Cheukting/mathqa huggingface dataset:
Question (general): a certain bus driver is paid a regular rate of $ 20 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 1000 in total compensation , how many total hours did he work that week ?
Options: a ) 46 , b ) 40 , c ) 44 , d ) 48 , e ) 49
Rationale: "for 40 hrs = 40 * 20 = 800 excess = 1000 - 800 = 200 for extra hours = . 75 ( 20 ) = 15 + 20 = 35 number of extra hrs = 200 / 35 = 5.71 = 6 approx . total hrs = 40 + 6 = 46 answer a 46"
Answer: a
Question (physics): a cistern normally takes 6 hours to be filled by a tap but because of a leak , 2 hours more . in how many hours will the leak empty a full cistern ?
Options: a ) 20 hours , b ) 24 hours , c ) 26 hours , d ) 18 hours , e ) none of these
Rationale: ∵ cistern fill in 6 hours . ∴ in 1 hour , filled part = 1 ⁄ 6 th now , due to leakage , filled part in 1 hour = 1 ⁄ 8 th part of the cistern emptied , due to leakage in 1 hour = 1 ⁄ 6 - 1 ⁄ 8 = 1 ⁄ 24 th ∴ the leakage will empty the full cistern in 24 hrs . answer b
Answer: b
Question (general): what is the greatest integer m for which the number 20 ! / 10 ^ m is an integer ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "10 ^ m = 2 ^ m * 5 ^ m . let ' s figure out how many 5 ' s are in the prime factorization of 20 ! the multiples of 5 are : 5 , 10 , 15 , 20 . thus 5 ^ 4 will divide 20 ! but 5 ^ 5 will not . clearly 2 ^ 4 will divide 20 ! so m = 4 is the largest possible integer . the answer is b ."
Answer: b
Question (general): what is the value of ( p + q ) / ( p - q ) if p / q is 4 ?
Options: a ) 5 / 3 , b ) 2 / 3 , c ) 2 / 6 , d ) 7 / 8 , e ) 8 / 7
Rationale: "( p + q ) / ( p - q ) = [ ( p / q ) + 1 ] / [ ( p / q ) - 1 ] = ( 4 + 1 ) / ( 4 - 1 ) = 5 / 3 = 5 / 3 answer : a"
Answer: a
Question (other): doughnuts , cookies and muffins in a pastry shop are in the ratio of 5 : 3 : 1 . if there are 50 doughnuts , the number of muffins in the shop is : .
Options: a ) 25 , b ) 30 , c ) 10 , d ) 15 , e ) 20
Rationale: explanation : let doughnuts = 5 x , cookies = 3 x & muffins = 1 x . now , 5 x = 50 hence x = 10 . number of muffins = 1 x which is 10 . answer : c
Answer: c
Question (general): what least number must be subtracted from 9679 so that the remaining number is divisible by 15 ?
Options: a ) 3 , b ) 1 , c ) 16 , d ) 4 , e ) 15
Rationale: "on dividing 9679 by 15 , we get remainder = 4 . required number be subtracted = 4 answer : d"
Answer: d
Question (general): the ages of two person differ by 20 years . if 8 years ago , the elder one be 5 times as old as the younger one , their present ages ( in years ) are respectively
Options: a ) 33 , 13 , b ) 25 , 5 , c ) 29 , 9 , d ) 50 , 30 , e ) 20,10
Rationale: let their ages be x and ( x + 20 ) years . then , 5 ( x - 8 ) = ( x + 20 - 8 ) = > 4 x = 52 = > x = 13 their present ages are 33 years and 13 year . answer : a
Answer: a
Question (general): a case of 12 rolls of paper towels sells for $ 9 . the cost of one roll sold individually is $ 1 . what is the percent of savings per roll for the 12 - roll package over the cost of 12 rolls purchased individually ?
Options: a ) 9 % , b ) 11 % , c ) 15 % , d ) 25 % , e ) 90 %
Rationale: "cost of 12 paper towels individually = 1 * 12 = 12 cost of a set of 12 paper towels = 9 cost of one roll = 9 / 12 = 3 / 4 = 0.75 savings per roll = 1 - . 75 = 0.25 % of savings is = . 25 / 1 * 100 = 25 % d is the answer ."
Answer: d
Question (gain): the difference between compound interest and simple interest on a certain amount of money at 5 % per annum for 2 years is 17 . find the sum :
Options: a ) 4500 , b ) 7500 , c ) 5000 , d ) 6800 , e ) none of these
Rationale: sol . ( d ) let the sum be 100 . therefore , si = 100 × 5 × 2100 = 10100 × 5 × 2100 = 10 and ci = 100 ( 1 + 5100 ) 2 − 100100 ( 1 + 5100 ) 2 − 100 ∴ = 100 × 21 × 2120 × 20 − 100 = 414 = 100 × 21 × 2120 × 20 − 100 = 414 difference of ci and si = 41 ⁄ 4 - 10 = 1 ⁄ 4 if the difference is 1 ⁄ 4 , the sum = 100 = > if the difference is 17 , the sum = 400 × 17 = 6800 answer d
Answer: d
Question (physics): a train speeds past a pole in 20 seconds and a platform 100 m long in 25 seconds . its length is ?
Options: a ) 188 m , b ) 876 m , c ) 251 m , d ) 150 m , e ) 400 m
Rationale: "let the length of the train be x meters and its speed be y m / sec . they , x / y = 20 = > y = x / 20 x + 100 / 25 = x / 20 x = 400 m . answer : e"
Answer: e
Question (gain): a sum of money at simple interest amounts to rs . 825 in 3 years and to rs . 850 in 4 years . the sum is ?
Options: a ) s . 738 , b ) s . 750 , c ) s . 650 , d ) s . 730 , e ) s . 735
Rationale: "s . i . for 1 year = ( 850 - 825 ) = rs . 25 s . i . for 3 years = 25 * 3 = rs . 75 principal = ( 825 - 75 ) = rs . 750 . answer : b"
Answer: b
Question (general): the difference between a number and its three - fourth is 100 . what is 25 % of that number ?
Options: a ) 120 , b ) 100 , c ) 125 , d ) 150 , e ) none of these
Rationale: "explanation : solution : let the number be x . then , x - 3 / 4 x = 100 = > x / 4 = 100 = > x = 400 . 25 % of x = 25 % of 400 = 25 / 100 * 400 = 100 . answer : b"
Answer: b
Question (general): the average of 1 st 3 of 4 numbers is 16 and of the last 3 are 15 . if the sum of the first and the last number is 11 . what is the last numbers ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 5 , e ) 7
Rationale: "a + b + c = 48 b + c + d = 45 a + d = 11 a – d = 3 a + d = 11 2 d = 8 d = 4 answer b"
Answer: b
Question (physics): john left home and drove at the rate of 45 mph for 2 hours . he stopped for lunch then drove for another 3 hours at the rate of 50 mph to reach his destination . how many miles did john drive ?
Options: a ) 235 miles . , b ) 245 miles . , c ) 240 miles . , d ) 265 miles . , e ) 275 miles .
Rationale: the total distance d traveled by john is given by d = 45 * 2 + 3 * 50 = 240 miles . answer c
Answer: c
Question (general): what least number must be subtracted from 3830 so that the remaining number is divisible by 15 ?
Options: a ) 3 , b ) 1 , c ) 5 , d ) 11 , e ) 15
Rationale: "on dividing 3830 by 15 , we get remainder = 5 . required number be subtracted = 5 answer : c"
Answer: c
Question (probability): in a bag containing 3 balls , a white ball was placed and then 1 ball was taken out at random . what isthe probability that theextracted ball would turn on to be white , if all possible hypothesis concerning the color of the balls that initially in the bag were equally possible ?
Options: a ) 2 / 3 , b ) 5 / 8 , c ) 3 / 5 , d ) 4 / 7 , e ) 5 / 8
Rationale: "since , all possible hypothesis regarding the colour of the balls are equally likely , therefore these could be 3 white balls , initially in the bag . ∴ required probability = 1 / 4 [ 1 + 3 / 4 + 1 / 2 + 1 / 4 ] = 1 / 4 [ ( 4 + 3 + 2 + 1 ) / 4 ] = 5 / 8 b"
Answer: b
Question (general): find a sum for 1 st 8 prime number ' s ?
Options: a ) 25 , b ) 28 , c ) 30 , d ) 77 , e ) 36
Rationale: "required sum = ( 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 ) = 77 note : 1 is not a prime number option d"
Answer: d
Question (general): if 1,000 microns = 1 decimeter , and 1 , 000,000 angstroms = 1 decimeter , how many angstroms equal 1 micron ?
Options: a ) 100 , b ) 10 , c ) 1,000 , d ) 10,000 , e ) 100,000
Rationale: "given that 1,000 microns = 1 decimeter = 1 , 000,000 angstroms so , 1 micron = 1 , 000,000 / 1,000 = 1,000 answer : c"
Answer: c
Question (physics): a flagpole 18 meters high casts a shadow of length 45 meters . if a building under similar conditions casts a shadow of length 50 meters , what is the height of the building ( in meters ) ?
Options: a ) 16 , b ) 20 , c ) 24 , d ) 28 , e ) 32
Rationale: "the height : length ratio will be equal in both cases . 18 / 45 = x / 50 x = 20 the answer is b ."
Answer: b
Question (general): if 7 ^ ( x - y ) = 343 and 7 ^ ( x + y ) = 16807 , what is the value of x ?
Options: a ) 3 , b ) 4 , c ) 2 , d ) 1 , e ) 7
Rationale: 7 ^ ( x - y ) = 343 = 7 ^ 3 = > x - y = 3 - - - - - - - - - - - - - - - - - - - - - - - - - - - ( equation 1 ) 7 ^ ( x + y ) = 16807 = 7 ^ 5 = > x + y = 5 - - - - - - - - - - - - - - - - - - - - - - - - - - - ( equation 2 ) ( equation 1 ) + ( equation 2 ) = > 2 x = 3 + 5 = 8 = > x = 8 / 2 = 4 answer is b
Answer: b
Question (gain): 242 students represent x percent of the boys at a school . if the boys at the school make up 50 % of the total school population of x students , what is x ?
Options: a ) 120 , b ) 150 , c ) 180 , d ) 200 , e ) 220
Rationale: "let b be the number of boys in the school . 242 = xb / 100 b = 0.5 x 24200 = 0.5 x ^ 2 x ^ 2 = 48400 x = 220 the answer is e ."
Answer: e
Question (physics): a certain number of workers can do a work in 75 days . if there were 10 workers more it could be finished in 10 days less . how many workers are there ?
Options: a ) 65 , b ) 30 , c ) 28 , d ) 24 , e ) 32
Rationale: "number of workers = 10 * ( 75 - 10 ) / 10 = 65 answer is a"
Answer: a
Question (general): a man spends 2 / 5 of his salary on house rent , 3 / 10 of his salary on food and 1 / 8 of his salary on conveyance . if he has $ 1400 left with him , find his expenditure on food and conveyance .
Options: a ) $ 8600 , b ) $ 2400 , c ) $ 1000 , d ) $ 3000 , e ) $ 3400
Rationale: remaining part of salary left = 1 - ( 2 / 5 + 3 / 10 + 1 / 8 ) = 1 - ( 33 / 40 ) = 7 / 40 let the monthly salary be $ x then , 7 / 40 of x = $ 1400 x = ( 1400 * 40 / 7 ) = $ 8600 expenditure on food = $ ( 3 / 10 * 800 ) = $ 2400 expenditure on conveyance = $ ( 1 / 8 * 8000 ) = $ 1000 $ 2400 + $ 1000 = $ 3400 so the answer is option e ) $ 3400
Answer: e
Question (gain): some of 15 % - intensity red paint is replaced with 25 % solution of red paint such that the new paint intensity is 30 % . what fraction of the original paint was replaced ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 3 / 2 , e ) 3 / 5
Rationale: "let total paint = 1 let amount replaced = x 15 ( 1 - x ) + 25 x = 30 x = 3 / 2 answer : d"
Answer: d
Question (gain): find the compound interest on $ 1200 for 2 years at 20 % p . a . if ci is component yearly ?
Options: a ) $ 120 , b ) $ 150 , c ) $ 548 , d ) $ 250 , e ) $ 300
Rationale: a = p ( 1 + r / 100 ) ^ t = 1200 ( 1 + 20 / 100 ) ^ 2 = $ 1728 ci = $ 548 answer is c
Answer: c
Question (physics): it takes avery 2 hours to build a brick wall while tom can do it in 4 hour . if the two start working together and after an hour avery leaves , how much time will it take tom to complete the wall on his own ?
Options: a ) 70 , b ) 20 , c ) 50 , d ) 60 , e ) 30
Rationale: avery takes 2 hours tom takes 4 hours efficiency of avery is 1 / 2 units / hr efficiency of tom is 1 / 4 units / hr combined efficiency of tom and avery is 1 / 2 + 1 / 4 = 3 / 4 units / hr since they worked for 1 hour they completed 3 / 4 units of work and 1 / 4 units of work is left which is to be completed by tom ( since avery left ) so time taken by tom to complete the remaining work will be 1 / 4 / 1 / 4 hours = > 1 * 60 = 60 minutes . . . answer will be ( d )
Answer: d
Question (general): how many of the integers between 25 and 45 are even ?
Options: a ) 21 , b ) 20 , c ) 11 , d ) 10 , e ) 9
Rationale: number start between 25 to 45 is 20 numbers half of them is even . . which is 10 answer : d
Answer: d
Question (general): bill made a profit of 10 % by selling a product . if he had purchased that product for 10 % less and sold it at a profit of 30 % , he would have received $ 28 more . what was his original selling price ?
Options: a ) $ 200 , b ) $ 260 , c ) $ 320 , d ) $ 380 , e ) $ 440
Rationale: "let p be the original purchase price of the product . bill originally sold the product for 1.1 * p . in the second scenario , the purchase price is 0.9 * p . a 30 % profit means the selling price would be 1.3 * 0.9 * p = 1.17 * p thus , according to the information in the question , 1.17 p - 1.1 p = 28 0.07 = 28 p = 400 the original selling price was 400 * 1.1 = 440 . the correct answer is e ."
Answer: e
Question (other): if 0.4 of a number is equal to 0.07 of another number , the ratio of the numbers i
Options: a ) 2 : 3 , b ) 7 : 40 , c ) 3 : 20 , d ) 20 : 3 , e ) none
Rationale: "sol . 0.4 a = 0.08 b â ‡ ” a / b = 0.07 / 0.40 = 7 / 40 . â ˆ ´ a : b = 7 : 40 . answer b"
Answer: b
Question (general): sixty 5 percent of a number is 21 less than 4 fifth of that number . what is the number
Options: a ) 140 , b ) 165 , c ) 150 , d ) 142 , e ) 174
Rationale: let the number be x . then , 4 * x / 5 – ( 65 % of x ) = 21 4 x / 5 – 65 x / 100 = 21 5 x = 2100 x = 140 . answer a 140
Answer: a
Question (geometry): a wooden cube whose edge length is 7 inches is composed of smaller cubes with edge lengths of one inch . the outside surface of the large cube is painted red and then it is split up into its smaller cubes . if one cube is randomly selected from the small cubes , what is the probability that the cube will have at least one red face ?
Options: a ) 59.8 % , b ) 63.6 % , c ) 67.2 % , d ) 70.5 % , e ) 73.6 %
Rationale: "there are a total of 7 * 7 * 7 = 343 cubes . all the exterior cubes will have at least one face painted red . the interior is formed by 5 * 5 * 5 = 125 cubes . the number of cubes with at least one side painted red is 343 - 125 = 218 cubes the probability that a cube has at least one side painted red is 218 / 343 which is about 63.6 % the answer is b ."
Answer: b
Question (general): two numbers a and b are such that the sum of 7 % of a and 4 % of b is two - third of the sum of 6 % of a and 8 % of b . find the ratio of a : b .
Options: a ) 2 : 1 , b ) 1 : 2 , c ) 4 : 9 , d ) 1 : 1 , e ) 3 : 2
Rationale: "explanation : 7 % of a + 4 % of b = 2 / 3 ( 6 % of a + 8 % of b ) 7 a / 100 + 4 b / 100 = 2 / 3 ( 6 a / 100 + 8 b / 100 ) ⇒ 7 a + 4 b = 2 / 3 ( 6 a + 8 b ) ⇒ 21 a + 12 b = 12 a + 16 b ⇒ 9 a = 4 b ⇒ ab = 4 / 9 ⇒ a : b = 4 : 9 answer : option c"
Answer: c
Question (general): the average weight of a class is x pounds . when a new student weighing 50 pounds joins the class , the average decreases by 1 pound . in a few months the student ’ s weight increases to 110 pounds and the average weight of the class becomes x + 4 pounds . none of the other students ’ weights changed . what is the value of x ?
Options: a ) 85 , b ) 86 , c ) 88 , d ) 90 , e ) 92
Rationale: "when the student weighs 80 pounds the average weight is x - 1 pounds ; when the student weighs 110 pounds the average weight is x + 4 pounds . so , the increase in total weight of 110 - 80 = 30 pounds corresponds to the increase in average weight of ( x + 4 ) - ( x - 1 ) = 5 pounds , which means that there are 30 / 5 = 6 students ( including the new one ) . so , initially there were 5 student . total weight = 5 x + 80 = 6 ( x - 1 ) - - > x = 85 pounds . answer : a ."
Answer: a
Question (physics): the speed of a car is 140 km in the first hour and 40 km in the second hour . what is the average speed of the car ?
Options: a ) 72 kmph , b ) 75 kmph , c ) 30 kmph , d ) 90 kmph , e ) 82 kmph
Rationale: "s = ( 140 + 40 ) / 2 = 90 kmph answer : d"
Answer: d
Question (physics): a train of 50 carriages , each of 60 meters length , when an engine also of 60 meters length is running at a speed of 60 kmph . in what time will the train cross a bridge 1.5 km long ?
Options: a ) 6 , b ) 3 , c ) 4 , d ) 4.5 , e ) 2
Rationale: "d = 50 * 60 + 1500 = 3000 m t = 4500 / 60 * 18 / 5 = 270 sec = 4.5 mins answer : d"
Answer: d
Question (geometry): how much space , in cubic units , is left vacant when maximum number of 5 x 5 x 5 cubes are fitted in a rectangular box measuring 10 x 15 x 18 ?
Options: a ) 50 , b ) 150 , c ) 250 , d ) 350 , e ) 450
Rationale: "no of cubes that can be accommodated in box = ( 10 * 15 * 18 ) / ( 5 * 5 * 5 ) 15 * 10 in numerator can be perfectly divided by 5 * 5 in denominator . side with length 18 ca n ' t be perfectly divided by 5 and hence is the limiting factor . closet multiple of 5 less that 18 is 15 . so vacant area in cube = = 15 * 10 * ( 18 - 15 ) = 15 * 10 * 3 = 450 ans - e"
Answer: e
Question (physics): 12 buckets of water fill a tank when the capacity of each bucket is 49 litres . how many buckets will be needed to fill the same tank , if the capacity of each bucket is 7 litres ?
Options: a ) 39 , b ) 84 , c ) 80 , d ) 82 , e ) 86
Rationale: capacity of the tank = ( 12 ã — 49 ) litre number of buckets required of capacity of each bucket is 17 litre = 12 ã — 49 / 7 = 12 ã — 7 = 84 answer is b
Answer: b
Question (general): if n is an integer and 101 n ^ 2 is less than or equal to 8100 , what is the greatest possible value of n ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "101 * n ^ 2 < = 8100 n ^ 2 < = 8100 / 101 which will be less than 81 since 8100 / 100 = 81 which is the square of 9 next closest value of n where n ^ 2 < = 81 is 8 ans b"
Answer: b
Question (physics): if the perimeter of a rectangular garden is 950 m , its length when its breadth is 100 m is ?
Options: a ) 338 m , b ) 778 m , c ) 375 m , d ) 276 m , e ) 971 m
Rationale: "2 ( l + 100 ) = 950 = > l = 375 m answer : c"
Answer: c
Question (general): a certain league has two divisions . the respective divisions had 11 and 13 teams qualify for the playoffs . each division held its own double - elimination tournament - - where a team is eliminated from the tournament upon losing two games - - in order to determine its champion . the 4 division champions then played in a single - elimination tournament - - where a team is eliminated upon losing one game - - in order to determine the overall league champion . assuming that there were no ties and no forfeits , what is the maximum number of games that could have been played in order to determine the overall league champion ?
Options: a ) 41 , b ) 42 , c ) 45 , d ) 47 , e ) 49
Rationale: overall , there can be 47 minuses . tus , it is d .
Answer: d
Question (other): if the ratio of a to b is 5 to 3 and the ratio of b to c is 1 to 5 , what is the ratio of a to c ?
Options: a ) 4 / 15 , b ) 1 / 3 , c ) 2 / 5 , d ) 4 / 5 , e ) 7 / 6
Rationale: "a : b = 5 : 3 - - 1 b : c = 1 : 5 = > b : c = 3 : 15 - - 2 from 1 and 2 , we get a : c = 4 : 15 answer b"
Answer: b
Question (physics): it takes printer a 4 more minutes more than printer b to print 40 pages . working together , the two printers can print 50 pages in 6 minutes . how long will it take printer a to print 100 pages ?
Options: a ) 12 , b ) 18 , c ) 20 , d ) 24 , e ) 30
Rationale: "if it takes 4 more minutes for a to print 40 pages than it takes b , it takes 5 more minutes for a to print 50 pages than it takes b . thus if b is the number of minutes than b takes to print 50 pages , we can write : 1 / b + 1 / ( b + 5 ) = 1 / 6 ( since in 1 minute , they print 1 / 6 th of the 50 page job ) 6 ( 2 b + 5 ) = b ( b + 5 ) b ^ 2 - 7 b - 30 = 0 ( b - 10 ) ( b + 3 ) = 0 b = 10 thus it takes a 15 minutes to print 50 pages and 15 * 100 / 50 = 30 minutes to print 100 pages ( answer e )"
Answer: e
Question (general): what does the hexa number e 78 in radix 7 .
Options: a ) 12455 , b ) 14153 , c ) 14256 , d ) 13541 , e ) 14541
Rationale: conversion of hexa decimal to decimal ( e 78 ) = ( 8 * 16 ^ 0 ) + ( 7 * 16 ^ 1 ) + ( 14 * 16 ^ 2 ) = 8 + 112 + 3584 = 3704 conversion of decimal to radix 7 3704 / 7 : reminder : 1 and dividend : 529 529 / 7 : reminder : 4 and dividend : 75 75 / 7 : reminder : 5 and dividend : 10 10 / 7 : reminder : 3 and dividend : 1 1 / 7 : reminder 1 then finally result is : 13541 answer : d
Answer: d
Question (general): rs . 1170 is divided so that 4 times the first share , thrice the 2 nd share and twice the third share amount to the same . what is the value of the third share ?
Options: a ) rs . 720 , b ) rs . 920 , c ) rs . 537 , d ) rs . 540 , e ) rs . 637
Rationale: a + b + c = 1170 4 a = 3 b = 2 c = x a : b : c = 1 / 4 : 1 / 3 : 1 / 2 = 3 : 4 : 6 6 / 13 * 1170 = rs . 540 answer : d
Answer: d
Question (general): how much is 55 % of 40 is greater than 4 / 5 of 25 ?
Options: a ) 29 , b ) 776 , c ) 2 , d ) 12 , e ) 99
Rationale: "( 55 / 100 ) * 40 – ( 4 / 5 ) * 25 22 - 20 = 2 answer : c"
Answer: c
Question (general): find large number from below question the difference of two numbers is 1515 . on dividing the larger number by the smaller , we get 16 as quotient and the 15 as remainder
Options: a ) 1209 , b ) 1615 , c ) 1245 , d ) 1300 , e ) 1635
Rationale: "let the smaller number be x . then larger number = ( x + 1515 ) . x + 1515 = 16 x + 15 15 x = 1500 x = 100 large number = 100 + 1515 = 1615 answer : b"
Answer: b
Question (gain): the price of a t . v . set worth rs . 60000 is to be paid in 20 installments of rs . 1000 each . if the rate of interest be 6 % per annum , and the first installment be paid at the time of purchase , then the value of the last installment covering the interest as well will be ?
Options: a ) 22678 , b ) 59000 , c ) 26788 , d ) 19000 , e ) 26711
Rationale: "money paid in cash = rs . 1000 balance payment = ( 60000 - 1000 ) = rs . 59000 answer : b"
Answer: b
Question (physics): p and q can complete a work in 15 days and 10 days respectively . they started the work together and then q left after 2 days . p alone completed the remaining work . the work was finished in - - - days .
Options: a ) 12 , b ) 16 , c ) 20 , d ) 24 , e ) 28
Rationale: "explanation : work done by p in 1 day = 1 / 15 work done by q in 1 day = 1 / 10 work done by p and q in 1 day = 1 / 15 + 1 / 10 = 1 / 6 work done by p and q in 2 days = 2 × ( 1 / 6 ) = 1 / 3 remaining work = 1 – 1 / 3 = 2 / 3 time taken by p to complete the remaining work 2 / 3 = ( 2 / 3 ) / ( 1 / 15 ) = 10 days total time taken = 2 + 10 = 12 days answer : option a"
Answer: a
Question (geometry): a rectangular grass field is 65 m * 55 m , it has a path of 2.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 2 per sq m ?
Options: a ) 1350 , b ) 1971 , c ) 9676 , d ) 1679 , e ) 1250
Rationale: "area = ( l + b + 2 d ) 2 d = ( 65 + 55 + 2.5 * 2 ) 2 * 2.5 = > 625 625 * 2 = rs . 1250 answer : e"
Answer: e
Question (gain): how many liters of water must be evaporated from 50 liters of a 3 percent sugar solution to get a 5 percent sugar solution ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 10 , e ) 20
Rationale: "3 % sugar solution means that currently there are 1.5 liters of sugar and this amount must be 5 % of a reduced final amount ( 50 - x ) 1.5 = 0.05 * ( 50 - x ) 0.05 x = 1 x = 20 answer e"
Answer: e
Question (physics): the mall charges 40 cents for the first hour of parking and $ 3 for each additional hour until the customer reaches 4 hours , after that the parking fee is $ 2 per hour . if mr . park parked his car in the mall for 7 hours and 30 minutes , how much is he going to pay ?
Options: a ) $ 6.8 , b ) $ 12 . , c ) $ 13 . , d ) $ 14.5 . , e ) $ 15 .
Rationale: "0.40 + 2 * 2 + 1 * 2 + 0.40 = $ 6.8 answer : $ 6.8"
Answer: a
Question (general): david spends $ 350 buying his favorite dolls . if he buys only small lemonhead dolls , which are $ 2 cheaper than the large lemonhead dolls , he could buy 20 more dolls than if he were to buy only large lemonhead dolls . how much does a large lemonhead doll cost ?
Options: a ) $ 5 , b ) $ 7 , c ) $ 6 , d ) $ 8 , e ) $ 9
Rationale: if large doll costs $ 5 , then he can buy 350 / 5 = 70 large dolls and 350 / 3 = 116 small dolls . difference is more than 20 . discard . if large doll costs $ 7 , then he can buy 350 / 7 = 50 large dolls and 350 / 5 = 70 small dolls . difference is 20 , which is we wanted . answer b .
Answer: b
Question (general): ratio of ages of 3 persons is 4 : 7 : 9 , 8 years ago , the sum of their ages was 56 . find their present ages
Options: a ) 16 , 35,36 , b ) 12 , 28,36 , c ) 16 , 28,27 , d ) 16 , 28,36 , e ) none of these
Rationale: explanation : let the present ages are 4 x , 7 x , 9 x . = > ( 4 x - 8 ) + ( 7 x - 8 ) + ( 9 x - 8 ) = 56 = > 20 x = 80 = > x = 4 so their present ages are : 16 , 28,36 answer : option d
Answer: d