 kg , d ) 80 kg , e ) 70 kg
Rationale: total weight increased = 2 * 20 = 40 kg weight of the new man = 40 + 40 = 80 kg answer is d
Answer: d
Question (other): in a club with 310 peopl , 138 play tennis , 255 play baseball , and 94 people play both sports . how many people do not pla a sport ?
Options: a ) 9
b ) 8
c ) 4
d ) 10
e ) 11
Rationale: take 94 off the baseball players - - > 161 then 161 + 138 = 299 play either baseball or tennis 310 - 299 = 11 answer is e
Answer: e
Question (gain): a 14 % stock yielding 8 % is quoted at ?
Options: a ) 165 , b ) 170 , c ) 175 , d ) 180 , e ) 185
Rationale: "assume that face value = rs . 100 as it is not given to earn rs . 8 , money invested = rs . 100 to earn rs . 14 , money invested = 100 × 14 / 8 = rs . 175 ie , market value of the stock = rs . 175 answer is c ."
Answer: c
Question (other): at present the ratio between the ages of arun and deepak is 4 : 3 . after 6 years , arun ' s age will be 26 years . what is the age of deepak at present ?
Options: a ) 15 , b ) 21 , c ) 23 , d ) 12 , e ) 25
Rationale: let the present ages of arun and deepak be 4 x years and 3 x years respectively 4 x + 6 = 26 4 x = 20 x = 5 deepak ' s age = 3 x = 15 years answer is a
Answer: a
Question (physics): working together , jose and jane can complete an assigned task in 5 days . however , if jose worked alone and complete half the work and then jane takes over the task and completes the second half of the task , the task will be completed in 15 days . how long will jose take to complete the task if he worked alone ? assume that jane is more efficient than jose
Options: a ) 26 days , b ) 15 days , c ) 60 days , d ) 65 days , e ) 36 days
Rationale: "assume : jose does 1 job in x days , so jose does 1 / x job in a day jane does 1 job in y days , so jane does 1 / y job in a day together , they does ( x + y ) / xy job in a day . this is equals to 1 / 20 . so ( x + y ) / xy = 1 / 5 5 ( x + y ) = xy next , we ' re told 1 job takes 15 days to complete if jose and jane each does half the work . so since jose does 1 job in x days , he wil need x / 2 days to do half the job . jane similarly will need y / 2 days to do the other half . x / 2 + y / 2 = 15 x + y = 30 so xy = 150 the answer choices are : 26 days 15 days 60 days 65 days 36 days from the answer choices , so i ' ll go for 15 days for jose and 10 days for jane . answer : b"
Answer: b
Question (gain): two years ago , ram put $ 1,000 into a savings account . at the end of the first year , his account had accrued $ 100 in interest bringing his total balance to $ 1,100 . the next year , his account balance increased by 20 % . at the end of the two years , by what percent has sam ' s account balance increased from his initial deposit of $ 1,000 ?
Options: a ) 40 % , b ) 25 % , c ) 35 % , d ) 30 % , e ) 32 %
Rationale: "investment 1000 dollars 1 st year total gained = 100 total amount end of first year = 1100 second year account increased by 20 % = 1100 * 0.2 = 220 therefore total amount by second year end = 1320 so total percentage increase in money = ( 1320 - 1000 ) * 100 / 1000 = 32 % correct answer e = 32 %"
Answer: e
Question (general): a gets 3 times as much money as b gets , b gets only rs . 25 more then what c gets . the 3 gets rs . 645 in all . find the share of b ?
Options: a ) 134 , b ) 120 , c ) 218 , d ) 140 , e ) 145
Rationale: a + b + c = 645 a = 3 b 3 b + b + b - 25 = 645 5 b = 670 b = 134 answer : a
Answer: a