Cheukting/mathqa huggingface dataset:
Question (general): the average monthly income of p and q is rs . 6050 . the average monthly income of q and r is rs . 7050 and the average monthly income of p and r is rs . 8000 . the monthly income of p + q + r is :
Options: a ) 41100 , b ) 42000 , c ) 21100 , d ) 42200 , e ) 21000
Rationale: "explanation : let p , q and r represent their respective monthly incomes . then , we have : p + q = ( 6050 x 2 ) = 12100 . . . . ( i ) q + r = ( 7050 x 2 ) = 14100 . . . . ( ii ) p + r = ( 8000 x 2 ) = 16000 . . . . ( iii ) adding ( i ) , ( ii ) and ( iii ) , we get : 2 ( p + q + r ) = 42200 or p + q + r = 21100 . . . . ( iv ) ( p + q + r ) ' s monthly income = rs . 21100 . answer : c"
Answer: c
Question (physics): how many 4 digit numbers are there , if it is known that the first digit is even , the second is odd , the third is prime , the fourth ( units digit ) is divisible by 3 , and the digit 2 can be used only once ?
Options: a ) 20 , b ) 150 , c ) 225 , d ) 300 , e ) 320
Rationale: "4 options for the first digit : 2 , 4 , 6 , 8 ; 5 options for the second digit : 1 , 3 , 5 , 7 , 9 ; 4 options for the third digit : 2 , 3 , 5 , 7 ; 4 options for the fourth digit : 0 , 3 , 6 , 9 . four digit # possible without the restriction ( about the digit 2 ) : 4 * 5 * 4 * 4 = 320 numbers with two 2 - s , 2 x 2 x 1 * 5 * 1 * 4 = 20 . thus there are 320 - 20 = 300 such numbers . answer : d ."
Answer: d
Question (physics): in one hour , a boat goes 9 km along the stream and 5 km against the stream . the speed of the boat in still water ( in km / hr ) is :
Options: a ) 2 , b ) 4 , c ) 7 , d ) 12 , e ) 15
Rationale: "sol . speed in still water = 1 / 2 ( 9 + 5 ) kmph = 7 kmph . answer c"
Answer: c
Question (physics): a 70 cm long wire is to be cut into two pieces so that one piece will be 2 / 3 th of the other , how many centimeters will the shorter piece be ?
Options: a ) 35 , b ) 20 , c ) 28 , d ) 36 , e ) 30
Rationale: "1 : 2 / 3 = 3 : 2 2 / 5 * 70 = 28 answer : c"
Answer: c
Question (general): 165 liters of a mixture of milk and water contains in the ratio 3 : 2 . how much water should now be added so that the ratio of milk and water becomes 3 : 4 ?
Options: a ) 66 liters , b ) 32 liters , c ) 41 liters , d ) 50 liters , e ) 34 liters
Rationale: "milk = 3 / 5 * 165 = 99 liters water = 66 liters 99 : ( 66 + p ) = 3 : 4 198 + 3 p = 396 = > p = 66 66 liters of water are to be added for the ratio become 3 : 4 . answer : a"
Answer: a
Question (gain): raman mixed 54 kg of butter at rs . 150 per kg with 36 kg butter at the rate of rs . 125 per kg . at what price per kg should he sell the mixture to make a profit of 40 % in the transaction ?
Options: a ) 129 , b ) 287 , c ) 196 , d ) 188 , e ) 112
Rationale: "explanation : cp per kg of mixture = [ 54 ( 150 ) + 36 ( 125 ) ] / ( 54 + 36 ) = rs . 140 sp = cp [ ( 100 + profit % ) / 100 ] = 140 * [ ( 100 + 40 ) / 100 ] = rs . 196 . answer : c"
Answer: c
Question (general): average of money that group of 4 friends pay for rent each month is $ 800 . after one persons rent is increased by 25 % the new mean is $ 850 . what was original rent of friend whose rent is increased ?
Options: a ) 800 , b ) 900 , c ) 1000 , d ) 1100 , e ) 1200
Rationale: "0.25 x = 4 ( 850 - 800 ) 0.25 x = 200 x = 800 answer a"
Answer: a
Question (gain): a person borrows rs . 5000 for 2 years at 4 % p . a . simple interest . he immediately lends it to another person at 5 % p . a for 2 years . find his gain in the transaction per year .
Options: a ) 50 , b ) 150 , c ) 225 , d ) 112.5 , e ) 212.5
Rationale: "explanation : the person borrows rs . 5000 for 2 years at 4 % p . a . simple interest simple interest that he needs to pay = prt / 100 = 5000 × 4 × 2 / 100 = 400 he also lends it at 5 % p . a for 2 years simple interest that he gets = prt / 100 = 5000 × 5 × 2 / 100 = 500 his overall gain in 2 years = rs . 500 - rs . 400 = rs . 100 his overall gain in 1 year = 100 / 2 = rs . 50 answer : option a"
Answer: a
Question (gain): a chemist mixes one liter of pure water with x liters of a 30 % salt solution , and the resulting mixture is a 15 % salt solution . what is the value of x ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 1 , e ) 3
Rationale: "concentration of salt in pure solution = 0 concentration of salt in salt solution = 30 % concentration of salt in the mixed solution = 15 % the pure solution and the salt solution is mixed in the ratio of - - > ( 30 - 15 ) / ( 15 - 0 ) = 1 / 1 1 / x = 1 / 1 x = 1 answer : d"
Answer: d
Question (geometry): the surface of a cube is 96 sq cm . find its volume ?
Options: a ) 8 cc
b ) 9 cc
c ) 2 cc
d ) 4 cc
e ) 64 cc
Rationale: 6 a 2 = 96 = 6 * 16 a = 4 = > a 3 = 64 cc answer : e
Answer: e
Question (geometry): the largest four digit number which is a perfect cube , is :
Options: a ) 7000 , b ) 8000 , c ) 9261 , d ) 9999 , e ) none of these
Rationale: "explanation : 21 * 21 * 21 = 9261 option c"
Answer: c
Question (geometry): the angle between two hands at 3.45 is
Options: a ) 110 degree , b ) 115 degree , c ) 112 1 / 2 degree , d ) 117 degree , e ) 157 1 / 2 degree
Rationale: "theta degree = 11 / 2 m - 30 h = 11 / 2 ( 45 ) - 30 ( 3 ) = 247.5 - 90 = 157.5 or 157 1 / 2 degree answer : e"
Answer: e
Question (physics): pipe a and pipe b fill water into a tank of capacity 2000 litres , at a rate of 200 l / min and 50 l / min . pipe c drains at a rate of 25 l / min . pipe a is open for 1 min and closed , then pipe b is open for 2 min and closed . further the pipe c is opened and drained for another 2 min . this process is repeated until the tank is filled . how long will it take to fill the tank ?
Options: a ) 14 min , b ) 18 min , c ) 25 min , d ) 32 min , e ) 40 min
Rationale: "tank capacity : 2000 l , 1 st - 200 l / min for 1 min , volume filled : 200 l 2 nd - 100 l / min for 2 min , volume filled : 100 l 3 rd ( water draining ) : 25 l / min * 2 : 50 l total : ( 200 + 100 ) - 50 = 250 l filled for 1 cycle number of 250 in 2000 l tank : 2000 / 250 = 8 time taken to fill : 8 * total time = 8 * 5 = 40 ( option e )"
Answer: e
Question (geometry): a wooden cube whose edge length is 9 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 ) 52.9 % , b ) 55.4 % , c ) 58.3 % , d ) 61.7 % , e ) 64.5 %
Rationale: "there are a total of 9 * 9 * 9 = 729 cubes . all the exterior cubes will have at least one face painted red . the interior is formed by 7 * 7 * 7 = 343 cubes . the number of cubes with at least one side painted red is 729 - 343 = 386 cubes the probability that a cube has at least one side painted red is 386 / 729 which is about 52.9 % the answer is a ."
Answer: a
Question (physics): the sector of a circle has radius of 21 cm and central angle 110 o . find its perimeter ?
Options: a ) 91.5 , b ) 91.4 , c ) 91.7 , d ) 82.3 , e ) 91.1
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 110 / 360 * 2 * 22 / 7 * 21 ) + 2 ( 21 ) = 40.3 + 42 = 82.3 cm answer : d"
Answer: d
Question (general): how many positive integers less than 25 are prime numbers , odd multiples of 5 , or the sum of a positive multiple of 2 and a positive multiple of 4 ?
Options: a ) 27 , b ) 25 , c ) 24 , d ) 22 , e ) 20
Rationale: "9 prime numbers less than 28 : { 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 } 2 odd multiples of 5 : { 5 , 15 } 10 numbers which are the sum of a positive multiple of 2 and a positive multiple of 4 : { 6 , 8 , 10 , 12 , 14 , 16 , 18 , 20 , 22 , 24 } notice , that 5 is in two sets , thus total # of integers satisfying the given conditions is 9 + 2 + 10 - 1 = 20 . answer : e ."
Answer: e
Question (gain): in the first 10 overs of a cricket game , the run rate was only 3.2 . what should be the rate in the remaining 40 overs to reach the target of 282 runs ?
Options: a ) 6.25 , b ) 6.27 , c ) 6.23 , d ) 6.29 , e ) 6.39
Rationale: "required run rate = [ 282 - ( 3.2 * 10 ) ] / 40 = 250 / 40 = 6.25 ' answer : a"
Answer: a
Question (general): company m produces two kinds of stereos : basic and deluxe . of the stereos produced by company m last month , 2 / 3 were basic and the rest were deluxe . if it takes 7 / 5 as many hours to produce a deluxe stereo as it does to produce a basic stereo , then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos ?
Options: a ) 5 / 22 , b ) 4 / 22 , c ) 3 / 22 , d ) 9 / 22 , e ) 7 / 22
Rationale: # of basic stereos was 3 / 4 of total and # of deluxe stereos was 1 / 4 of total , let ' s assume total = 16 , then basic = 12 and deluxe = 4 . now , if time needed to produce one deluxe stereo is 1 unit than time needed to produce one basic stereo would be 7 / 5 units . total time for basic would be 12 * 1 = 12 and total time for deluxe would be 4 * 7 / 5 = 28 / 5 - - > total time for both of them would be 12 + 28 / 5 = 88 / 5 - - > deluxe / total = 28 / 5 / 88 / 5 = 28 / 88 = 7 / 22 e
Answer: e
Question (geometry): rectangular tile each of size 80 cm by 40 cm must be laid horizontally on a rectangular floor of size 130 cm by 230 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 ) 6 , b ) 2 , c ) 8 , d ) 9 , e ) 7
Rationale: "area of tile = 80 * 40 = 3200 area of floor = 130 * 230 = 29900 no of tiles = 29900 / 3200 = 9.34 so , the no of tile = 9 answer : d"
Answer: d
Question (general): find large number from below question the difference of two numbers is 1395 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder
Options: a ) 1235 , b ) 1345 , c ) 1678 , d ) 1767 , e ) 1671
Rationale: "let the smaller number be x . then larger number = ( x + 1395 ) . x + 1395 = 6 x + 15 5 x = 1380 x = 276 large number = 276 + 1395 = 1671 e"
Answer: e
Question (general): find the principle on a certain sum of money at 5 % per annum for 3 1 / 5 years if the amount being rs . 1740 ?
Options: a ) rs . 1000 , b ) rs . 1550 , c ) rs . 1510 , d ) rs . 1500 , e ) none of these
Rationale: "explanation : 1740 = p [ 1 + ( 5 * 16 / 5 ) / 100 ] p = 1500 answer : option d"
Answer: d
Question (general): the average of temperatures at noontime from monday to friday is 50 ; the lowest one is 45 , what is the possible maximum range of the temperatures ?
Options: a ) 20 , b ) 25 , c ) 40 , d ) 45 , e ) 75
Rationale: "average = 50 , sum of temperatures = 50 * 5 = 250 as the min temperature is 45 , max would be 250 - 4 * 45 = 70 - - > the range = 70 ( max ) - 45 ( min ) = 25 answer : b ."
Answer: b
Question (general): a grocer has a sale of rs . 800 , rs . 900 , rs . 1000 , rs . 700 and rs . 800 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 850 ?
Options: a ) s . 440 , b ) s . 850 , c ) s . 450 , d ) s . 900 , e ) s . 950
Rationale: "total sale for 5 months = rs . ( 800 + 900 + 1000 + 700 + 800 ) = rs . 4200 required sale = rs . [ ( 850 x 6 ) - 4200 ] = rs . ( 5100 - 4200 ) = rs . 900 . option d"
Answer: d
Question (physics): two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 18 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ?
Options: a ) 565 , b ) 444 , c ) 676 , d ) 767 , e ) 408
Rationale: "1 h - - - - - 2 ? - - - - - - 60 12 h rs = 16 + 18 = 34 t = 12 d = 34 * 12 = 408 answer : e"
Answer: e
Question (physics): a can finish a piece of work in 5 days . b can do it in 16 days . they work together for two days and then a goes away . in how many days will b finish the work ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "2 / 4 + ( 2 + x ) / 16 = 1 = > x = 6 days answer : c"
Answer: c
Question (other): what is the greatest positive integer n such that 3 ^ n is a factor of 54 ^ 100 ?
Options: a ) 100 , b ) 200 , c ) 300 , d ) 600 , e ) 900
Rationale: "54 = 3 ^ 3 * 2 . 54 ^ 100 = 3 ^ 300 * 2 ^ 100 the answer is c ."
Answer: c
Question (general): when a random experiment is conducted , the probability that event a occurs is 1 / 5 . if the random experiment is conducted 5 independent times , what is the probability that event a occurs exactly twice ?
Options: a ) 36 / 625 , b ) 48 / 625 , c ) 64 / 625 , d ) 98 / 625 , e ) 128 / 625
Rationale: "one case is : 1 / 5 * 1 / 5 * 4 / 5 * 4 / 5 * 4 / 5 = 64 / 3125 the total number of possible cases is 5 c 2 = 10 p ( event a occurs exactly twice ) = 10 * ( 64 / 3125 ) = 128 / 625 the answer is e ."
Answer: e
Question (physics): in a lake , there is a patch of lily pads . every day , the patch doubles in size . if it takes 48 days for the patch to cover the entire lake , how long would it take for the patch to cover half of the lake ?
Options: a ) 45 , b ) 56 , c ) 47 , d ) 57 , e ) 49
Rationale: "explanation : with all the talk of doubling and halves , your brain jumps to the conclusion that to solve the problem of when the lily patch covers half the lake , all you have to do is divide the number of days it took to fill the lake ( 48 ) in half . it ' s understandable but wrong . the problem says that the patch doubles in size every day , which means that on any day , the lily patch was half the size the day before . so if the patch reaches the entire size of the lake on the 48 th day , it means the lily pad was half the size of the lake on day 47 . correct answer is c ) 47"
Answer: c
Question (general): the least common multiple of positive integer d and 3 - digit integer n is 690 . if n is not divisible by 3 and d is not divisible by 2 , what is the value of n ?
Options: a ) 115 , b ) 230 , c ) 460 , d ) 575 , e ) 690
Rationale: the lcm of n and d is 690 = 2 * 3 * 5 * 23 . d is not divisible by 2 , thus 2 goes to n n is not divisible by 3 , thus 3 goes to d . from above : n must be divisible by 2 and not divisible by 3 : n = 2 * . . . in order n to be a 3 - digit number it must take all other primes too : n = 2 * 5 * 23 = 230 . answer : b .
Answer: b
Question (general): in a renowned city , the average birth rate is 7 people every two seconds and the death rate is 3 people every two seconds . estimate the size of the population net increase that occurs in one day .
Options: a ) 172,700 , b ) 172,800 , c ) 172,900 , d ) 173,000 , e ) 173,100
Rationale: "this question can be modified so that the birth rate is given every m seconds and the death rate is given every n seconds . for this particular question : increase in the population every 2 seconds = 7 - 3 = 4 people . total 2 second interval in a day = 24 * 60 * 60 / 2 = 43,200 population increase = 43,200 * 4 = 172,800 . hence b ."
Answer: b
Question (general): two trains of equal are running on parallel lines in the same direction at 46 km / hr and 36 km / hr . the faster train passes the slower train in 54 sec . the length of each train is ?
Options: a ) 50 , b ) 26 , c ) 75 , d ) 28 , e ) 21
Rationale: "let the length of each train be x m . then , distance covered = 2 x m . relative speed = 46 - 36 = 10 km / hr . = 10 * 5 / 18 = 25 / 9 m / sec . 2 x / 54 = 25 / 9 = > x = 75 . answer : c"
Answer: c
Question (general): a number is doubled and 8 is added . if the resultant is trebled , it becomes 84 . what is that number ?
Options: a ) 10 , b ) 6 , c ) 8 , d ) none of these , e ) can not be determined
Rationale: "solution let the number be x . then , 3 ( 2 x + 8 ) ‹ = › 84 ‹ = › 2 x + 8 = 28 ‹ = › 2 x = 20 x = 10 . answer a"
Answer: a
Question (physics): a train 100 m in length crosses a telegraph post in 12 seconds . the speed of the train is ?
Options: a ) 16 kmph , b ) 30 kmph , c ) 54 kmph , d ) 18 kmph , e ) 19 kmph
Rationale: "s = 100 / 12 * 18 / 5 = 30 kmph answer : b"
Answer: b
Question (gain): by selling a book for 250 , 20 % profit was earned . what is the cost price of the book ?
Options: a ) a ) 215 , b ) b ) 208 , c ) c ) 230 , d ) d ) 235 , e ) e ) 240
Rationale: "sp = 120 % of cp ; : . cp = 250 × 100 / 120 = 208 option ' b '"
Answer: b
Question (other): 50 liters of a mixture contains milk and water in the ratio 3 : 2 . if 5 liters of this mixture be replaced by 5 liters of milk , the ratio of milk to water in the new mixture would be ?
Options: a ) 6 : 5 , b ) 6 : 2 , c ) 6 : 4 , d ) 7 : 4 , e ) 7 : 2
Rationale: "quantity of milk in 50 liters if mix = 50 * 3 / 5 = 30 liters quantity of milk in 55 liters of new mix = 30 + 5 = 35 liters quantity of water in it = 55 - 35 = 20 liters ratio of milk and water in new mix = 35 : 20 = 7 : 4 answer is d"
Answer: d
Question (geometry): the area of a square garden is q square feet and the perimeter is p feet . if q = 2 p + 48 , what is the perimeter of the garden in feet ?
Options: a ) 36 , b ) 40 , c ) 44 , d ) 48 , e ) 52
Rationale: "let x be the length of one side of the square garden . x ^ 2 = 8 x + 48 x ^ 2 - 8 x - 48 = 0 ( x - 12 ) ( x + 4 ) = 0 x = 12 , - 4 p = 4 ( 12 ) = 48 the answer is d ."
Answer: d
Question (general): the average of 10 numbers is calculated as 5 . it is discovered later on that while calculating the average , one number namely 36 was wrongly read as 26 . the correct average is ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "10 * 5 + 36 – 26 = 60 / 10 = 6 answer : e"
Answer: e
Question (general): if ( 10 ^ 4 * 3.456789 ) ^ 14 is written as a single term , how many digits would be to the right of the decimal place ?
Options: a ) 9 , b ) 14 , c ) 21 , d ) 28 , e ) 42
Rationale: 3.456789 ^ 14 has 6 * 14 = 84 decimal places . 10 ^ 56 moves the decimal place to the right 56 places . ( 10 ^ 4 * 3.456789 ) ^ 14 has 84 - 56 = 28 digits after the decimal point . the answer is d .
Answer: d
Question (other): find the compound ratio of ( 2 : 3 ) , ( 6 : 11 ) and ( 11 : 5 ) is
Options: a ) 3 : 2 , b ) 2 : 1 , c ) 1 : 2 , d ) 4 : 5 , e ) 2 : 3
Rationale: "required ratio = 2 / 3 * 6 / 11 * 11 / 5 = 2 / 1 = 4 : 5 answer is d"
Answer: d
Question (general): how many digits are required to write numbers between 1 to 100 .
Options: a ) 196 , b ) 158 , c ) 192 , d ) 200 , e ) none
Rationale: "explanation : single digits are from 1 to 9 = 9 digits doubt digits are from 10 to 99 = 90 x 2 = 180 digits 100 needs 3 digits . total 192 digits correct option : c"
Answer: c
Question (physics): a , b , c can complete a piece of work in 16 , 6,12 days . working together , they complete the same work in how many days ?
Options: a ) 2 , b ) 48 / 15 , c ) 7 / 9 , d ) 10 , e ) 24 / 7
Rationale: a + b + c 1 day work = 1 / 16 + 1 / 6 + 1 / 12 = 15 / 48 a , b , c together will complete the job in 48 / 15 days answer is b
Answer: b
Question (general): the population of a bacteria culture doubles every 2 minutes . approximately how many minutes will it take for the population to grow from 1,000 to 100,000 bacteria
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "the question basically asks how many minutes it takes for a population to increase by factor 100 ( 100,000 / 1,000 = 100 ) . now you know that every two minutes the population doubles , i . e . is multiplied by 2 . so the equation becomes : 2 ^ x > = 100 , where x represents the number of times the population doubles . a lot of people remember that 2 ^ 10 = 1,024 . hence , 2 ^ 7 = 128 , i . e . the population has to double 7 times . since it takes the population 2 minutes to double once it takes 7 * 2 minutes = 14 minutes to double 7 times . thus , solution c = 14 is correct ."
Answer: c
Question (general): certain stocks in january were 10 % less than they were in february and 20 % greater than they were in march . what was the percentage decrease in the stocks from february to march ?
Options: a ) 5 % , b ) 10 % , c ) 20 % , d ) 25 % , e ) 50 %
Rationale: let j , f , m be the values of the stock in jan , feb and march . thus , per the question , j = 0.9 f = 1.2 m - - - - > m = 0.75 f thus the % decrease from f to m = ( f - m ) / ( f ) * 100 = ( f - 0.75 f ) / f * 100 = 0.25 * 100 = 25 % , d is the correct answer .
Answer: d
Question (physics): to asphalt 1 km road , 30 men spent 12 days working 8 hours per day . how many days , 20 men will spend to asphalt a road of 2 km working 15 hours a day ?
Options: a ) 23 , b ) 22 , c ) 21 , d ) 20 , e ) 19.2
Rationale: "man - hours required to asphalt 1 km road = 30 * 12 * 8 = 2880 man - hours required to asphalt 2 km road = 2880 * 2 = 5760 man - hours available per day = 20 * 15 = 300 therefore number of days = 5760 / 300 = 19.2 days ans = e"
Answer: e
Question (gain): a scuba diver descends at a rate of 80 feet per minute . a diver dive from a ship to search for a lost ship at the depth of 4000 feet below the sea level . . how long will he take to reach the ship ?
Options: a ) 70 minutes , b ) 72 minutes , c ) 50 minutes , d ) 66 minutes , e ) 67 minutes
Rationale: "time taken to reach = 4000 / 80 = 50 minutes answer : c"
Answer: c
Question (geometry): the roof of an apartment building is rectangular and its length is 4 times longer than its width . if the area of the roof is 784 feet squared , what is the difference between the length and the width of the roof ?
Options: a ) 38 . , b ) 40 . , c ) 42 . , d ) 44 . , e ) 46 .
Rationale: "let the width = x x * 4 x = 784 x ^ 2 = 196 x = 14 length = 4 * 14 = 56 difference = 56 - 14 = 42 c is the answer"
Answer: c
Question (physics): two water pumps , working simultaneously at their respective constant rates , took exactly 5 hours to fill a certain swimming pool . if the constant rate of one pump was 1.5 times the constant rate of the other , how many hours would it have taken the slower pump to fill the pool if it had worked alone at its constant rate ?
Options: a ) 8.5 , b ) 10.5 , c ) 12.5 , d ) 14.5 , e ) 16.5
Rationale: let x be the rate of the slower pump . then 1.5 x is the rate of the faster pump . both pumps together can fill 1 / 5 of the pool each hour . 2.5 x = 1 / 5 x = 1 / 12.5 = 2 / 25 the slower pump could fill the pool in 25 / 2 = 12.5 hours . the answer is c .
Answer: c
Question (general): a certain box has 8 cards and each card has one of the integers from 1 to 8 inclusive . each card has a different number . if 2 different cards are selected at random , what is the probability that the sum of the numbers written on the 2 cards is less than the average ( arithmetic mean ) of all the numbers written on the 8 cards ?
Options: a ) 1 / 8 , b ) 1 / 12 , c ) 1 / 14 , d ) 1 / 18 , e ) 1 / 28
Rationale: "the average of the numbers is 4.5 the total number of ways to choose 2 cards from 8 cards is 8 c 2 = 28 . the ways to choose 2 cards with a sum less than the average are : { 1,2 } , { 1,3 } the probability is 2 / 28 = 1 / 14 the answer is c ."
Answer: c
Question (general): a positive number x is multiplied by 4 , and this product is then divided by 3 . if the positive square root of the result of these two operations equals x , what is the value of x ?
Options: a ) 9 / 4 , b ) 3 / 2 , c ) 4 / 3 , d ) 2 / 3 , e ) 1 / 2
Rationale: sq rt ( 4 x / 3 ) = x = > 4 x / 3 = x ^ 2 = > x = 4 / 3 ans - c
Answer: c
Question (general): a survey of n people in the town of eros found that 50 % of them preferred brand a . another survey of 100 people in the town of angie found that 60 % preferred brand a . in total , 55 % of all the people surveyed together preferred brand a . what is the total number of people surveyed ?
Options: a ) 50 , b ) 100 , c ) 150 , d ) 200 , e ) 250
Rationale: "it is simply a weighted average question . since the given average of 50 % and 60 % is 55 % ( right in the middle ) , it means the number of people surveyed in eros ( n ) is same as the number of people surveyed in angie . so n = 100 total = 100 + 100 = 200 answer ( d )"
Answer: d