Cheukting/mathqa huggingface dataset:
Question (general): when positive integer x is divided by positive integer y , the remainder is 1.44 . if x / y = 96.12 , what is the value of y ?
Options: a ) 96 , b ) 75 , c ) 48 , d ) 25 , e ) 12
Rationale: "when positive integer x is divided by positive integer y , the remainder is 1.44 - - > x = qy + 1.44 ; x / y = 96.12 - - > x = 96 y + 0.12 y ( so q above equals to 96 ) ; 0.12 y = 1.44 - - > y = 12 . answer : e ."
Answer: e
Question (physics): bruce and anne can clean their house in 4 hours working together at their respective constant rates . if anne ’ s speed were doubled , they could clean their house in 3 hours working at their respective rates . how many e hours does it currently take anne to clean the house on her own ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 12 , e ) 14
Rationale: lets suppose anne and bruce take a and b hrs working separately so in 1 hour they can together finish 1 / a + 1 / b portion of the work which equals 1 / 4 ( as the work is completed in 4 hours ) after anne doubles her rate of work the portion completed by the both is 1 / a + 2 / b which is equal to 1 / 3 ( as the work is completed in e = 3 hours ) solving these 2 equations we can find b as 12 so , d
Answer: d
Question (general): sophia finished 23 of a book . she calculated that she finished 90 more pages than she has yet to read . how long is her book ?
Options: a ) 180 , b ) 200 , c ) 250 , d ) 270 , e ) 300
Rationale: "let x be the total number of pages in the book , then she finished 23 ⋅ x pages . then she has x − 23 ⋅ x = 13 ⋅ x pages left . 23 ⋅ x − 13 ⋅ x = 90 13 ⋅ x = 90 x = 270 . so answer is d ."
Answer: d
Question (general): on dividing a n by 9 , remainder is 8 . the quotient obtained when divided by 11 , leaves remainder 9 . now the quotient when divided by 13 , leaves remainder 8 . find the remainder when when the n is divided by 1287
Options: a ) 871 , b ) 881 , c ) 891 , d ) 904 , e ) 987
Rationale: take from the last step division suppose no . is n which is divided by 13 and remainder 8 = 13 n + 8 now 13 n + 8 will be the no . which is divided by 11 and remainder is 9 = [ 11 * ( 13 n + 8 ) ] + 9 now this no . is used for the very first step which is divider is 9 and remainder is 8 = { 9 * [ 11 * ( 13 n + 8 ) ] + 9 } + 8 solve and ans is 881 answer : b
Answer: b
Question (general): a sports retailer ordered white and yellow tennis balls in equal number but the dispatch clerk of the tennis ball company erred and dispatched 50 extra yellow balls and making ratio of white balls to yellow balls 7 / 11 . how many tennis balls did the retailer order originally .
Options: a ) 17.5 , b ) 130 , c ) 175 , d ) 195 , e ) 220
Rationale: "white : yellow = x : ( x + 50 ) = 7 : 11 - - > 11 x = 7 x + 350 - - > x = 87.5 . the total # of balls originally x + x = 87.5 + 87.5 = 175 . answer : c ."
Answer: c
Question (physics): two cars are traveling in the same direction along the same route . the red car travels at a constant speed of 10 miles per hour , and the black car is traveling at a constant speed of 50 miles per hour . if the red car is 20 miles ahead of the black car , how many hours will it take the black car to overtake the red car ?
Options: a ) 0.1 , b ) 0.5 , c ) 1 , d ) 1.2 , e ) 2
Rationale: "option b 20 + 10 t = 50 t t = 0.5"
Answer: b
Question (geometry): an equilateral triangle and three squares are combined as shown above , forming a shape of area 48 + 4 √ 3 . what is the perimeter of the shape formed by the triangle and squares ?
Options: a ) 18
b ) 27
c ) 36
d ) 48
e ) 64
Rationale: triangle area = root ( 3 ) s ^ 2 / 4 area of 3 squares together = 3 s ^ 2 root ( 3 ) s ^ 2 / 4 + 3 s ^ 2 = 48 + 4 root ( 3 ) root ( 3 ) / 4 s ^ 2 = 4 root ( 3 ) s ^ 2 = 16 = > s = 4 there are 3 sides of each square = 3 ( 4 ) ( 3 ) = 36 option c
Answer: c
Question (gain): if 10 litres of an oil of rs . 54 per litres be mixed with 5 litres of another oil of rs . 66 per litre then what is the rate of mixed oil per litre ?
Options: a ) rs . 49.17 , b ) rs . 58 , c ) rs . 54.17 , d ) rs . 55.33 , e ) none of the above
Rationale: "54 * 10 = 540 66 * 5 = 330 870 / 15 = 58 answer : b"
Answer: b
Question (physics): a tank is filled by 3 pipes a , b , c in 10 hours . pipe c is twice as fast as b and b is twice as fast as a . how much will pipe a alone take to fill the tank ?
Options: a ) 20 hr , b ) 52 hr , c ) 70 hr , d ) 66 hr , e ) 48 hr
Rationale: "suppose pipe a alone take x hours to fill the tank then pipe b and c will take x / 2 and x / 4 hours respectively to fill the tank . 1 / x + 2 / x + 4 / x = 1 / 10 7 / x = 1 / 10 x = 70 hours answer is c"
Answer: c
Question (general): the difference between a positive proper fraction and its reciprocal is 9 / 20 . the fraction is
Options: a ) 4 / 5 , b ) 7 / 11 , c ) 7 / 13 , d ) 7 / 15 , e ) 8 / 11
Rationale: let the required fraction be x . then 1 - x = 9 x 20 1 - x 2 = 9 x 20 20 - 20 x 2 = 9 x 20 x 2 + 9 x - 20 = 0 20 x 2 + 25 x - 16 x - 20 = 0 5 x ( 4 x + 5 ) - 4 ( 4 x + 5 ) = 0 ( 4 x + 5 ) ( 5 x - 4 ) = 0 x = 4 / 5 a )
Answer: a
Question (physics): rahul can do a work in 3 days while rajesh can do the same work in 2 days . both of them finish the work together and get $ 2250 . what is the share of rahul ?
Options: a ) $ 50 , b ) $ 40 , c ) $ 60 , d ) $ 100 , e ) $ 900
Rationale: "rahul ' s wages : rajesh ' s wages = 1 / 3 : 1 / 2 = 2 : 3 rahul ' s share = 2250 * 2 / 5 = $ 900 answer is e"
Answer: e
Question (physics): a can complete the job in 3 hours and b can complete the same job in 3 hours . a works for 1 hour and then b joins and both complete the job . what fraction of the job did b complete
Options: a ) 1 / 6 , b ) 3 / 10 , c ) 1 / 2 , d ) 5 / 6 , e ) 8 / 9
Rationale: 1 / 6 = a
Answer: a
Question (physics): hcf and lcm two numbers are 20 and 396 respectively . if one of the numbers is 36 , then the other number is ?
Options: a ) 36 , b ) 66 , c ) 132 , d ) 264 , e ) 220
Rationale: 20 * 396 = 36 * x x = 220 answer : e
Answer: e
Question (geometry): a bag has 1 , 3 , 5 , 7 , 9,11 and 13 cm sticks . find the probability that they they will form a triangle if 3 sticks are drawn ?
Options: a ) 13 / 35 , b ) 14 / 35 , c ) 1 / 2 , d ) 5 / 6 , e ) 5 / 5
Rationale: explanation : total cases : = 7 c 3 = 35 favourable cases : ( 3 , 5,7 ) , ( 3 , 7,9 ) , ( 3 , 9,11 ) , ( 3 , 11,13 ) , ( 5 , 7,9 ) , ( 5 , 7,11 ) , ( 5 , 9,11 ) , ( 5 , 9,13 ) , ( 5 , 11,13 ) , ( 7 , 9,11 ) , ( 7 , 9,13 ) , ( 7 , 11,13 ) , ( 9 , 11,13 ) = total 13 . [ others are rejected because to form a triangle it is necessary that the sum of 2 small sides must be greater than the third greatest side . ] hence ( a ) is correct answer . answer : a
Answer: a
Question (general): a number whose fifth part increased by 5 is equal to its fourth part diminished by 5 , is
Options: a ) 160 , b ) 180 , c ) 200 , d ) 220 , e ) none of these
Rationale: "x / 5 + 5 = x / 4 - 5 = > x / 5 - x / 4 = 10 x / 20 = 10 = > x = 200 answer : c ."
Answer: c
Question (physics): a train running at the speed of 60 km / hr crosses a pole in 15 seconds . what is the length of the train ?
Options: a ) 187 m , b ) 250 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 * 15 ) m = 250 m . answer : b"
Answer: b
Question (general): what is the least number which should be added to 2982 so that the sum is exactly divisible by 5 , 6 , 4 , and 3 ?
Options: a ) 14 , b ) 18 , c ) 22 , d ) 26 , e ) 30
Rationale: "l . c . m . of 5 , 6 , 4 and 3 = 60 . when dividing 2982 by 60 , the remainder is 42 . the number to be added = 60 - 42 = 18 . the answer is b ."
Answer: b
Question (other): the ratio of toddlers to infants at a day care center is 7 to 3 . if 12 more infants join the day care to change the ratio to 7 to 5 , how many toddlers are there at this day care center ?
Options: a ) 24 , b ) 36 , c ) 42 , d ) 72 , e ) 120
Rationale: 5 x - 3 x = 12 so , 2 x = 6 hence no of toddlers is 6 * 7 = 42 answer will be ( c ) 42
Answer: c
Question (general): if x and y are integers such that | y + 3 | ≤ 3 and 2 y – 3 x + 6 = 0 , what is the least possible value e of the product xy ?
Options: a ) - 12 , b ) - 3 , c ) 0 , d ) 2 , e ) none of the above
Rationale: how to deal with inequalities involving absolute values ? first example shows us the so callednumber case in this case we have | y + 3 | ≤ 3 which is generalized | something | ≤ some number . first we solve as if there were no absolute value brackets : y + 3 ≤ 3 y ≤ 0 so y is 0 or negative second scenario - remove the absolute value brackets . put a negative sign around the other side of the inequality , andflip the sign : y + 3 > = - 3 y > = - 6 therefore we have a possible range for y : - 6 = < y < = 0 ok , so far so good , we ' re half way through . what about x ? here ' s the formula : 2 y – 3 x + 6 = 0 , rewrite it as 2 y + 6 = 3 x . you can say that 2 y + 6 is a multiple of 3 ( = 3 x ) . so all values which must be integer must also satisfy this constraint . i ' m just saying that , so it ' s easier to evaluate all the possible numbers ( - 6 , - 3 , 0 ) . if you plug in y = 0 , x will be 2 and xy = 0 as the lowest possible value e . hence , answer choice c is the one to go .
Answer: c
Question (physics): without stoppages , a train travels certain distance with an average speed of 400 km / h , and with stoppages , it covers the same distance with an average speed of 360 km / h . how many minutes per hour the train stops ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "due to stoppages , it covers 40 km less . time taken to cover 40 km = 40 â  „ 400 h = 1 â  „ 10 h = 1 â  „ 10 ã — 60 min = 6 min answer d"
Answer: d
Question (physics): express a speed of 18 kmph in meters per second ?
Options: a ) 10 mps , b ) 06 mps , c ) 09 mps , d ) 05 mps , e ) 11 mps
Rationale: d 5 mps 18 * 5 / 18 = 5 mps
Answer: d
Question (gain): two men started from the same place walk at the rate of 10 kmph and 12 kmph respectively . what time will they take to be 16 km apart , if they walk in the same direction ?
Options: a ) 5 hours , b ) 6 hours , c ) 8 hours , d ) 16 hours , e ) 12 hours
Rationale: "to be 2 km apart they take 1 hour to be 10 km apart they take = 1 / 2 * 16 = 8 hours answer is c"
Answer: c
Question (general): each of the 30 boxes in a certain shipment weighs either 10 pounds or 20 pounds , and the average ( arithmetic mean ) weight of the boxes in the shipment is 18 pounds . if the average weight of the boxes in the shipment is to be reduced to 15 pounds by removing some of the 20 - pound boxes , how many 20 - pound boxes must be removed ?
Options: a ) 8 , b ) 12 , c ) 18 , d ) 20 , e ) 24
Rationale: "if the average of 10 - pound and 20 - pound boxes is 18 , the ratio of 10 - pound boxes : 20 - pound boxes is 1 : 4 . so out of 30 boxes , 6 are 10 - pound boxes and 24 are 20 - pound boxes . if the average of 10 and 20 - pound boxes is to be 15 , the ratio of 10 - pound boxes : 20 - pound boxes should be 1 : 1 . the number of 10 pound boxes remain the same so we still have 6 of them . to get a ratio of 1 : 1 , the number of 20 - pound boxes must be 6 . we need to remove 18 of the 20 - pound boxes . the answer is c ."
Answer: c
Question (physics): a train 280 m long , running with a speed of 72 km / hr will pass a tree in ?
Options: a ) 17 sec , b ) 16 sec , c ) 18 sec , d ) 14 sec , e ) 12 sec
Rationale: "speed = 72 * 5 / 18 = 20 m / sec time taken = 280 * 1 / 20 = 14 sec answer : d"
Answer: d
Question (general): in a coconut grove , ( x + 4 ) trees yield 60 nuts per year , x trees yield 120 nuts per year and ( x – 4 ) trees yield 180 nuts per year . if the average yield per year per tree be 100 , find x .
Options: a ) 3 , b ) 4 , c ) 8 , d ) 9 , e ) none of the above
Rationale: ( x + 4 ) × 60 + x × 120 + ( x − 4 ) × 180 / ( x + 4 ) + x + ( x − 4 ) = 100 ⇒ 360 x − 480 / 3 x = 100 ⇒ 60 x = 480 ⇒ x = 8 answer c
Answer: c
Question (general): what is the sum of the greatest common factor and the lowest common multiple of 12 and 36 ?
Options: a ) 48 , b ) 22 , c ) 32 , d ) 36 , e ) 38
Rationale: "prime factorization of 12 = 2 x 2 x 3 prime factorization of 36 = 2 x 2 x 3 x 3 gcf = 12 lcm = 36 sum = 48 . answer a ."
Answer: a
Question (general): what is the sum of all the prime numbers greater than 30 but less than 50 ?
Options: a ) 126 , b ) 199 , c ) 198 , d ) 188 , e ) 122
Rationale: "required sum = ( 31 + 37 + 41 + 43 + 47 ) = 199 note : 1 is not a prime number answer b"
Answer: b
Question (physics): in one hour , a boat goes 16 km along the stream and 6 km against the stream . the speed of the boat in still water ( in km / hr ) is :
Options: a ) 3 , b ) 11 , c ) 8 , d ) 9 , e ) 10
Rationale: "solution speed in still water = 1 / 2 ( 16 + 6 ) kmph . = 11 kmph . answer b"
Answer: b
Question (general): what is the sum of the integers from - 150 to 155 , inclusive ?
Options: a ) 865 , b ) 955 , c ) 1050 , d ) 765 , e ) 750
Rationale: "in an arithmetic progression , the nth term is given by tn = a + ( n - 1 ) d here tn = 155 , a = - 150 , d = 1 hence , 155 = - 150 + ( n - 1 ) or n = 306 sum of n terms can be calculated by sn = n / 2 ( a + l ) a = first term , l = last term , n = no . of terms sn = 306 * ( - 150 + 155 ) / 2 sn = 306 * 5 / 2 = 765 answer : d"
Answer: d
Question (physics): how long does a train 120 m long running at the speed of 70 km / hr takes to cross a bridge 150 m length ?
Options: a ) 12.7 sec , b ) 13.9 sec , c ) 18.1 sec , d ) 17.1 sec , e ) 19.7 sec
Rationale: "speed = 70 * 5 / 18 = 19.4 m / sec total distance covered = 120 + 150 = 270 m . required time = 270 / 19.4 ' = 13.9 sec . answer : b"
Answer: b
Question (physics): in a garden , there are 10 rows and 12 columns of mango trees . the distance between the two trees is 2 metres and a distance of two metres is left from all sides of the boundary of the garden . what is the length of the garden ?
Options: a ) 22 , b ) 24 , c ) 26 , d ) 28 , e ) 30
Rationale: "between the 12 mango trees , there are 11 gaps and each gap has 2 meter length also , 2 meter is left from all sides of the boundary of the garden . hence , length of the garden = ( 11 ã — 2 ) + 2 + 2 = 26 meter answer is c ."
Answer: c
Question (general): a palindrome is a number that reads the same forward and backward , such as 121 . how many odd , 4 - digit numbers are palindromes ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 90 , e ) 2500
Rationale: first recognize you only need to consider the first two digits ( because the second two are just the first two flipped ) there are 90 possibilities for the first two digits of a 4 digit number , 10 - 99 inclusive . everything starting with a 1 , 3,5 , 7,9 will be odd , which is 5 / 9 ths of the combinations . 5 / 9 * 90 = 50 answer : c
Answer: c
Question (general): in an aquarium there is 14 purple fish , 8 orange fish , 12 pink fish , 3 golden fish . how many fish are there in an aquarium ?
Options: a ) 27 , b ) 37 , c ) 17 , d ) 47 , e ) 07
Rationale: 14 + 8 + 12 + 3 = 37 . answer is b
Answer: b
Question (general): last year , for every 100 million vehicles that traveled on a certain highway , 100 vehicles were involved in accidents . if 2 billion vehicles traveled on the highway last year , how many of those vehicles were involved in accidents ? ( 1 billion = 1,000 , 000,000 )
Options: a ) 500 , b ) 1500 , c ) 2500 , d ) 2000 , e ) 1000
Rationale: "to solve we will set up a proportion . we know that “ 100 million vehicles is to 100 accidents as 2 billion vehicles is to x accidents ” . to express everything in terms of “ millions ” , we can use 2,000 million rather than 2 billion . creating a proportion we have : 100 / 100 = 2,000 / x cross multiplying gives us : 100 x = 2,000 * 100 x = 20 * 100 = 2000 answer : d"
Answer: d
Question (gain): two men started from the same place walk at the rate of 10 kmph and 12 kmph respectively . what time will they take to be 40 km apart , if they walk in the same direction ?
Options: a ) 5 hours , b ) 40 hours , c ) 8 hours , d ) 20 hours , e ) 30 hours
Rationale: "to be 2 km apart they take 1 hour to be 10 km apart they take = 1 / 2 * 40 = 20 hours answer is d"
Answer: d
Question (general): the population of locusts in a certain swarm doubles every two hours . if 4 hours ago there were 1000 locusts in the swarm , in approximately how many hours will the swarm population exceed 128000 locusts ?
Options: a ) 12 , b ) 8 , c ) 4 , d ) 10 , e ) 16
Rationale: - 4 hours : 1,000 - 2 hours : 2,000 now : 4,000 + 2 hours : 8,000 + 4 hours : 16,000 + 6 hours : 32,000 + 8 hours : 64,000 + 10 hours : 128,000 answer : d
Answer: d
Question (geometry): an error 2 % in excess ismade while measuring the side ofa square . the % of error in the calculated area of the square is ?
Options: a ) 4.00 %
b ) 4.04 %
c ) 4.16 %
d ) 4.30 %
e ) 5 %
Rationale: 100 cm is read as 102 cm . a 1 = ( 100 x 100 ) cm 2 and a 2 ( 102 x 102 ) cm 2 . ( a 2 - a 1 ) = [ ( 102 ) 2 - ( 100 ) 2 ] = ( 102 + 100 ) x ( 102 - 100 ) = 404 cm 2 . percentage error = 404 x 100 % = 4.04 % 100 x 100 b
Answer: b
Question (general): if x is the product of the positive integers from 1 to 9 , inclusive , and if i , k , m , and p are positive integers such that x = 2 i 3 k 5 m 7 px = 2 i 3 k 5 m 7 p , then i + k + m + p =
Options: a ) 4 , b ) 7 , c ) 8 , d ) 11 , e ) 13
Rationale: "x = 9 ! = 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = ( 3 ^ 2 ) * ( 2 ^ 3 ) * 7 * ( 2 * 3 ) * 5 * 2 ^ 2 * 3 * 2 * 1 = 2 ^ 7 * 3 ^ 4 * 5 * 7 = 2 ^ i * 3 ^ k * 5 ^ m * 7 ^ p i + k + m + p = 7 + 4 + 1 + 1 = 13 answer e"
Answer: e
Question (other): of the diplomats attending a summit conference , 22 speak french , 32 do not speak russian , and 20 % of the diplomats speak neither french nor russian . if 10 % of the diplomats speak both languages , then how many diplomats attended the conference ?
Options: a ) 72 , b ) 96 , c ) 100 , d ) 120 , e ) 150
Rationale: "{ total } = { french } + { russian } - { both } + { neither } { total } = 22 + ( { total } - 32 ) - ( 0.1 * { total } ) + 0.2 * { total } solving gives { total } = 100 . answer : c ."
Answer: c
Question (gain): a football team lost 5 yards and then gained 10 . what is the team ' s progress ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: "for lost , use negative . for gain , use positive . progress = - 5 + 10 = 5 yards c"
Answer: c
Question (general): find the sum of first 20 natural numbers
Options: a ) 470 , b ) 210 , c ) 465 , d ) 463 , e ) 485
Rationale: "explanation : sum of n natural numbers = n ( n + 1 ) / 2 = 20 ( 20 + 1 ) / 2 = 20 ( 21 ) / 2 = 210 answer : option b"
Answer: b
Question (gain): weights of two friends ram and shyam are in the ratio 2 : 5 . if ram ' s weight is increased by 10 % and total weight of ram and shyam become 82.8 kg , with an increases of 15 % . by what percent did the weight of shyam has to be increased ?
Options: a ) 17 % , b ) 10 % , c ) 21 % , d ) 16 % , e ) none
Rationale: "solution : given ratio of ram and shayam ' s weight = 2 : 5 hence , ( x - 15 ) / ( 15 - 10 ) = 2 / 5 or , x = 17 % . answer : option a"
Answer: a
Question (general): what is the tens digit of 36 ^ 12 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "36 ^ 10 = 6 ^ 24 ( 6 ^ 2 ) = 6 * 6 = 36 ( 6 ^ 3 ) = 36 * 6 = . 16 ( 6 ^ 4 ) = . 16 * 6 = . . 96 ( 6 ^ 5 ) = . . 96 * 6 = . . 76 ( 6 ^ 6 ) = . . 76 * 6 = . . . 56 ( 6 ^ 7 ) = . . . . 56 * 6 = . . . . 36 if you see there is a pattern here in tens digits 3 , 1,9 , 7,5 , 3,1 and so on . . . continue the pattern up to 6 ^ 24 ( dont actually calculate full values ) and answer is e : 9"
Answer: e
Question (general): the smallest number which when diminished by 8 , is divisible 8 , 16 , 24 , 32 and 40 is :
Options: a ) 1008 , b ) 1015 , c ) 488 , d ) 490 , e ) 590
Rationale: "required number = ( l . c . m . of 8 , 16 , 24 , 32 , 40 ) + 8 = 480 + 8 = 488 answer : option c"
Answer: c
Question (general): how many numbers from 2 to 15 are exactly divisible by 2 ?
Options: a ) a ) 2 , b ) b ) 3 , c ) c ) 5 , d ) d ) 7 , e ) e ) 8
Rationale: "2 / 2 = 1 and 15 / 2 = 7 7 - 1 = 6 6 + 1 = 7 numbers . answer : d"
Answer: d
Question (geometry): the area of a triangle is with base 3 m and height 4 m ?
Options: a ) 4 m 2 , b ) 6 m 2 , c ) 18 m 2 , d ) 19 m 2 , e ) 12 m 2
Rationale: "1 / 2 * 3 * 4 = 6 m 2 answer : b"
Answer: b
Question (general): calculate 469160 x 9999 = ?
Options: a ) 4691130840 , b ) 4686970743 , c ) 4691100843 , d ) 4586870843 , e ) none
Rationale: "answer 469160 x 9999 = 469160 x ( 10000 - 1 ) = 4691600000 - 469160 = 4691130840 . option : a"
Answer: a
Question (general): the average age of students of a class is 15.8 years . the average age of boys in the class is 16.4 years and that of the girls is 15.4 years , the ratio of the number of boys to the number of girls in the class is :
Options: a ) 2 : 9 , b ) 2 : 3 , c ) 2 : 1 , d ) 2 : 2 , e ) 2 : 6
Rationale: "explanation : let the ratio be k : 1 . then , k * 16.4 + 1 * 15.4 = ( k + 1 ) * 15.8 < = > ( 16.4 - 15.8 ) k = ( 15.8 - 15.4 ) < = > k = 0.4 / 0.6 = 2 / 3 . required ratio = 2 / 3 : 1 = 2 : 3 . answer : b"
Answer: b
Question (gain): at what rate percent on simple interest will rs . 850 amount to rs . 950 in 5 years ?
Options: a ) 2.35 % , b ) 5.95 % , c ) 4.35 % , d ) 5.33 % , e ) 6.33 %
Rationale: "100 = ( 850 * 5 * r ) / 100 r = 2.35 % answer : a"
Answer: a
Question (probability): if 4 people are selected from a group of 9 married couples , what is the probability that none of them would be married to each other ?
Options: a ) 1 / 33 , b ) 2 / 85 , c ) 1 / 3 , d ) 56 / 85 , e ) 11 / 85
Rationale: if we are to select 4 people from 9 couples without any restriction , how many ways can we make the selection ? 18 ! / 4 ! 14 ! = 3060 if we are to select 4 people from 9 couples with restriction that no married couple can both make it to the group , only a representative ? 9 ! / 4 ! 5 ! = 126 but we know that to select a person from each couple , take 2 possibilities 126 * 2 * 2 * 2 * 2 = 2016 probability = desired / all possibilities = 2016 / 3060 = 56 / 85 answer : d
Answer: d
Question (general): joe went on a diet 4 months ago when he weighed 222 pounds . if he now weighs 198 pounds and continues to lose at the same average monthly rate , in approximately how many months will he weigh 180 pounds ?
Options: a ) 3 , b ) 3.5 , c ) 3 , d ) 4.5 , e ) 5
Rationale: 222 - 198 = 24 pounds lost in 4 months 24 / 4 = 6 , so joe is losing weight at a rate of 6 pounds per month . . . . in approximately how many months will he weigh 180 pounds ? a simple approach is to just list the weights . now : 198 lbs in 1 month : 192 lbs in 2 months : 186 lbs in 3 months : 180 lbs answer : c
Answer: c
Question (general): how many integers are divisible by 3 between 10 ! and 10 ! + 40 inclusive ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 13 , e ) 10
Rationale: "d - 7 10 ! is divisible by 3 there are 12 numbers between 10 ! and 10 ! + 40 that are divisible by 3 . hence 13"
Answer: d
Question (physics): if the perimeter of a rectangular stadium is 800 m , its length when its breadth is 300 m is ?
Options: a ) 500 , b ) 400 , c ) 300 , d ) 200 , e ) 100
Rationale: 2 ( l + 300 ) = 800 = > l = 100 m answer : e
Answer: e
Question (other): the ratio between the current age of a and b is 6 : 7 . if b is 4 years old than a . what will be the ratio of the ages of a and b after 4 years ?
Options: a ) 7 : 8 , b ) 8 : 9 , c ) 4 : 6 , d ) 4 : 8 , e ) 5 : 8
Rationale: a 7 : 8 if a ’ s age and b ’ s age will be 6 a years and 7 a years correspondingly then , 7 a – 6 a = 4 a = 4 needed ratio = ( 6 a + 4 ) : ( 7 a + 4 ) = 28 : 32 = 7 : 8
Answer: a
Question (general): the milk level in a rectangular box measuring 56 feet by 25 feet is to be lowered by 6 inches . how many gallons of milk must be removed ? ( 1 cu ft = 7.5 gallons )
Options: a ) 100 , b ) 250 , c ) 750 , d ) 5250 , e ) 5635
Rationale: "6 inches = 1 / 2 feet ( there are 12 inches in a foot . ) , so 56 * 25 * 1 / 2 = 700 feet ^ 3 of milk must be removed , which equals to 700 * 7.5 = 5250 gallons . answer : d ."
Answer: d
Question (general): what is the sum of all even numbers from 1 to 501 ?
Options: a ) 122821 , b ) 281228 , c ) 281199 , d ) 62750 , e ) 128111
Rationale: "explanation : 500 / 2 = 250 250 * 251 = 62750 answer : d"
Answer: d