Cheukting/mathqa huggingface dataset:
Question (gain): sam invested rs . 3000 @ 10 % per annum for one year . if the interest is compounded half - yearly , then the amount received by sam at the end of the year will be ?
Options: a ) 2554.0 , b ) 3387.0 , c ) 2503.0 , d ) 3307.5 , e ) 16537.11
Rationale: "p = rs . 3000 ; r = 10 % p . a . = 5 % per half - year ; t = 1 year = 2 half - year amount = [ 3000 * ( 1 + 5 / 100 ) 2 ] = ( 3000 * 21 / 20 * 21 / 20 ) = rs . 3307.50 answer : d"
Answer: d
Question (geometry): the parameter of a square is equal to the perimeter of a rectangle of length 7.5 cm and breadth 6.5 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places ) ?
Options: a ) 10.2 , b ) 10.27 , c ) 10.23 , d ) 10.21 , e ) 10.25
Rationale: "let the side of the square be a cm . parameter of the rectangle = 2 ( 7.5 + 5.5 ) = 26 cm parameter of the square = 26 cm i . e . 4 a = 26 a = 6.5 diameter of the semicircle = 6.5 cm circimference of the semicircle = 1 / 2 ( â ˆ  ) ( 6.5 ) = 1 / 2 ( 22 / 7 ) ( 6.5 ) = 143 / 14 = 10.21 cm to two decimal places answer : d"
Answer: d
Question (physics): a space shuttle orbits the earth at about 12 kilometers per second . this speed is equal to how many kilometers per hour ?
Options: a ) 480 , b ) 2,880 , c ) 4,800 , d ) 28,800 , e ) 43,200
Rationale: "seconds in 1 hours : 60 s in 1 min 60 min in 1 hr 60 * 60 = 3600 sec in 1 hr 12 * 3600 = 43,200 answer : e"
Answer: e
Question (general): a collection of books went on sale , and 2 / 3 of them were sold for $ 1.50 each . if none of the 36 remaining books were sold , what was the total amount received for the books that were sold ?
Options: a ) $ 180 , b ) $ 135 , c ) $ 108 , d ) $ 60 , e ) $ 54
Rationale: since 2 / 3 of the books in the collection were sold , 1 / 3 were not sold . the 36 unsold books represent 1 / 3 of the total number of books in the collection , and 2 / 3 of the total number of books equals 2 ( 36 ) or 72 . the total proceeds of the sale was 72 ( $ 1.50 ) or $ 108 . the best answer is therefore c .
Answer: c
Question (general): if 213 × 16 = 3408 , then 0.16 × 2.13 is equal to :
Options: a ) 0.3408 , b ) 3.408 , c ) 34.08 , d ) 340.8 , e ) none of these
Rationale: "solution 0.16 × 2.13 = ( 16 / 100 x 213 / 100 ) = ( 16 x 213 / 10000 ) = 3408 / 10000 = 0.3408 . answer a"
Answer: a
Question (general): what is the smallest positive integer x such that 80 - x is the cube of a positive integer
Options: a ) 16 , b ) 12 , c ) 47 , d ) 9 , e ) 12
Rationale: "given 80 - x is a perfect cube so we will take 64 = 4 * 4 * 4 80 - x = 64 x = 80 - 64 = 16 correct option is a"
Answer: a
Question (general): the l . c . m of two numbers is 495 and their h . c . f is 5 . if the sum of the numbers is 10 , then their difference is :
Options: a ) 10 , b ) 46 , c ) 70 , d ) 90 , e ) 100
Rationale: "let the numbers be x and ( 100 - x ) . then , x ( 100 - x ) = 5 * 495 x 2 - 100 x + 2475 = 0 ( x - 55 ) ( x - 45 ) = 0 x = 55 or 45 the numbers are 45 and 55 . required difference = 55 - 45 = 10 . answer : a"
Answer: a
Question (other): if two dice are thrown together , the probability of getting a square number on both the dice is
Options: a ) 5 / 12 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 12 , e ) 2 / 3
Rationale: the number of exhaustive outcomes is 36 . let e be the event of getting a sqaure number on both the dice . p ( e ) = 3 / 36 = 1 / 12 . d )
Answer: d
Question (geometry): what is the area of a square field whose diagonal of length 28 m ?
Options: a ) 288 , b ) 289 , c ) 200 , d ) 112 , e ) 392
Rationale: "d 2 / 2 = ( 28 * 28 ) / 2 = 392 answer : e"
Answer: e
Question (general): in 1982 and 1983 , company b ’ s operating expenses were $ 12.0 million and $ 13.0 million , respectively , and its revenues were $ 15.6 million and $ 18.8 million , respectively . what was the percent increase in company b ’ s profit ( revenues minus operating expenses ) from 1982 to 1983 ?
Options: a ) 3 % , b ) 61 1 / 9 % , c ) 25 % , d ) 33 1 / 3 % , e ) 60 %
Rationale: "profit in 1982 = 15.6 - 12 = 3.6 million $ profit in 1983 = 18.8 - 13 = 5.8 million $ percentage increase in profit = ( 5.8 - 3.6 ) / 3.6 * 100 % = 61 1 / 9 % answer b"
Answer: b
Question (physics): 16 machines can do a work in 10 days . how many machines are needed to complete the work in 40 days ?
Options: a ) 10 , b ) 6 , c ) 4 , d ) 7 , e ) 5
Rationale: "required number of machines = 16 * 10 / 40 = 4 answer is c"
Answer: c
Question (general): the salary of a , b , c , d , e is rs . 8000 , rs . 5000 , rs . 15000 , rs . 7000 , rs . 9000 per month respectively , then the average salary of a , b , c , d , and e per month is
Options: a ) rs . 7000 , b ) rs . 8000 , c ) rs . 8800 , d ) rs . 9000 , e ) none
Rationale: "answer average salary = 8000 + 5000 + 15000 + 7000 + 9000 / 5 = rs . 8800 correct option : c"
Answer: c
Question (general): if n is a prime number greater than 19 , what is the remainder when n ^ 2 is divided by 12 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5
Rationale: "there are several algebraic ways to solve this question , but the easiest way is as follows : since we can not have two correct answers just pick a prime greater than 19 , square it and see what would be the remainder upon division of it by 12 . n = 23 - - > n ^ 2 = 529 - - > remainder upon division 529 by 12 is 1 . answer : b ."
Answer: b
Question (general): total number of 4 digit number do not having the digit 3 or 6 .
Options: a ) 22 , b ) 28 , c ) 27 , d ) 19 , e ) 11
Rationale: answer : d
Answer: d
Question (general): the average weight of a , b and c is 43 kg . if the average weight of a and b be 40 kg and that of b and c be 43 kg , then the weight of b is :
Options: a ) 33 kg , b ) 31 kg , c ) 32 kg , d ) 36 kg , e ) 37 kg
Rationale: "let a , b , c represent their respective weights . then , we have : a + b + c = ( 45 x 3 ) = 129 . . . . ( i ) a + b = ( 40 x 2 ) = 80 . . . . ( ii ) b + c = ( 43 x 2 ) = 86 . . . . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 166 . . . . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 37 . b ' s weight = 37 kg . e"
Answer: e
Question (geometry): the length of rectangle is thrice its breadth and its perimeter is 80 m , find the area of the rectangle ?
Options: a ) 360 , b ) 376 , c ) 299 , d ) 276 , e ) 111
Rationale: "2 ( 3 x + x ) = 80 l = 36 b = 10 lb = 36 * 10 = 360 a"
Answer: a
Question (other): a dog breeder currently has 9 breeding dogs . 6 of the dogs have exactly 1 littermate , and 3 of the dogs have exactly 2 littermates . if 2 dogs are selected at random , what is the probability r that both selected dogs are not littermates ?
Options: a ) 1 / 6 , b ) 2 / 9 , c ) 5 / 6 , d ) 7 / 9 , e ) 8 / 9
Rationale: "we have three pairs of dogs for the 6 with exactly one littermate , and one triplet , with each having exactly two littermates . so , in fact there are two types of dogs : those with one littermate - say a , and the others with two littermates - b . work with probabilities : choosing two dogs , we can have either one dog of type b or none ( we can not have two dogs both of type b ) . the probability of choosing one dog of type b and one of type a is 3 / 9 * 6 / 8 * 2 = 1 / 2 ( the factor of 2 for the two possibilities ba and ab ) . the probability r of choosing two dogs of type a which are not littermates is 6 / 9 * 4 / 8 = 1 / 3 ( choose one a , then another a which is n ' t the previous one ' s littermate ) . the required probability is 1 / 2 + 1 / 3 = 5 / 6 . find the probability for the complementary event : choose aa or bb . probability of choosing two dogs of type a who are littermates is 6 / 9 * 1 / 8 = 1 / 12 . probability of choosing two dogs of type b ( who necessarily are littermates ) is 3 / 9 * 2 / 8 = 1 / 12 . again , we obtain 1 - ( 1 / 12 + 1 / 12 ) = 5 / 6 . answer : c"
Answer: c
Question (physics): a train running at the speed of 60 km / hr crosses a pole in 21 seconds . what is the length of the train ?
Options: a ) 350 m , b ) 278 m , c ) 876 m , d ) 150 m , e ) 267 m
Rationale: "speed = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec length of the train = ( speed x time ) = ( 50 / 3 * 21 ) m = 350 m . answer : a"
Answer: a
Question (general): a number when divided by 214 gives a remainder 35 , what remainder will be obtained by dividing the same number 14 ?
Options: a ) 7 , b ) 10 , c ) 11 , d ) 2 , e ) 3
Rationale: "explanation : 214 + 35 = 249 / 14 = 11 ( remainder ) answer : c"
Answer: c
Question (general): a number whose fifth part increased by 3 is equal to its fourth part diminished by 3 is ?
Options: a ) 120 , b ) 180 , c ) 200 , d ) 220 , e ) none
Rationale: "answer let the number be n . then , ( n / 5 ) + 3 = ( n / 4 ) - 3 â ‡ ’ ( n / 4 ) - ( n / 5 ) = 6 â ‡ ’ ( 5 n - 4 n ) / 20 = 6 â ˆ ´ n = 120 option : a"
Answer: a
Question (general): a military camp has a food reserve for 250 personnel for 40 days . if after 15 days 50 more personnel are added to the camp , find the number of days the reserve will last for ?
Options: a ) 25 , b ) 67 , c ) 26 , d ) 29 , e ) 18
Rationale: explanation : as the camp has a reserve for 250 personnel that can last for 40 days , after 10 days the reserve left for 250 personnel is for 30 days . now 50 more personnel are added in the camp . hence , the food reserve for 300 personnel will last for : 250 : 300 : : x : 30 … … . . ( it is an indirect proportion as less men means more days ) x = ( 250 * 30 ) / 300 x = 25 days answer : a
Answer: a
Question (general): what is x if x + 2 y = 12 and y = 3 ?
Options: a ) a ) 10 , b ) b ) 8 , c ) c ) 6 , d ) d ) 4 , e ) e ) 2
Rationale: "x = 12 - 2 y x = 12 - 6 . x = 6 answer : c"
Answer: c
Question (gain): in how many years rs 200 will produce the same interest at 10 % as rs . 1000 produce in 2 years at 12 %
Options: a ) 13 , b ) 9 , c ) 11 , d ) 12 , e ) 10
Rationale: explanation : clue : firstly we need to calculate the si with prinical 1000 , time 2 years and rate 12 % , it will be rs . 240 then we can get the time as time = ( 100 * 240 ) / ( 200 * 10 ) = 12 option d
Answer: d
Question (gain): a store ’ s selling price of $ 2240 for a certain computer would yield a profit of 40 percent of the store ’ s cost for the computer . what selling price would yield a profit of 60 percent of the computer ’ s cost ?
Options: a ) $ 2400 , b ) $ 2464 , c ) $ 2560 , d ) $ 2732 , e ) $ 2800
Rationale: "1.4 x = 2240 x = 2240 / 1.4 so , 1.6 x = 2240 * 1.6 / 1.4 = 2560 answer : - c"
Answer: c
Question (physics): a person buys 18 local tickets for rs 110 . each first class ticket costs rs 10 and each second class ticket costs rs 3 . what will another lot of 18 tickets in which the numbers of first class and second class tickets are interchanged cost ?
Options: a ) 112 , b ) 118 , c ) 121 , d ) 124 , e ) none of these
Rationale: explanation : let , there are x first class ticket and ( 18 - x ) second class tickets . then , 110 = 10 x + 3 ( 18 − x ) . = > 110 = 10 x + 54 − 3 x . = > 7 x = 56 . = > x = 8 . if the number of the first class and second class tickets are interchanged , then the total cost would be 10 × 10 + 3 × 8 = 124 . answer : d
Answer: d
Question (general): for all numbers a and b , the operationis defined by ab = ( a + 2 ) ( b – 3 ) . if 3 y = – 30 , then y =
Options: a ) – 15 , b ) – 6 , c ) - 3 , d ) 6 , e ) 15
Rationale: ( 3 + 2 ) ( y - 3 ) = - 30 . . x - 3 = - 6 . . x = - 3 c
Answer: c
Question (physics): a train 250 m long running at 72 kmph crosses a platform in 40 sec . what is the length of the platform ?
Options: a ) 450 m , b ) 200 m , c ) 250 m , d ) 270 m , e ) 300 m
Rationale: "d = 72 * 5 / 18 = 40 = 800 â € “ 250 = 450 m answer : a"
Answer: a
Question (general): out of 3 given numbers , the first one is twice the second and 3 times the third . if the average of these numbers is 88 , then the difference between first and third is .
Options: a ) 92 , b ) 39 , c ) 87 , d ) 96 , e ) none
Rationale: sum of three number is = 88 * 3 = 264 let three numbers are a , b , c and a is the highest and c is the lowest then , 2 b = a so b = a / 2 and 3 c = a so c = a / 3 we can write , a + b + c = 264 a + a / 2 + a / 3 = 264 11 a / 6 = 264 a = 144 so , c = 144 / 3 = 48 so there difference is = 144 - 48 = 96 answer d
Answer: d
Question (gain): an item is being sold for $ 10 each . however , if a customer will “ buy at least 3 ” they have a promo discount of 32 % . also , if a customer will “ buy at least 10 ” items they will deduct an additional 8 % to their “ buy at least 3 ” promo price . if sam buys 10 pcs of that item how much should he pay ?
Options: a ) $ 92.00 , b ) $ 88.00 , c ) $ 87.04 , d ) $ 80.96 , e ) $ 70.00
Rationale: "without any discount sam should pay 10 * 10 = $ 100 . now , the overall discount would be slightly less than 40 % , thus he must pay slightly more than $ 60 . only answer choice e fits . answer : e ."
Answer: e
Question (physics): r is the set of positive odd integers less than 200 , and s is the set of the squares of the integers in r . how many elements does the intersection of r and s contain ?
Options: a ) none , b ) two , c ) four , d ) five , e ) seven
Rationale: "r is the set of positive odd integers less than 200 , and s is the set of the squares of the integers in r . how many elements does the intersection of r and s contain ? r = 1,3 , 5,7 , 9,11 , 13,15 . . . s = 1 , 9,25 , 49,81 . . . numbers : 1 , 9 , 25 , 49 , 81 , 121 , and 169 are odd integers ( less than 200 ) that are in both sets . solution : seven answer : e"
Answer: e
Question (general): the cost to park a car in a certain parking garage is $ 9.00 for up to 2 hours of parking and $ 1.75 for each hour in excess of 2 hours . what is the average ( arithmetic mean ) cost per hour to park a car in the parking garage for 9 hours ?
Options: a ) $ 1.09 , b ) $ 1.67 , c ) $ 2.25 , d ) $ 2.36 , e ) $ 2.50
Rationale: "total cost of parking for 9 hours = 9 $ for the first 2 hours and then 1.75 for ( 9 - 2 ) hours = 9 + 7 * 1.75 = 21.25 thus the average parking price = 21.25 / 9 = 2.36 $ d is the correct answer ."
Answer: d
Question (gain): find the compound interest on $ 30000 in 2 years at 4 % per annum , the interest being compounded half - yearly ?
Options: a ) $ 645.56 , b ) $ 824.32 , c ) $ 954.26 , d ) $ 2472.96 , e ) $ 1020.45
Rationale: "principle = $ 10000 rate = 2 % half yearly = 4 half years amount = 30000 * ( 1 + 2 / 100 ) ^ 4 = 30000 * 51 / 50 * 51 / 50 * 51 / 50 * 51 / 50 = $ 32472.96 c . i . = 32472.96 - 10000 = $ 2472.96 answer is d"
Answer: d
Question (general): the average waight of a , b , c is 45 kg . the avg wgt of a & b be 40 kg & that of b , c be 43 kg . find the wgt of b .
Options: a ) 34 kg , b ) 40 kg , c ) 42 kg , d ) 41 kg , e ) 31 kg
Rationale: ". let a , b , c represent their individual wgts . then , a + b + c = ( 45 * 3 ) kg = 135 kg a + b = ( 40 * 2 ) kg = 80 kg & b + c = ( 43 * 2 ) kg = 86 kg b = ( a + b ) + ( b + c ) - ( a + b + c ) = ( 80 + 86 - 135 ) kg = 31 kg . answer is e ."
Answer: e
Question (gain): of the 600 residents of clermontville , 35 % watch the television show island survival , 40 % watch lovelost lawyers and 50 % watch medical emergency . if all residents watch at least one of these 3 shows and 18 % watch exactly 2 of these shows , then how many clermontville residents z watch all of the shows ?
Options: a ) 150 , b ) 108 , c ) 42 , d ) 21 , e ) - 21
Rationale: oa is d . 100 = a + b + c - ab - ac - bc + abc , which is the same as the following formula 100 = a + b + c + ( - ab - ac - bc + abc + abc + abc ) - 2 abc . the term between parantheses value 18 % so the equation to resolve is 100 = 35 + 40 + 50 - 18 - 2 abc therefore the value of abc is z = 3.5 % of 600 , is 21 . d is the correct answer
Answer: d
Question (general): john ' s marks wrongly entered as 82 instead of 62 . due to that the average marks for the class got increased by half ( 1 / 2 ) . the number of john in the class is ?
Options: a ) 70 , b ) 78 , c ) 80 , d ) 84 , e ) 90
Rationale: otal increase in marks = x x 1 = x 2 2 x / 2 = ( 82 - 62 ) x / 2 = 40 x = 80 . c
Answer: c
Question (physics): a train running at the speed of 90 km / hr crosses a pole in 10 seconds . find the length of the train .
Options: a ) 150 , b ) 180 , c ) 250 , d ) 200 , e ) 225
Rationale: "speed = 90 * ( 5 / 18 ) m / sec = 25 m / sec length of train ( distance ) = speed * time 25 * 10 = 250 meter answer : c"
Answer: c
Question (geometry): milk is poured from a full rectangular container with dimensions 4 inches by 9 inches by 10 inches into a cylindrical container with a diameter of 6 inches . if the milk does not overflow , how many inches high will the milk reach ?
Options: a ) 60 / π
b ) 24
c ) 40 / π
d ) 10
e ) 3 π
Rationale: let the height of level of milk in the cylinder = h since , volume of milk is constant . therefore 4 * 9 * 10 = π π * 3 ^ 2 * h = > π * h = 40 = > h = 40 / ( π ) answer c
Answer: c
Question (gain): if 65 % of a number is greater than 5 % of 60 by 23 , what is the number ?
Options: a ) 65 , b ) 40 , c ) 55 , d ) 30 , e ) 60
Rationale: "explanation : 65 / 100 * x - 5 / 100 * 60 = 23 65 / 100 * x - 3 = 23 65 / 100 * x = 26 x = 26 * 100 / 65 x = 40 answer : option b"
Answer: b
Question (other): 8 men and 2 boys working together can do 4 times as much work as a man and a boy . working capacity of man and boy is in the ratio
Options: a ) 1 : 2 , b ) 1 : 3 , c ) 2 : 1 , d ) 2 : 3 , e ) none of these
Rationale: explanation : let 1 man 1 day work = x 1 boy 1 day work = y then 8 x + 2 y = 4 ( x + y ) = > 4 x = 2 y = > x / y = 2 / 4 = > x : y = 1 : 2 option a
Answer: a
Question (general): the difference between the place value and the face value of 7 in the numeral 856973 is
Options: a ) 63 , b ) 6973 , c ) 5994 , d ) 6084 , e ) none of these
Rationale: ( place value of 7 ) - ( face value of 7 ) = ( 70 - 7 ) = 63 answer : option a
Answer: a
Question (general): if a person walks at 15 km / hr instead of 5 km / hr , he would have walked 20 km more . the actual distance traveled by him is ?
Options: a ) 50 km , b ) 76 km , c ) 18 km , d ) 10 km , e ) 97 km
Rationale: "let the actual distance traveled be x km . then , x / 5 = ( x + 20 ) / 15 10 x - 100 = > x = 10 km . answer : d"
Answer: d
Question (geometry): the diameter of a cylindrical tin is 4 cm and height is 5 cm . find the volume of the cylinder ?
Options: a ) 33 , b ) 45 , c ) 20 , d ) 77 , e ) 21
Rationale: "r = 2 h = 5 π * 2 * 2 * 5 = 20 π cc answer : c"
Answer: c
Question (physics): the sum of 3 consecutive numbers is definitely
Options: a ) positive . , b ) divisible by 2 . , c ) divisible by 4 . , d ) divisible by 3 . , e ) divisible by 5 .
Rationale: "if 1 st term is x : x + ( x + 1 ) + ( x + 2 ) = 3 x + 3 - - - > always divisible by 3 if 2 nd term is x : ( x - 1 ) + x + ( x + 1 ) = 3 x - - - > always divisible by 3 if 3 rd term is x : ( x - 2 ) + ( x - 1 ) + x = 3 x - 3 - - - > always divisible by 3 answer : d"
Answer: d
Question (general): for all even integers n , h ( n ) is defined to be the sum of the even integers between 6 and n , inclusive . what is the value of h ( 18 ) / h ( 10 ) ?
Options: a ) 1.8 , b ) 4 , c ) 6 , d ) 18 , e ) 60
Rationale: "concept : when terms are in arithmetic progression ( a . p . ) i . e . terms are equally spaced then mean = median = ( first + last ) / 2 and sum = mean * number of terms h ( 18 ) = [ ( 6 + 18 ) / 2 ] * 7 = 84 h ( 10 ) = ( 6 + 10 ) / 2 ] * 3 = 24 h ( 18 ) / h ( 10 ) = ( 84 ) / ( 24 ) ~ 4 answer : b"
Answer: b
Question (gain): 20 % of a 6 litre solution and 60 % of 4 litre solution are mixed . what percentage of the mixture of solution
Options: a ) 36 % , b ) 35 % , c ) 34 % , d ) 33 % , e ) 32 %
Rationale: 20 % of 6 litre is ( 6 * 20 / 100 ) = 1.2 litre 60 % of 4 litre is ( 60 * 4 / 100 ) = 2.4 litre the mixture is 3.6 litre so the percentage is ( 3.6 * 100 / 10 ) = 36 % answer : a
Answer: a
Question (gain): population of a city decreases by 10 % at the end of first year and increases by 10 % at the end of second year and again decreases by 10 % at the end of third year . if the population of the city at the end of third year is 4455 , then what was the population of the city at the beginning of the first year ?
Options: a ) 5000 , b ) 4500 , c ) 4950 , d ) 1000 , e ) 2000
Rationale: m . f = 90 / 100 * 110 * 100 * 90 / 100 = 81 * 11 / 1000 population before 3 yrs = i . q / m . f = 4455 * 1000 / 81 * 11 = 5000 answer : a
Answer: a
Question (physics): a contractor is engaged for 30 days on the condition thathe receives rs . 25 for each day he works & is fined rs . 7.50 for each day is absent . he gets rs . 425 in all . for how many days was he absent ?
Options: a ) 8 , b ) 10 , c ) 15 , d ) 17 , e ) 19
Rationale: 30 * 25 = 750 425 - - - - - - - - - - - 325 25 + 7.50 = 32.5 325 / 32.5 = 10 b
Answer: b
Question (physics): stalin and heather are 20 miles apart and walk towards each other along the same route . stalin walks at constant rate that is 1 mile per hour faster than heather ' s constant rate of 5 miles / hour . if heather starts her journey 20 minutes after stalin , how far from the original destination has heather walked when the two meet ?
Options: a ) 4 miles , b ) 6 miles , c ) 9 miles , d ) 10 miles , e ) 12 mile
Rationale: original distance between s and h = 20 miles . speed of s = 5 + 1 = 6 mph , speed of h = 5 mph . time traveled by h = t hours - - - > time traveled by s = t + 20 / 60 = t + 2 / 6 hours . now , the total distances traveled by s and h = 20 miles - - - > 6 * ( t + 2 / 6 ) + 5 * t = 20 - - - > t = 8 / 11 hours . thus h has traveled for 8 / 11 hours giving you a total distance for h = 5 * 8 / 11 ~ 4 miles . a is thus the correct answer . p . s . : based on the wording of the question , you should calculatehow far from theoriginal destination has heather walkedwhen the two meet . ' original destination ' for h does not make any sense . original destination for h was situated at a distance of 20 miles .
Answer: a
Question (other): what is the square root of 16 ?
Options: a ) 8 , b ) 4 , c ) 35 , d ) 42 , e ) 86
Rationale: "4 x 4 = 16 answer b"
Answer: b
Question (gain): a bag marked at $ 240 is sold for $ 120 . the rate of discount is ?
Options: a ) 10 % , b ) 25 % , c ) 20 % , d ) 50 % , e ) 45 %
Rationale: "rate of discount = 120 / 240 * 100 = 50 % answer is d"
Answer: d
Question (general): the average weight of 8 person ' s increases by 2 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 ) 70 kg , b ) 80 kg , c ) 81 kg , d ) 90 kg , e ) 91 kg
Rationale: "total weight increased = ( 8 x 2 ) kg = 16 kg . weight of new person = ( 65 + 16 ) kg = 81 kg . c )"
Answer: c
Question (general): the mean proportional between 4 and 9 is ?
Options: a ) 33 , b ) 77 , c ) 35 , d ) 88 , e ) 29
Rationale: "7 / 20 * 100 = 35 answer : b"
Answer: b
Question (gain): a man buy a book in rs 50 & sale it rs 100 . what is the rate of profit ? ? ?
Options: a ) 10 % , b ) 100 % , c ) 30 % , d ) 25 % , e ) 28 %
Rationale: "cp = 50 sp = 100 profit = 100 - 50 = 50 % = 50 / 50 * 100 = 100 % answer : b"
Answer: b
Question (physics): a cistern has a leak which would empty the cistern in 20 minutes . a tap is turned on which admits 6 liters a minute into the cistern , and it is emptied in 24 minutes . how many liters does the cistern hold ?
Options: a ) 480 , b ) 287 , c ) 720 , d ) 270 , e ) 927
Rationale: "1 / x - 1 / 20 = - 1 / 24 x = 120 120 * 6 = 720 answer : c"
Answer: c
Question (gain): a group of students was interviewed for that if it was asked whether or not they speak french and / or english . among those who speak french , 20 speak english well , while 60 of them do not speak english . if 60 % of students do not speak french , how many students were surveyed ?
Options: a ) 250 , b ) 225 , c ) 175 , d ) 195 , e ) 200
Rationale: "number of students who speak french are 60 + 20 = 80 of total students , the percentage of students who do not speak french was 60 % - - > percentage of who do is 40 % 80 - - - - - - - 40 % x - - - - - - - 100 % x = 80 * 100 / 40 = 200 = number of all students answer is e"
Answer: e