Cheukting/mathqa huggingface dataset:
Question (general): in the graduating class of a certain college , 48 percent of the students are male and 52 percent are female . in this class 40 percent of the male and 20 percent of the female students are 25 years old or older . if one student in the class is randomly selected , approximately what is the probability that he or she will be less than 25 years old ?
Options: a ) 0.9 , b ) 0.7 , c ) 0.45 , d ) 0.3 , e ) 0.25
Rationale: "percent of students who are 25 years old or older is 0.4 * 48 + 0.2 * 52 = ~ 30 , so percent of people who are less than 25 years old is 100 - 30 = 70 . answer : b ."
Answer: b
Question (physics): a train 300 m long , running with a speed of 54 km / hr will pass a tree in ?
Options: a ) 17 sec , b ) 16 sec , c ) 20 sec , d ) 14 sec , e ) 12 sec
Rationale: "speed = 54 * 5 / 18 = 15 m / sec time taken = 300 * 1 / 15 = 20 sec answer : c"
Answer: c
Question (general): a , b and c rents a pasture for rs . 899 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should c pay ?
Options: a ) 270 , b ) 279 , c ) 267 , d ) 255 , e ) 552
Rationale: "12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 9 / 29 * 899 = 279 answer : b"
Answer: b
Question (general): a student got twice as many sums wrong as he got right . if he attempted 27 sums in all , how many did he solve correctly ?
Options: a ) 12 , b ) 16 , c ) 18 , d ) 9 , e ) 12
Rationale: "explanation : suppose the boy got x sums right and 2 x sums wrong . then , x + 2 x = 27 3 x = 27 x = 9 . answer : d"
Answer: d
Question (general): the compound interest on a sum for 2 years is rs . 832 and the simple interest on the same sum for the same period is rs . 800 . the difference between the compound and simple interest for 3 years will be
Options: a ) rs . 48 , b ) rs . 98.56 , c ) rs . 66.56 , d ) rs . 66.58 , e ) none of these
Rationale: explanation : given that simple interest for 2 years is rs . 800 i . e . , simple interest for 1 st year is rs . 400 and simple interest for 2 nd year is also rs . 400 compound interest for 1 st year will be 400 and compound interest for 2 nd year will be 832 - 400 = 432 you can see that compound interest for 2 nd year is more than simple interest for 2 nd year by 432 - 400 = rs . 32 i . e , rs . 32 is the interest obtained for rs . 400 for 1 year rate , r = 100 × si / pt = ( 100 × 32 ) / ( 400 × 1 ) = 8 % difference between compound and simple interest for the 3 rd year = simple interest obtained for rs . 832 = prt / 100 = ( 832 × 8 × 1 ) / 100 = rs . 66.56 total difference between the compound and simple interest for 3 years = 32 + 66.56 = rs . 98.56 answer : option b
Answer: b
Question (general): when a merchant imported a certain item , he paid a 7 percent import tax on the portion of the total value of the item in excess of $ 1000 . if the amount of the import tax that the merchant paid was $ 94.50 , what was the total value of the item ?
Options: a ) $ 2,350 , b ) $ 2,850 , c ) $ 3,250 , d ) $ 3,400 , e ) $ 3,750
Rationale: let x be the value in excess of $ 1,000 . 0.07 x = 94.5 x = $ 1,350 the total value was $ 1,350 + $ 1,000 = $ 2,350 . the answer is a .
Answer: a
Question (gain): the owner of a furniture shop charges his customer 24 % more than the cost price . if a customer paid rs . 8463 for a computer table , then what was the cost price of the computer table ?
Options: a ) 6727 , b ) 6825 , c ) 6728 , d ) 6725 , e ) 2871
Rationale: ": cp = sp * ( 100 / ( 100 + profit % ) ) = 8463 ( 100 / 124 ) = rs . 6825 . answer : b"
Answer: b
Question (physics): 15 beavers , working together in a constant pace , can build a dam in 4 hours . how many hours will it take 20 beavers that work at the same pace , to build the same dam ?
Options: a ) 2 . , b ) 4 . , c ) 5 . , d ) 6 , e ) 3 .
Rationale: "total work = 15 * 4 = 60 beaver hours 20 beaver * x = 60 beaver hours x = 60 / 20 = 3 answer : e"
Answer: e
Question (physics): find the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 14 cm
Options: a ) 178 cm 2 , b ) 179 cm 2 , c ) 266 cm 2 , d ) 167 cm 2 , e ) 197 cm 2
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 14 ) = 266 cm 2 answer : c"
Answer: c
Question (general): the sum q of prime numbers that are greater than 60 but less than 70 is
Options: a ) 67 , b ) 128 , c ) 191 , d ) 197 , e ) 260
Rationale: a prime number is a number that has only two factors : 1 and itself . therefore , a prime number is divisible by two numbers only . let ' s list the numbers from 61 to 69 . 61 , 62 , 63 , 64 , 65 , 66 , 67 , 68 , 69 immediately we can eliminate the even numbers because they are divisible by 2 and thus are not prime . we are now left with : 61 , 63 , 65 , 67 , 69 we can next eliminate 65 because 65 is a multiple of 5 . we are now left with 61 , 63 , 67 , 69 . to eliminate any remaining values , we would look at those that are multiples of 3 . if you don ’ t know an easy way to do this , just start with a number that is an obvious multiple of 3 , such as 60 , and then keep adding 3 . we see that 60 , 63 , 66 , 69 are all multiples of 3 and therefore are not prime . thus , we can eliminate 63 and 69 from the list because they are not prime . finally , we are left with 61 and 67 , and we must determine whether they are divisible by 7 . they are not , and therefore they must be both prime . thus , the sum q of 61 and 67 is 128 . answer b .
Answer: b
Question (general): at the wholesale store you can buy an 8 - pack of hot dogs for $ 1.55 , a 20 - pack for $ 3.05 , and a 400 - pack for $ 22.95 . what is the greatest number of hot dogs you can buy at this store with $ 200 ?
Options: a ) 1,108 , b ) 3,300 , c ) 2,108 , d ) 2,124 , e ) 2,256
Rationale: "we have $ 200 and we have to maximize the number of hot dogs that we can buy with this amount . let ' s try to find out what is the maximum number of hot dogs that we can buy for a lesser amount of money , which in this case is 400 for $ 22.95 . for the sake of calculation , let ' s take $ 23 . 23 x 8 gives 184 , i . e . a total of 400 x 8 = 3200 hot dogs . we are left with ~ $ 16 . similarly , let ' s use $ 3 for calculation . we can buy 5 20 - pack hot dogs ( 3 x 5 ) , a total of 20 x 5 = 100 hot dogs . so we have 3300 hot dogs . 2108 looks far - fetched ( since we are not likely to be left with > $ 1.55 ) . hence , ( b ) 3300 ( answer b )"
Answer: b
Question (general): if n is a positive integer and the product of all integers from 1 to n , inclusive , is a multiple of 990 , what is the least possible value of n ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "you need to primarily find the primes of 990 : 2 , 3,3 , 5,11 the integer must contain all these primes by knowing 11 is an prime , we know the answer can be b , c , d or e as these all contain 11 . 11 = 1 , 2,3 , 4,5 , 6,7 , 8,9 , 10,11 11 contains the 2 , 3,5 and 11 explicitly and the second 3 comes from the 6 ( 2 * 3 ) , therefore the answer is 11 . this is because we know a number that contains all the primes of 990 will be a multiple of 990 . answer : b"
Answer: b
Question (general): the probability that a man will be alive for 10 more yrs is 1 / 2 & the probability that his wife will alive for 10 more yrs is 1 / 3 . the probability that none of them will be alive for 10 more yrs , is
Options: a ) 1 / 2 , b ) 1 , c ) 1 / 3 , d ) 3 / 4 , e ) 2
Rationale: "sol . required probability = pg . ) x p ( b ) = ( 1 — d x ( 1 — i ) = : x 1 = 1 / 3 ans . ( c )"
Answer: c
Question (general): if a * b = 2 a - 3 b + ab , then 3 * 5 + 5 * 3 is equal to
Options: a ) 22 , b ) 25 , c ) 26 , d ) 28 , e ) 23
Rationale: 3 * 5 + 5 * 3 = ( 2 x 3 - 3 x 5 + 3 x 5 ) + ( 2 x 5 - 3 x 3 + 5 x 3 ) = 22 answer a 22
Answer: a
Question (general): a special municipal payroll tax charges not tax on a payroll less than $ 200,000 and only 0.2 % on a company ’ s payroll above $ 200,000 . if belfried industries paid $ 200 in this special municipal payroll tax , then they must have had a payroll of ?
Options: a ) $ 180,000 , b ) $ 202,000 , c ) $ 220,000 , d ) $ 300,000 , e ) $ 2 , 200,000
Rationale: answer : d , ( with different approach ) : the 200 paid is 0.2 % of the additional amount above 200,000 . let it be x now 0.2 % of x = 200 therefore x = 100,000 total = 200,000 + x = 300,000
Answer: d
Question (general): if 25 ^ 5 × 5 ^ ( - 1 ) = ( 125 ) ^ x , then what is the value of x ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: 25 ^ 5 × 5 ^ ( - 1 ) = ( 125 ) ^ x ( 5 ^ 2 ) ^ 5 × 5 ^ ( - 1 ) = 5 ^ 3 x 5 ^ 10 x 5 ^ ( - 1 ) = 5 ^ 3 x ; since all of the bases are the same now , we can equate the exponents in the next step 10 - 1 = 3 x 9 = 3 x x = 3 ans . b ) 3
Answer: b
Question (physics): a lady starts from p towards q and realizes that at a point r , if he walks 50 km further he will be at a point s , which is as far away from r as it is from q . what is the distance between p and q if the distance between p and r is half the distance from r to q ? ( assume that p , q , r and s are all on the same straight line )
Options: a ) 150 km , b ) 200 km , c ) 250 km , d ) 125 km , e ) 155 km
Rationale: p ___ 50 _____ r ___ 50 _____ s ____ 50 ___ q the above figure gives the locations of p , r , s & q in relation to each other . answer : a
Answer: a
Question (other): how many odd factors does 250 have ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: "start with the prime factorization : 250 = 2 * 5 * 7 for odd factors , we put aside the factor of two , and look at the other prime factors . set of exponents = { 1 , 1 } plus 1 to each = { 2 , 2 } product = 2 * 2 = 4 therefore , there are 4 odd factors of 250 . answer : b ."
Answer: b
Question (general): in kaya ' s teacher ' s desk there are 24 pink highlighters , 28 yellow highlighters , and 25 blue highlighters . how many highlighters are there in all ?
Options: a ) 11 , b ) 22 , c ) 77 , d ) 33 , e ) 88
Rationale: "add the numbers of highlighters . 24 + 28 + 25 = 77 . answer is c ."
Answer: c
Question (physics): a train speeds past a pole in 10 seconds and a platform 50 m long in 20 seconds . its length is :
Options: a ) 30 m . , b ) 40 m . , c ) 60 m . , d ) 50 m . , e ) 70 m .
Rationale: "let the length of the train be x meters and its speed be y m / sec . they , x / y = 10 = > y = x / 10 x + 50 / 20 = x / 10 x = 50 m . answer : option d"
Answer: d
Question (general): the sum of two numbers is 528 and their h . c . f is 33 . the number of pairs of numbers satisfying the above condition is
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "let the required numbers be 33 a and 33 b . then 33 a + 33 b = 528 \ inline \ fn _ jvn \ rightarrow a + b = 16 . now , co - primes with sum 16 are ( 1,15 ) , ( 3,13 ) , ( 5,11 ) and ( 7,9 ) . \ inline \ fn _ jvn \ therefore required numbers are ( 33 x 1 , 33 x 15 ) , ( 33 x 3 , 33 x 13 ) , ( 33 x 5 , 33 x 11 ) , ( 33 x 7 , 33 x 9 ) the number of such pairs is 4 answer : a"
Answer: a
Question (general): the average age of 50 students in a class is 10 years . if teacher ' s age is also included then average increases 1 year then find the teacher ' s age ?
Options: a ) 59 , b ) 55 , c ) 61 , d ) 45 , e ) 36
Rationale: "total age of 50 students = 50 * 10 = 500 total age of 51 persons = 51 * 11 = 561 age of teacher = 561 - 500 = 61 years answer is c"
Answer: c
Question (general): the denominator of a fraction is 6 greater than the numerator . if the numerator and the denominator are increased by 1 , the resulting fraction is equal to 4 â  „ 5 . what is the value of the original fraction ?
Options: a ) 17 / 23 , b ) 23 / 29 , c ) 29 / 35 , d ) 31 / 37 , e ) 33 / 39
Rationale: "let the numerator be x . then the denominator is x + 6 . x + 1 / x + 7 = 4 / 5 . 5 x + 5 = 4 x + 28 . x = 23 . the original fraction is 23 / 29 . the answer is b ."
Answer: b
Question (general): consider the sets tn = { n , n + 1 , n + 2 , n + 3 , n + 4 ) , where n = 1 , 2 , 3 , … , 96 . how many of these sets contain 6 or any integral multiple thereof ( i . e . , any one of the numbers 6 , 12 , 18 , … ) ?
Options: a ) 80 , b ) 81 , c ) 82 , d ) 83 , e ) 84
Rationale: explanation : if n = 1 , then the set t 1 = { 1 , 23 , 45 } , and it does not have 6 or any multiples . n = 2 to n = 6 has 6 in the set . n = 7 , has the set t 7 = { 7 , 89 , 1011 } , and no 6 or multiples . so 1 in every 6 members do not have 6 or multiples of 6 . so , till n = 96 , there are 16 sets of “ 6 members ” ( 16 * 6 = 96 ) and 16 sets do not have 6 or its multiples , while the remaining 80 sets have . answer : a
Answer: a
Question (gain): car z travels 55 miles per gallon of gasoline when driven at a constant rate of 45 miles per hour , but travels 20 percent fewer miles per gallon of gasoline when driven at a constant rate of 60 miles per hour . how many miles does car z travel on 10 gallons of gasoline when driven at a constant rate of 60 miles per hour ?
Options: a ) 320 , b ) 375.2 , c ) 400 , d ) 408.3 , e ) 440
Rationale: the question stem asks us for the distance possible with 10 gallons of fuel at a constant speed of 60 miles per hour . we therefore first calculate the fuel efficiency at that speed . the stem tells us that at 45 miles / hour , the car will run 55 miles / gallon and at 60 miles / hour , that distance decreases by 20 % . we can therefore conclude that the car will travel 44 miles / gallon at a constant speed of 60 miles / gallon . with 10 gallons of fuel , the car can therefore travel 44 miles / gallon * 10 gallons = 440 miles . answer e .
Answer: e
Question (geometry): a certain farmer pays $ 70 per acre per month to rent farmland . how much does the farmer pay per month to rent a rectangular plot of farmland that is 360 feet by 605 feet ? ( 43,560 square feet = 1 acre )
Options: a ) $ 5,330 , b ) $ 3,360 , c ) $ 1,350 , d ) $ 360 , e ) $ 1050
Rationale: basically the question an error . 1 acre = 43,560 square feet and if it is then the answer is 1050 ( e )
Answer: e
Question (geometry): if a square mirror has a 20 - inch diagonal , what is the approximate perimeter t of the mirror , in inches ?
Options: a ) 40 , b ) 60 , c ) 80 , d ) 100 , e ) 120
Rationale: "if you draw the square and diagonal inside the square . u can see square becomes part of two triangles opposite to each other . and we know the property of the triangle , addition of two sides of triangle must be greater than its diagonal in order to complete the triangle . and each side must be less than 20 and perimeter t must be less than 80 , so we can eliminate answer choice c , d and e . so side 1 + side 2 > 20 , that means side 1 or side 2 must be > 10 . so we can eliminate the answer choice a . now we are left with is b"
Answer: b
Question (physics): a clock shows the time as 9 a . m . if the minute hand gains 6 minutes every hour , how many minutes will the clock gain by 6 p . m . ?
Options: a ) 30 min , b ) 35 min , c ) 45 min , d ) 50 min , e ) 54 min
Rationale: "there are 9 hours in between 9 a . m . to 6 p . m . 9 * 6 = 54 minutes . answer : e"
Answer: e
Question (general): 20 people went to a hotel for combine dinner party 12 of them spent rs . 70 each on their dinner and rest spent 4 more than the average expenditure of all the 20 . what was the total money spent by them .
Options: a ) 1628.4 , b ) 1534 , c ) 1453 , d ) 1496 , e ) none of these
Rationale: "solution : let average expenditure of 20 people be x . then , 20 x = 12 * 70 + 8 * ( x + 4 ) ; or , 20 x = 12 * 70 + 8 x + 32 ; or , x = 72.667 ; so , total money spent = 72.67 * 20 = rs . 1453.4 . answer : option c"
Answer: c
Question (general): how many integers k greater than 100 and less than 600 are there such that if the hundreds and the unit digits of k are reversed , the resulting integer is k + 99 ?
Options: a ) 40 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "not sure if this is the shortest . . but this is how i did this there are 8 sets of integers with hundreds and units digits exchanged that satisfies k + 99 . 1 . 102 | 201 ( satisfies k + 99 , where k = 102 ) 2 . 203 | 302 ( satisfies k + 99 , where k = 203 ) 3 . . . . 4 . 405 | 504 each set has 10 such numbers . 1 . 102 | 201 ( still k + 99 holds good ) 2 . 112 | 211 3 . 122 | 221 4 . 132 | 231 5 . . . . 6 . . . . 7 . . . . 8 . . . . 9 . 182 | 281 10 . 192 | 291 therefore , 4 sets with 10 such number in each set will give 4 x 10 = 40 integers . a"
Answer: a
Question (other): the ratio of the two natural numbers is 5 : 6 . if a certain number is added to both the numbers , the ratio becomes 7 : 8 . if the larger number exceeds the smaller number by 10 , find the number added ?
Options: a ) 17 , b ) 14 , c ) 10 , d ) 16 , e ) 20
Rationale: "let the two numbers be 5 x and 6 x . let the numbers added to both so that their ratio becomes 7 : 8 be k . ( 5 x + k ) / ( 6 x + k ) = 7 / 8 = > 40 x + 8 k = 42 x + 7 k = > k = 2 x . 6 x - 5 x = 10 = > x = 10 k = 2 x = 20 . answer : c"
Answer: c
Question (gain): what annual payment will discharge a debt of rs . 1060 due in 2 years at the rate of 5 % compound interest ?
Options: a ) 993.2 , b ) 551.25 , c ) 570.07 , d ) 543.33 , e ) 646.33
Rationale: "explanation : let each installment be rs . x . then , x / ( 1 + 5 / 100 ) + x / ( 1 + 5 / 100 ) 2 = 1060 820 x + 1060 * 441 x = 570.07 so , value of each installment = rs . 570.07 answer : option c"
Answer: c
Question (general): 50 % of the population of a village is 23040 . the total population of the village is ?
Options: a ) 32256 , b ) 24000 , c ) 44936 , d ) 46080 , e ) none
Rationale: "answer ∵ 50 % of p = 23040 ∴ p = ( 23040 x 100 ) / 50 = 46080 correct option : d"
Answer: d
Question (physics): if the perimeter of a rectangular house is 1400 m , its length when its breadth is 300 m is ?
Options: a ) 300 , b ) 400 , c ) 500 , d ) 600 , e ) 700
Rationale: 2 ( l + 300 ) = 1400 = > l = 400 m answer : b
Answer: b
Question (gain): the price of an item is discounted 4 percent on day 1 of a sale . on day 2 , the item is discounted another 4 percent , and on day 3 , it is discounted an additional 10 percent . the price of the item on day 3 is what percentage of the sale price on day 1 ?
Options: a ) 82.5 % , b ) 89.9 % , c ) 87.7 % , d ) 86.4 % , e ) 83.3 %
Rationale: "let initial price be 100 price in day 1 after 4 % discount = 96 price in day 2 after 4 % discount = 92.16 price in day 3 after 10 % discount = 82.94 so , price in day 3 as percentage of the sale price on day 1 will be = 82.94 / 96 * 100 = > 86.4 % answer will definitely be ( d )"
Answer: d
Question (general): if a # b = ab – b + b ^ 2 , then 3 # 4 =
Options: a ) 2 , b ) 8 , c ) 15 , d ) 24 , e ) 35
Rationale: "solution - simply substitute 3 and 4 in equation in the place of a and b respectively . 3 # 4 = 3 * 4 - 4 + 4 ^ 2 = 12 - 4 + 16 = 24 . ans d"
Answer: d
Question (other): what number has a 4 : 1 ratio to the number 100 ?
Options: a ) 40 , b ) 200 , c ) 400 , d ) 800 , e ) 4000
Rationale: "4 : 1 = x : 100 x = 4 * 100 x = 400 answer : c"
Answer: c
Question (gain): after 10 % of the inhabitants of a village disappeared , a panic set in during which 25 % of the remaining inhabitants left the village . at that time , the population was reduced to 5535 . what was the number of original inhabitants ?
Options: a ) 7900 , b ) 8200 , c ) 8500 , d ) 8800 , e ) 9100
Rationale: "let the total number of original inhabitants be x . ( 75 / 100 ) * ( 90 / 100 ) * x = 5535 ( 27 / 40 ) * x = 5535 x = 5535 * 40 / 27 = 8200 the answer is b ."
Answer: b
Question (general): is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 42 , then how old is b ?
Options: a ) 16 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 42 5 x = 40 = > x = 8 hence , b ' s age = 2 x = 16 years . answer : a"
Answer: a
Question (gain): today joelle opened an interest - bearing savings account and deposited $ 7,000 . if the annual interest rate is 5 percent compounded interest , and she neither deposits nor withdraws money for exactly 2 years , how much money will she have in the account ?
Options: a ) $ 7727.50 , b ) $ 7717.50 , c ) $ 7737.50 , d ) $ 7747.50 , e ) $ 7757.50
Rationale: "interest for 1 st year = 7000 * 5 / 100 = 350 interest for 2 nd year = 7350 * 5 / 100 = 367.50 total = 7000 + 350 + 367.50 = 7717.50 answer : b"
Answer: b
Question (general): last year the range of the annual bonus of the 100 employees at company x was $ 20000 . if the annual bonus of each of the 100 employees this year is 10 percent greater than it was last year , what is the range of the annual bonus of the 100 employees this year ?
Options: a ) $ 27000 , b ) $ 22000 , c ) $ 33000 , d ) $ 16000 , e ) $ 43000
Rationale: let the lowest bonus be x . therefore , highest bonus is x + 20000 . now bonus of each employee is increased by 10 % . therefore the bonus will remain arranged in the same order as before . or lowest bonus = 1.1 x and highest = 1.1 * ( x + 20000 ) or range = highest - lowest = 1.1 * ( x + 20000 ) - 1.1 x = 22000 , hence , b
Answer: b
Question (gain): the list price of an article is rs . 65 . a customer pays rs . 56.16 for it . he was given two successive discounts , one of them being 10 % . the other discount is ?
Options: a ) 3 % , b ) 4 % , c ) 7 % , d ) 8 % , e ) 9 %
Rationale: "explanation : 65 * ( 90 / 100 ) * ( ( 100 - x ) / 100 ) = 56.16 x = 4 % answer : option b"
Answer: b
Question (geometry): a spirit and water solution is sold in a market . the cost per liter of the solution is directly proportional to the part ( fraction ) of spirit ( by volume ) the solution has . a solution of 1 liter of spirit and 1 liter of water costs 50 cents . how many cents does a solution of 1 liter of spirit and 3 liters of water cost ?
Options: a ) 13
b ) 33
c ) 56
d ) 50
e ) 52
Rationale: c . 50 cents yes , ensure that you understand the relation thoroughly ! cost per liter = k * fraction of spirit 50 cents is the cost of 2 liters of solution ( 1 part water , 1 part spirit ) . so cost per liter is 25 cents . fraction of spirit is 1 / 2 . 25 = k * ( 1 / 2 ) k = 50 cost per liter = 50 * ( 1 / 4 ) ( 1 part spirit , 3 parts water ) cost for 4 liters = 50 * ( 1 / 4 ) * 4 = 50 cents d . 50 cents
Answer: d
Question (physics): two trains are running in opposite directions in the same speed . the length of each train is 120 meter . if they cross each other in 12 seconds , the speed of each train ( in km / hr ) is
Options: a ) 30 km / hr , b ) 36 km / hr , c ) 80 km / hr , d ) 90 km / hr , e ) none of these
Rationale: "explanation : distance covered = 120 + 120 = 240 m time = 12 s let the speed of each train = x . then relative velocity = x + x = 2 x 2 x = distance / time = 240 / 12 = 20 m / s speed of each train = x = 20 / 2 = 10 m / s = 10 * 18 / 5 km / hr = 36 km / hr option b"
Answer: b
Question (geometry): what is the measure of the radius of the circle inscribed in a triangle whose sides measure 8 , 15 and 21 units ?
Options: a ) 8.5 units , b ) 2.6 units , c ) 3 units , d ) 5 units , e ) 12 units
Rationale: "sides are 8 , 15 and 21 . . . thus it is right angle triangle since 21 ^ 2 = 8 ^ 2 + 15 ^ 2 therefore , area = 1 / 2 * 15 * 8 = 60 we have to find in - radius therefore , area of triangle = s * r . . . . where s = semi - perimeter and r = in - radius now s = semi - perimeter = 21 + 15 + 8 / 2 = 22 thus , 60 = 22 * r and hence r = in - radius = 2.6 option b"
Answer: b
Question (general): if ( 4 - x ) / ( 5 + x ) = x , what is the value of x ^ 2 + 6 x - 4 ?
Options: a ) - 3 , b ) 0 , c ) 2 , d ) 4 , e ) 6
Rationale: "( 4 - x ) = x * ( 5 + x ) ( 4 - x ) = 5 x + x ^ 2 0 = x ^ 2 + 6 x - 4 the answer is b ."
Answer: b
Question (general): a certain bus driver is paid a regular rate of $ 16 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 $ 1004 in total compensation , how many total hours did he work that week ?
Options: a ) 36 , b ) 40 , c ) 44 , d ) 48 , e ) 53
Rationale: "for 40 hrs = 40 * 16 = 640 excess = 1004 - 640 = 364 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 364 / 28 = 13 total hrs = 40 + 13 = 53 answer e 53"
Answer: e