Cheukting/mathqa huggingface dataset:
Question (general): one ton has 2200 pounds , and one pound has 16 ounces . how many packets containing wheat weighing 16 pounds and 4 ounces each would totally fill a gunny bag of capacity 13 tons ?
Options: a ) 1760 , b ) 1700 , c ) 2350 , d ) 2500 , e ) 8000
Rationale: 16 pounds and 4 ounces = 16 * 16 + 4 = 260 ounces . 13 tons = 13 * 2200 pound = 13 * 2200 * 16 ounces . hence the answer is ( 13 * 2200 * 16 ) / 260 = 1760 . answer : a .
Answer: a
Question (general): find the greatest number which leaves the same remainder when it divides 25 , 62 and 105 .
Options: a ) 1 , b ) 8 , c ) 12 , d ) 16 , e ) none of these
Rationale: "105 - 62 = 43 62 - 25 = 37 105 - 25 = 80 the h . c . f of 37 , 43 and 80 is 1 . answer : a"
Answer: a
Question (general): if 16 ^ y = 2 ^ 16 , what is y ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 10 , e ) 12
Rationale: "16 ^ y = 2 ^ 4 y = 2 ^ 16 4 y = 16 y = 4 the answer is b ."
Answer: b
Question (general): an automobile parts supplier charges $ 25 per package of gaskets . when a customer orders more than 10 packages of gaskets , the supplier charges 4 / 5 the price for each package in excess of 10 . during a certain week , the supplier sold 60 packages of gaskets . if 25 percent of the gaskets went to company x , 15 percent to company y , and the rest to company z , what was the total amount , in dollars , that the parts supplier received in payment for the gaskets ?
Options: a ) 1305 , b ) 1545 , c ) 1375 , d ) 1345 , e ) 1455
Rationale: "$ 25 per packet of gasket in case a customer orders less than 10 in case a customer orders > 10 price per gasket = 25 * 4 / 5 = 20 a certain week the supplier sold 60 gasket 1 . he sold 25 % of the gaskets to x = 15 gaskets = 25 * 10 + 20 * 5 = 250 + 100 = 350 2 . he sold 15 % of the gaskets to y = 9 gaskets = 25 * 9 = 225 3 . he sold remaining 60 % to z = 36 gaskets = 25 * 10 = 250 + 20 * 26 = 770 thus , total money earned 350 + 225 + 770 = 1345 answer is d"
Answer: d
Question (general): two kinds of vodka are mixed in the ratio 1 : 2 and 2 : 1 and they are sold fetching the profit 20 % and 20 % respectively . if the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4 / 3 and 5 / 3 times respectively , then the mixture will fetch the profit of
Options: a ) 18 % , b ) 20 % , c ) 21 % , d ) 23 % , e ) can not be determined
Rationale: answer : a .
Answer: a
Question (general): the value of a scooter depreciates in such a way that its value of the end of each year is 3 / 4 of its value of the beginning of the same year . if the initial value of the scooter is rs . 40,000 , what is the value at the end of 5 years ?
Options: a ) 3277 , b ) 2977 , c ) 9492 , d ) 6077 , e ) 17112
Rationale: "explanation : 40,000 * ( 3 / 4 ) ^ 5 answer : c"
Answer: c
Question (gain): what percent of 16 is 16 percent of 1 ?
Options: a ) 0.001 , b ) 1 , c ) 0.1 , d ) 100 , e ) 101 .
Rationale: "16 % of 1 = ( 16 / 100 ) * 1 = 16 / 100 to determine what percentage of 16 this is : [ 16 ] [ / 100 * 16 ] * 100 = 1 % ans : b"
Answer: b
Question (physics): what is the length of a bridge ( in meters ) , which a train 148 meters long and travelling at 45 km / h can cross in 30 seconds ?
Options: a ) 211 , b ) 219 , c ) 227 , d ) 235 , e ) 243
Rationale: "speed = 45 km / h = 45000 m / 3600 s = 25 / 2 m / s in 30 seconds , the train can travel 25 / 2 * 30 = 375 meters 375 = length of train + length of bridge length of bridge = 375 - 148 = 227 meters the answer is c ."
Answer: c
Question (physics): at a loading dock , each worker on the night crew loaded 3 / 4 as many boxes as each worker on the day crew . if the night crew has 4 / 7 as many workers as the day crew , what fraction of all the boxes loaded by the two crews did the day crew load ?
Options: a ) 7 / 10 , b ) 2 / 5 , c ) 3 / 5 , d ) 4 / 5 , e ) 5 / 8
Rationale: "method : x = no . of boxes loaded by day crew . boxes by night crew = 3 / 4 * 4 / 7 x = 3 / 7 x % loaded by day crew = x / ( x + 3 / 7 x ) = 7 / 10 answer a"
Answer: a
Question (gain): in 2008 , the profits of company n were 10 percent of revenues . in 2009 , the revenues of company n fell by 20 percent , but profits were 11 percent of revenues . the profits in 2009 were what percent of the profits in 2008 ?
Options: a ) 80 % , b ) 105 % , c ) 88 % , d ) 124.2 % , e ) 138 %
Rationale: "x = profits r = revenue x / r = 0,1 x = 10 r = 100 2009 : r = 80 x / 80 = 0,11 = 11 / 100 x = 80 * 11 / 100 x = 8.8 8.8 / 10 = 0.88 = 88 % , answer c"
Answer: c
Question (other): in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the ` ` sport ' ' formulation , the ratio of flavoring to corn syrup is 3 times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of the ` ` sport ' ' formulation contains 3 ounces of corn syrup , how many ounces of water does it contain ?
Options: a ) 45 , b ) 50 , c ) 55 , d ) 60 , e ) 63
Rationale: f : c : w 1 : 12 : 30 sport version : f : c 3 : 12 f : w 1 : 60 or 3 : 180 so c : f : w = 12 : 3 : 180 c / w = 12 / 180 = 3 ounces / x ounces x = 3 * 180 / 12 = 45 ounces of water answer : a
Answer: a
Question (general): one year before the age of pramila was 4 times than her daughter swati . after 6 years the age of pramila will be 24 year greater than the age of swati . then calculate the ratio of ages of pramila and swati ?
Options: a ) 5 : 3 , b ) 16 : 3 , c ) 11 : 3 , d ) 11 : 5 , e ) 9 : 4
Rationale: let 1 year before age of swati = x years and age of pramila = 4 x years swati present age = ( x + 1 ) and pramila present age = ( 4 x + 1 ) after 6 year age of swati = ( x + 7 ) , age of pramila = ( 4 x + 7 ) so , 4 x + 7 - ( x + 7 ) = 243 x = 24 , x = 8 . ratio = ( 4 x + 7 ) : ( x + 1 ) = 33 : 9 = 11 : 3 answer c
Answer: c
Question (physics): somehow or other i got talked into buying something on the installment plan . i ' m notsure i got a good deal . the payments to date , according to my checkbook , have reached rs . 96 . the second year cost rs . 2.00 more than the first year ; the third year cost rs . 3.00 more thanthe second ; and the fourth year cost me rs . 4.00 more than the third . what were mypayments the first year ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 24 , e ) 26
Rationale: let payments for the first year = x given , x + x + 2 + x + 5 + x + 9 = 96 4 x + 16 = 96 x = 20 answer : b
Answer: b
Question (general): if x is a sum of all even integers on the interval 23 . . . 65 and y is their number , what is the gcd ( x , y ) ?
Options: a ) 1 , b ) 21 , c ) 26 , d ) 52 , e ) 1014
Rationale: "x = 24 + 16 + . . . + 64 = ( largest + smallest ) / 2 * ( # of terms ) = ( 24 + 64 ) / 2 * 21 = 44 * 16 . gcd of 21 and 44 * 21 is 21 . answer : b ."
Answer: b
Question (general): a cube with its sides numbered 1 through 6 is rolled twice , first landing on a and then landing on b . if any roll of the cube yields an equal chance of landing on any of the numbers 1 through 6 , what is the probability w that a + b is prime ?
Options: a ) 0 , b ) 1 / 12 , c ) 5 / 12 , d ) 7 / 18 , e ) 4 / 9
Rationale: "total # of outcomes is 6 * 6 = 36 ; favorable outcomes : a - b - - > prime 1 - 1 - - > 2 ; 1 - 2 - - > 3 ; 2 - 1 - - > 3 ; 1 - 4 - - > 5 ; 4 - 1 - - > 5 ; 2 - 3 - - > 5 ; 3 - 2 - - > 5 ; 1 - 6 - - > 7 ; 6 - 1 - - > 7 ; 2 - 5 - - > 7 ; 5 - 2 - - > 7 ; 3 - 4 - - > 7 ; 4 - 3 - - > 7 ; 6 - 5 - - > 11 ; 5 - 6 - - > 11 . total of 15 favorable outcomes w = 15 / 36 . answer : c ."
Answer: c
Question (physics): the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 750 resolutions ?
Options: a ) 277 m , b ) 704 m , c ) 278 m , d ) 288 m , e ) 1056 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 750 resolutions . = 750 * 2 * 22 / 7 * 22.4 = 105600 cm = 1056 m answer : e"
Answer: e
Question (physics): a car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 450 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ?
Options: a ) 370 , b ) 365 , c ) 360 , d ) 380 , e ) 350
Rationale: "c 450 * t = 1 km = > t = 1 / 450 km / h v * ( t + 2 / 3600 ) = 1 v ( 1 / 450 + 2 / 3600 ) = 1 = > v = 360 km / h"
Answer: c
Question (gain): a sum of rs . 2795 is lent into two parts so that the interest on the first part for 8 years at 3 % per annum may be equal to the interest on the second part for 3 years at 5 % per annum . find the second sum ?
Options: a ) 1642 , b ) 1640 , c ) 1720 , d ) 2795 , e ) 6386
Rationale: "( x * 8 * 3 ) / 100 = ( ( 2795 - x ) * 3 * 5 ) / 100 24 x / 100 = 41925 / 100 - 15 x / 100 39 x = 41925 = > x = 1075 second sum = 2795 – 1075 = 1720 answer : c"
Answer: c
Question (general): in one year , the population , of a village increased by 25 % and in the next year , it decreased by 25 % . if at the end of 2 nd year , the population was 18750 , what was it in the beginning ?
Options: a ) 7787 , b ) 8000 , c ) 1988 , d ) 1277 , e ) 20000
Rationale: "x * 125 / 100 * 75 / 100 = 18750 x * 0.9375 = 18750 x = 18750 / 0.9375 = > 20000 answer : e"
Answer: e
Question (general): a small pool filled only with water will require an additional 300 gallons of water in order to be filled to 85 % of its capacity . if pumping in these additional 300 gallons of water will increase the amount of water in the pool by 30 % , what is the total capacity of the pool in gallons ?
Options: a ) 1000 , b ) 1250 , c ) 1300 , d ) 1529.41 , e ) 1625
Rationale: "300 gallons of water increases capacity by 30 % that means 30 % is 300 gallons , so 100 % would be = 300 * 100 / 30 = 1000 gallons now 1000 + 300 gallons is 85 % capacity of tank . so 100 % capacity would be = 1300 * 100 / 85 = 1529.41 d is the answer"
Answer: d
Question (gain): if 85 % of 3 / 5 of a number is 36 , then the number is ?
Options: a ) 80 , b ) 100 , c ) 70.5 , d ) 90 , e ) none of these
Rationale: "let the number be x . then 85 % of 3 / 5 of x = 36 85 / 100 * 3 / 5 * x = 36 x = ( 36 * 100 / 51 ) = 70.5 required number = 70.5 . correct option : c"
Answer: c
Question (other): a jar contains a mixture of ab in the ratio 3 : 2 . when 10 l of mixture is replaced with liquid b , ratio becomes 2 : 3 . how many liters of liquid a was present in mixture initially .
Options: a ) 18 , b ) 15 , c ) 16 , d ) 20 , e ) 25
Rationale: "10 litres of mixture that is replaced will contain 6 litres of a and 4 litres of b ( as a : b = 3 : 2 ) let the initial volume of the mixture be 3 k + 2 k = 5 k so by condition , [ 3 k - 6 ] / [ 2 k - 4 + 10 ] = 2 / 3 9 k - 18 = 4 k - 8 + 20 5 k = 12 + 18 k = 6 solve for k which is k = 6 so initial volume of liquid a = 3 k = 18 litres answer : a"
Answer: a
Question (gain): √ 3 percent of 3 √ 3 =
Options: a ) 5.2 , b ) 1.0 , c ) 0.1 , d ) 2.0 , e ) 5.0
Rationale: "the other solutions are great , but here ' s one more approach . first , we scan the answer choices to see that they are quite spread apart . this means we can also use someapproximation all test - takers must memorize the following approximations : √ 2 ≈ 1.4 √ 3 ≈ 1.7 so , √ 3 percent of 3 √ 3 ≈ 1.7 percent of ( 3 ) ( 1.7 ) ≈ ( 1.7 / 100 ) ( 5.1 ) ≈ 8.67 / 100 ≈ 0.08 check the answer choices to see that c is the only answer that ' s close . answer : c"
Answer: c
Question (gain): machine a produces 100 parts twice as fast as machine b does . machine b produces 100 parts in 40 minutes . if each machine produces parts at a constant rate , how many parts does machine a produce in 10 minutes ?
Options: a ) 20 , b ) 50 , c ) 60 , d ) 40 , e ) 30
Rationale: "machine b produces 100 part in 40 minutes . machine a produces 100 parts twice as fast as b , so machine a produces 100 parts in 40 / 2 = 20 minutes . now , machine a produces 100 parts in 20 minutes which is 100 / 20 = 5 parts / minute . 5 parts x a total of 10 minutes = 50 b"
Answer: b
Question (other): an order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2 . subsequently , the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter . find the ratio of the areas of the carpets in both the cases ?
Options: a ) 8 : 6 , b ) 8 : 7 , c ) 8 : 9 , d ) 8 : 4 , e ) 8 : 1
Rationale: let the length and breadth of the carpet in the first case be 3 x units and 2 x units respectively . let the dimensions of the carpet in the second case be 7 y , 3 y units respectively . from the data , . 2 ( 3 x + 2 x ) = 2 ( 7 y + 3 y ) = > 5 x = 10 y = > x = 2 y required ratio of the areas of the carpet in both the cases = 3 x * 2 x : 7 y : 3 y = 6 x 2 : 21 y 2 = 6 * ( 2 y ) 2 : 21 y 2 = 6 * 4 y 2 : 21 y 2 = 8 : 7 answer : b
Answer: b
Question (other): of the diplomats who attended a summit conference : 20 spoke french , 32 did not speak english and 20 % of the diplomats spoke neither french nor english . if 10 % of the diplomats spoke both french and english , then how many diplomats attended the conference ?
Options: a ) 70 , b ) 96 , c ) 108 , d ) 120 , e ) 150
Rationale: 2 x 2 matrix will be the easiest way to calculate this . text in black : given statements text in red : calculated values thus d = 120 is the correct answer
Answer: d
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 .
Options: a ) $ 400 , b ) $ 1400 , c ) $ 3400 , d ) $ 2400 , e ) $ 4400
Rationale: "part of salary left = 1 - ( 2 / 5 + 3 / 10 + 1 / 8 ) = 7 / 40 let the monthly salary be $ x then ( 7 / 40 ) of x = 1400 x = 8000 expenditure on food = $ 2400 option d"
Answer: d
Question (gain): in the fifth grade at parkway elementary school there are 420 students . 312 students are boys and 250 students are playing soccer . 82 % of the students that play soccer are boys . how many girl student are in parkway that is not playing soccer ?
Options: a ) 63 . , b ) 73 . , c ) 81 , d ) 91 , e ) 108
Rationale: "total students = 420 boys = 312 , girls = 108 total playing soccer = 250 82 % of 250 = 205 are boys who play soccer . girls who play soccer = 45 . total girls who do not play soccer = 108 - 45 = 63 . correct option : a"
Answer: a
Question (general): x , a , z , and b are single digit positive integers . x = 1 / 5 a . z = 1 / 5 b . ( 10 a + b ) – ( 10 x + z ) could not equal
Options: a ) 36 , b ) 33 , c ) 44 , d ) 64 , e ) 56
Rationale: a = 5 x , b = 5 z therefore ( 5 x * 10 + 5 z ) - ( 10 x + z ) = ( 5 - 1 ) ( 10 x + z ) = . ( 10 x + z ) number should be divisible by 4 b
Answer: b
Question (general): how much water should be added to 10 liters of a 20 % - solution of alcohol to reduce the concentration of alcohol in the solution by 75 % ?
Options: a ) 25 liters , b ) 27 liters , c ) 30 liters , d ) 32 liters , e ) 35 liters
Rationale: "let x ltr water to be added 2 ltr alcohol to be represented as ( 20 ( 1 - 3 / 4 ( new soln . = 10 + x ) ) ) 2 = 5 % * ( 10 + x ) - - - - - - - - > x = 30 answer : c"
Answer: c
Question (general): on a game show , a contestant is given 3 keys , each of which opens exactly one of 3 identical boxes . the first box contains $ 5 , the second $ 500 , and the third $ 5000 . the contestant assigns each key to one of the boxes and wins the amount of money contained in any box that is opened by the key assigned to it . what is the probability that a contestant will win more than $ 5000 ?
Options: a ) 1 / 9 , b ) 4 / 6 , c ) 3 / 6 , d ) 1 / 2 , e ) 1 / 6
Rationale: let ' s call the boxes that contain $ 5 , $ 500 , and $ 5000 , respectively , box a , box b , box c . these are opened , respectively , by key a , key b , and key c . we want to know the probability of winning more than $ 5000 . notice that if the distribution of keys is : box a = key b box b = key a box c = key c then the contestant wins exactly $ 5000 , not more than $ 5000 . the only configuration that leads to winning more than $ 1000 is : box a = key a box b = key b box c = key c i . e . , getting all three keys correct . that ' s the only way to be more than $ 5000 . so , really , the question can be rephrased : what is the probability of guessing the order of keys so that each key matches the correct box ? well , for a set of three items , the number of possible permutations is 3 ! = 3 * 2 * 1 = 6 . of those 6 possible permutations , only one of them leads to all three keys being paired with the right box . so , the answer is probability = 1 / 6 answer : e
Answer: e
Question (physics): sakshi can do a piece of work in 20 days . tanya is 25 % more efficient than sakshi . the number of days taken by tanya to do the same piece of work :
Options: a ) 15 , b ) 16 , c ) 18 , d ) 25 , e ) 10
Rationale: "solution ratio of times taken by sakshi and tanya = 125 : 100 = 5 : 4 . suppose tanya taken x days to do the work . 5 : 4 : : 20 : x ⇒ x = ( 20 x 4 / 5 ) ⇒ x = 16 days . hence , tanya takes 16 days is complete the work . answer b"
Answer: b
Question (physics): there are 18 stations between hyderabad and bangalore . how many second class tickets have to be printed , so that a passenger can travel from any station to any other station ?
Options: a ) 987 , b ) 177 , c ) 357 , d ) 267 , e ) 380
Rationale: "the total number of stations = 20 from 20 stations we have to choose any two stations and the direction of travel ( i . e . , hyderabad to bangalore is different from bangalore to hyderabad ) in ² ⁰ p ₂ ways . ² ⁰ p ₂ = 20 * 19 = 380 . answer : e"
Answer: e
Question (geometry): the perimeter of a square is 28 cm . what is the perimeter of a circle whose radius is equal to the side of the square ? ( in cm )
Options: a ) 14
b ) 28
c ) 42
d ) 44
e ) 56
Rationale: side of the square = 28 / 4 = 7 diameter of the circle = 7 x 2 = 14 perimeter of the circle = ï € xd = ( 22 / 7 ) x 14 = 44 cm answer : d
Answer: d
Question (physics): a boat traveled upstream 90 miles at an average speed of ( v - 3 ) miles per hour and then traveled the same distance downstream at an average speed of ( v + 3 ) miles per hour . if the trip upstream took a half hour longer than the trip downstream , then how many hours did it take the boat to travel downstream ?
Options: a ) 2.5 , b ) 2.4 , c ) 2.3 , d ) 2.2 , e ) 2.1
Rationale: 90 / ( v - 3 ) = 90 / ( v + 3 ) + 0.5 hours = > 90 ( v + 3 ) = ( v - 3 ) [ 90 + 0.5 v + 1.5 ] 90 v + 270 = ( v - 3 ) ( 183 / 2 + v / 2 ) 180 v + 540 = ( v - 3 ) ( 183 + v ) = 183 v - 549 + v ^ 2 - 3 v v ^ 2 - 1089 = 0 = > v = 33 miles / hr = > time downstream = 90 / 36 = 30 / 12 = 5 / 2 = 2.5 hrs answer a 2.5
Answer: a
Question (general): in a certain country 1 / 3 of 4 = 6 . assuming the same proportion , what would be the value of 1 / 6 of 20 ?
Options: a ) 14 , b ) 15 , c ) 20 , d ) 22 , e ) 25
Rationale: "b 15"
Answer: b
Question (physics): working together , a and b can do a job in 6 days . b and c can do the same job in 10 days , while c and a can do it in 7.5 days . how long will it take if all a , b and c work together to complete the job ?
Options: a ) 4 days , b ) 5 days , c ) 8 days , d ) 9 days , e ) 10 days
Rationale: a and b 1 day work = 1 / 6 b and c 1 day work = 1 / 10 c and a 1 day work = 1 / 7.5 a , b , c 1 day work = ( 1 / 6 + 1 / 10 + 1 / 7.5 ) * 1 / 2 = 1 / 5 so a . b . c completes work in 5 days answer : b
Answer: b
Question (general): from below option 49 is divisible by which one ?
Options: a ) a ) 2 , b ) b ) 3 , c ) c ) 4 , d ) d ) 5 , e ) e ) 7
Rationale: 49 / 7 = 7 e
Answer: e
Question (gain): ramesh purchased a refrigerator for rs . 12500 after getting a discount of 20 % on the labelled price . he spent rs . 125 on transport and rs . 250 on installation . at what price should it be sold so that the profit earned would be 12 % if no discount was offered ?
Options: a ) 17608 , b ) 17920 , c ) 17604 , d ) 17600 , e ) 117601
Rationale: "price at which the tv set is bought = rs . 12,500 discount offered = 20 % marked price = 12500 * 100 / 80 = rs . 15625 the total amount spent on transport and installation = 125 + 250 = rs . 375 \ total price of tv set = 15625 + 375 = rs . 16000 the price at which the tv should be sold to get a profit of 10 % if no discount was offered = 16000 * 112 / 100 = rs . 17920 . answer : b"
Answer: b
Question (general): if x / ( 12 p ) is an even prime number , where x is a positive integer and p is a prime number , what is the least value of x ?
Options: a ) 22 , b ) 33 , c ) 44 , d ) 48 , e ) 99
Rationale: x / ( 12 p ) = even prime number x = even prime number * 11 p least value of x = lowest even prime number * 12 * lowest value of p = 2 * 12 * 2 = 48 answer d
Answer: d
Question (general): there are 8 players in a chess group , and each player plays each of the others once . given that each game is played by two players , how many total games will be played ?
Options: a ) 10 , b ) 30 , c ) 28 , d ) 60 , e ) 90
Rationale: "10 players are there . two players play one game with one another . so 8 c 2 = 8 * 7 / 2 = 28 so option c is correct"
Answer: c
Question (general): a driver just filled the car ' s gas tank with 45 liters of gasohol , a mixture consisting of 5 % ethanol and 95 % gasoline . if the car runs best on a mixture consisting of 10 % ethanol and 90 % gasoline , how many liters of ethanol must be added into the gas tank for the car to achieve optimum performance ?
Options: a ) 1.3 , b ) 1.7 , c ) 2.1 , d ) 2.5 , e ) 2.9
Rationale: "let x be the number of liters of ethanol added to the gas tank . 0.05 ( 45 ) + x = 0.1 ( 45 + x ) 0.9 x = 4.5 - 2.25 = 2.25 x = 2.5 liters the answer is d ."
Answer: d
Question (general): think of a number , divide it by 5 and add 23 to it . the result is 42 . what is the number thought of ?
Options: a ) 24 , b ) 77 , c ) 297 , d ) 267 , e ) 95
Rationale: "explanation : 42 - 23 = 19 19 x 5 = 95 answer : e"
Answer: e
Question (gain): ms . lopez deposits $ 100 in an account that pays 20 % interest , compounded semiannually . how much money will there be in the account at the end of one year ?
Options: a ) $ 118.00 , b ) $ 120.00 , c ) $ 121.00 , d ) $ 122.00 , e ) $ 140.00
Rationale: "et me explain the concept for those who are not familiar with compounded semi annually / quarterly etc . . it basically means , here , that the interest will be paid twice , after 6 months and at the end of year . . so twice . . but interest is 20 % , which will get distributed semiannually that is 10 % . . . so the q literally means . . after 6 months . . 100 * 10 / 100 + 100 = 110 . . at the end of year 110 * 10 / 100 + 110 = 121 . . or we put it in compound interest formula . . where ci = 10 % , t is 2 and p = 100 . . so amount = 100 ( 1 + 10 / 100 ) ^ 2 = 100 * 1.1 * 1.1 = 121 . . answer : c"
Answer: c
Question (general): here ' s an easy question of averages , but let ' s try to see innovative ways of solving this . a class has 12 boys and x girls . average score of boys and girls is 84 and 92 respectively . the average of the whole class is 86 , what is the value of x ?
Options: a ) a ) 6 , b ) b ) 4 , c ) c ) 8 , d ) d ) 10 , e ) e ) 12
Rationale: 12 ( 84 ) + 92 x / 12 + x = 86 1008 + 92 x / 12 + x = 86 1008 + 92 x = 86 ( 12 + x ) 1008 + 92 x = 1032 + 86 x x ' s one side , numbers one side we get , 92 x - 86 x = 1032 - 1008 6 x = 24 hence , x = 4 answer b
Answer: b
Question (gain): the present population of a town is 1000 . population increase rate is 20 % p . a . find the population of town after 2 years ?
Options: a ) 1440 , b ) 1220 , c ) 1400 , d ) 1500 , e ) 1620
Rationale: "p = 1000 r = 20 % required population of town = p * ( 1 + r / 100 ) ^ t = 1000 * ( 1 + 20 / 100 ) ^ 2 = 1000 * ( 6 / 5 ) ^ 2 = 1440 ( approximately ) answer is a"
Answer: a
Question (gain): if rs . 7500 are borrowed at c . i at the rate of 4 % per annum , then after 4 years the amount to be paid is ?
Options: a ) 3377 , b ) 2688 , c ) 2688 , d ) 8774 , e ) 1268
Rationale: "a = 7500 ( 26 / 25 ) ^ 4 = 8774 answer : d"
Answer: d