Cheukting/mathqa huggingface dataset:
Question (physics): two thirds of the roads from a to b are at least 5 miles long , and 3 / 4 of the roads from b to c are at least 5 miles long . if you randomly pick a road from a to b and then randomly pick a road from b to c , what is the probability that at least one of the roads you pick is at least 5 miles long ?
Options: a ) 1 / 6 , b ) 1 / 4 , c ) 2 / 3 , d ) 3 / 4 , e ) 11 / 12
Rationale: so please : find the probability of the event thatnoneof the roads you pick will be at least 5 miles long and subtract from 1 to get the probability thatat least oneof the roads you pick will be at least 5 miles long : p = 1 - 1 / 3 * 1 / 4 = 11 / 12 . answer : e .
Answer: e
Question (general): if x = 6 and y = − 2 , what is the value of ( x − 2 y ) ^ y ?
Options: a ) − 100 , b ) 0.01 , c ) 0.25 , d ) 4 , e ) 8
Rationale: "( x − 2 y ) ^ y = ( 6 − 2 ( − 2 ) ) ^ − 2 = 1 / ( 6 + 4 ) ^ 2 = 1 / 100 = 0.01 answer : b"
Answer: b
Question (geometry): a rectangular swimming pool is 8 feet by 20 feet . a deck that has uniform width surrounds the pool . the total area of the pool and deck is 540 square feet . what is the width of the deck ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "let the width = w total area of the pool and deck = ( 2 w + 8 ) ( 2 w + 20 ) we can test the answer choices along with unit digit method a ) 2 feet . . . . . . . . . . . 12 * 24 has unit digit 8 . . . . . . . . . . eliminate b ) 2.5 feet . . . . . . . . . 13 * 25 has unit digit 5 . . . . . . . . . . eliminate c ) 3 feet . . . . . . . . . . . . 14 * 26 has unit digit 4 . . . . . . . . . . . hold d ) 4 feet . . . . . . . . . . . . 16 * 28 has unit digit 8 . . . . . . . . . . . eliminate e ) 5 feet . . . . . . . . . . . . 18 * 30 has unit digit 0 . . . . . . . . . . . eliminate answer : e w = 5"
Answer: e
Question (physics): a 270 m long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds . what is the length of the other train ?
Options: a ) 230 m , b ) 240 m , c ) 260 m , d ) 320 m , e ) 350 m
Rationale: "speed of first train = ( 120 * 5 / 18 ) m / sec = 100 / 3 m / sec speed of other train = ( 80 * 5 / 18 ) m / sec = 200 / 9 m / sec time to cross each other = 9 sec let x be the length of 2 nd train therefore 9 = ( 270 + x ) / ( 100 / 3 + 200 / 9 ) 500 = 270 + x 230 m = x answer : a"
Answer: a
Question (general): a sum of money is to be divided among ann , bob and chloe . first , ann receives $ 4 plus one - half of what remains . next , bob receives $ 4 plus one - third of what remains . finally , chloe receives the remaining $ 32 . how much money t did bob receive ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 52
Rationale: "notice that we need not consider ann ' s portion in the solution . we can just let k = the money remaining after ann has received her portion and go from there . our equation will use the fact that , once we remove bob ' s portion , we have $ 32 for chloe . so , we getk - bob ' s $ = 32 bob received 4 dollars plus one - third of what remained once bob receives $ 4 , the amount remaining is k - 4 dollars . so , bob gets a 1 / 3 of that as well . 1 / 3 of k - 4 is ( k - 4 ) / 3 so altogether , bob receives 4 + ( k - 4 ) / 3 so , our equation becomes : k - [ 4 + ( k - 4 ) / 3 ] = 32 simplify to get : k - 4 - ( k - 4 ) / 3 = 32 multiply both sides by 3 to get : 3 k - 12 - k + 4 = 96 simplify : 2 k - 8 = 96 solve : k = 52 plug this k - value intok - bob ' s $ = 32 to get : 52 - bob ' s $ = 32 so , bob ' s $ t = 20 answer : b"
Answer: b
Question (physics): maxwell leaves his home and walks toward brad ' s house at the same time that brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 40 kilometers , maxwell ' s walking speed is 3 km / h , and brad ' s running speed is 5 km / h . what is the distance traveled by maxwell when they meet in the middle ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 15 , e ) 14
Rationale: "consider max starts from point a and brad starts from point b and move towards each other . assume they shall meet at point o after time ' t ' . the question asks us to find oa . from the question stem we can make out : - distance oa = 50 km - distance ob = > 3 xt = 40 - 5 xt ( i . e distance = speed x time ) = > 8 t = 40 hence t = 5 oa = 3 x 5 = 15 km answer : d"
Answer: d
Question (general): in a urban village of india named ` ` owlna ' ' , 70 % people have refrigerator , 75 % people have television , 65 % people got computers and 95 % got air - conditionor . how many people ( minimum ) got all these luxury .
Options: a ) 5 % , b ) 7 % , c ) 3 % , d ) 9 % , e ) 15 %
Rationale: a 10 % 100 - [ ( 100 - 65 ) + ( 100 - 95 ) + ( 100 - 75 ) + ( 100 - 70 ) ] = 100 - ( 30 + 25 + 35 + 5 ) = 100 - 95
Answer: a
Question (other): in a group of 12 engineers , 4 engineers have a phd degree ; the others have only an ms or bs degree . a team of 4 engineers is to be chosen which must have at least 1 engineer with a phd , how many different teams can be chosen ?
Options: a ) 495 , b ) 70 , c ) 245 , d ) 425 , e ) 555
Rationale: "the problem asks for a combination , since order does n ' t matter . now , selecting r items from a set of n gives the combination formula : ncr = n ! / r ! ( n - r ) ! n = 12 r = 4 so , total teams is 12 c 4 = 12 ! / ( 4 ! ( 12 - 4 ) ! ) = 495 , and n = 12 - 4 = 8 r = 4 for teams without a phd is 8 c 4 = 8 ! / ( 4 ! ( 8 - 4 ) ! ) = 70 , so , teams with at least 1 phd = 495 - 70 = 425 answer : d"
Answer: d
Question (gain): what will be the ci on a sum of rs . 25000 after 3 years at the rate of 12 per year ?
Options: a ) rs . 10100 , b ) rs . 10110 , c ) rs . 10123.20 , d ) rs . 10135.50 , e ) rs . 10167.20
Rationale: amount = rs . 25000 x 1 + 12 3 100 = rs . 25000 x 28 x 28 x 28 25 25 25 = rs . 35123.20 c . i . = rs . ( 35123.20 - 25000 ) = rs . 10123.20 c
Answer: c
Question (general): if a person walks at 15 km / hr instead of 10 km / hr , he would have walked 10 km more . the actual distance traveled by him is ?
Options: a ) 50 km , b ) 30 km , c ) 18 km , d ) 16 km , e ) 97 km
Rationale: "let the actual distance traveled be x km . then , x / 10 = ( x + 10 ) / 15 5 x - 150 = > x = 30 km . answer : b"
Answer: b
Question (geometry): a rectangular grass field is 85 m * 55 m , it has a path of 2.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 2 per sq m ?
Options: a ) 1450 , b ) 1971 , c ) 9676 , d ) 1679 , e ) 2691
Rationale: "area = ( l + b + 2 d ) 2 d = ( 85 + 55 + 2.5 * 2 ) 2 * 2.5 = > 725 725 * 2 = rs . 1450 answer : a"
Answer: a
Question (physics): the speed at which a man can row a boat in still water is 18 kmph . if he rows downstream , where the speed of current is 3 kmph , what time will he take to cover 60 metres ?
Options: a ) 16 seconds , b ) 15.4 seconds , c ) 26 seconds , d ) 12 seconds , e ) 18 seconds
Rationale: "speed of the boat downstream = 18 + 3 = 21 kmph = 21 * 5 / 18 = 35 / 9 m / s hence time taken to cover 60 m = 60 * 9 / 35 = 15.4 seconds . answer : b"
Answer: b
Question (physics): two trains are moving at 50 kmph and 70 kmph in opposite directions . their lengths are 170 m and 100 m respectively . the time they will take to pass each other completely is ?
Options: a ) 3 sec , b ) 8 sec , c ) 9 sec , d ) 5 sec , e ) 7 sec
Rationale: "70 + 50 = 120 * 5 / 18 = 100 / 3 mps d = 170 + 100 = 270 m t = 270 * 3 / 100 = 8 sec answer : b"
Answer: b
Question (general): having scored 96 runs in the 19 th inning , a cricketer increases his average score by 4 . what will be his average score after 19 innings ?
Options: a ) 28 , b ) 27 , c ) 26 , d ) 22 , e ) 24
Rationale: "explanation : let the average score of the first 18 innings be n 18 n + 96 = 19 ( n + 4 ) = > n = 20 so , average score after 19 th innings = x + 4 = 24 . answer : e"
Answer: e
Question (physics): what is the greatest possible length which can be used to measure exactly the lengths 8 m , 4 m 20 cm and 12 m 20 cm ?
Options: a ) 10 cm , b ) 30 cm , c ) 25 cm , d ) 20 cm , e ) 35 cm
Rationale: "required length = hcf of 800 cm , 420 cm , 1220 cm = 20 cm answer : option d"
Answer: d
Question (general): what least number should be added to 1019 , so that the sum is completely divisible by 25 ?
Options: a ) 4 , b ) 3 , c ) 2 , d ) 0 , e ) 6
Rationale: 1019 ã · 25 = 40 with remainder = 19 19 + 6 = 25 . hence 6 should be added to 1019 so that the sum will be divisible by 25 answer : option e
Answer: e
Question (other): in a school having roll strength 286 , the ratio of boys and girls is 8 : 5 . if 22 more girls get admitted into the school , the ratio of boys and girls becomes
Options: a ) 12 : 7
b ) 10 : 7
c ) 8 : 7
d ) 4 : 3
e ) none
Rationale: solution : boys : girls = 8 : 5 ; ( let the boys = 8 x ; girl = 5 x ) total strength = 286 ; 8 x + 5 x = 286 ; 13 x = 286 ; or , x = 286 / 13 = 22 ; boys = 176 and girls = 110 ; 22 more girls get admitted then number of girls become , ( 5 x + 22 ) = 110 + 22 = 132 ; now , new ratio of boys and girls = 176 : 132 = 4 : 3 . answer : option d
Answer: d
Question (general): if x = 1 + √ 2 , then what is the value of x 4 - 4 x 3 + 4 x 2 + 5 ?
Options: a ) - 1 , b ) 0 , c ) 6 , d ) 2 , e ) 3
Rationale: "answer x = 1 + √ 2 ∴ x 4 - 4 x 3 + 4 x 2 + 5 = x 2 ( x 2 - 4 x + 4 ) + 5 = x 2 ( x - 2 ) 2 + 5 = ( 1 + √ 2 ) 2 ( 1 + √ 2 - 2 ) 2 + 5 = ( √ 2 + 1 ) 2 ( √ 2 - 1 ) 2 + 5 = [ ( √ 2 ) 2 - ( 1 ) 2 ] 2 + 5 = ( 2 - 1 ) 2 = 1 + 5 = 6 correct option : c"
Answer: c
Question (other): the ratio of sum of squares of first n natural numbers to square of sum of first n natural numbers is 17 : 325 . the value of n is
Options: a ) 15
b ) 25
c ) 35
d ) 30
e ) none of these
Rationale: sum of 1 st n natural no . s is n ( n + 1 ) / 2 , sum of sqaures of 1 st n natural no . s is n ( n + 1 ) ( 2 n + 1 ) / 6 , the ratio of sum of squares of first n natural numbers to square of sum of first n natural numbers = n ( n + 1 ) ( 2 n + 1 ) * 2 * 2 / ( n * n * ( n + 1 ) * ( n + 1 ) ) = 2 ( 2 n + 1 ) / ( 3 n ( n + 1 ) ) now by hit and trial for the given options , if we put 25 then this will give 17 / 325 therefore the answer is 25 answer : b
Answer: b
Question (physics): a man is walking at a speed of 10 km per hour . after every kilometre , he takes rest for 5 minutes . how much time will be take to cover a distance of 5 kilometres ?
Options: a ) 48 min . , b ) 50 min . , c ) 45 min . , d ) 55 min . , e ) none of these
Rationale: rest time = number of rest × time for each rest = 4 × 5 = 20 minutes total time to cover 5 km = ( 5 ⁄ 10 × 60 ) minutes + 20 minutes = 50 minutes answer b
Answer: b
Question (gain): an error 4 % in excess is made while measuring the side of a square . the percentage of error in the calculated area of the square is
Options: a ) 8.04 % , b ) 8.14 % , c ) 8.23 % , d ) 8.16 % , e ) 8.5 %
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 ) = [ ( 104 ) 2 - ( 100 ) 2 ] = ( 104 + 100 ) x ( 104 - 100 ) = 816 cm 2 . percentage error = 8.16 d"
Answer: d
Question (gain): harkamal purchased 8 kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) 1000 , b ) 1055 , c ) 1065 , d ) 1075 , e ) 1080
Rationale: "cost of 8 kg grapes = 70 × 8 = 560 . cost of 9 kg of mangoes = 55 × 9 = 490 . total cost he has to pay = 560 + 490 = 1055 . b )"
Answer: b
Question (general): if x and y are integers such that ( x + 1 ) ^ 2 is less than or equal to 9 and ( y - 1 ) ^ 2 is less than 64 , what is the sum of the maximum possible value of xy and the minimum possible value of xy ?
Options: a ) - 16 , b ) - 8 , c ) 0 , d ) 14 , e ) 16
Rationale: "( x + 1 ) ^ 2 < = 9 x < = 2 x > = - 4 ( y - 1 ) ^ 2 < 64 y < 9 y > - 7 max possible value of xy is - 4 × - 6 = 24 minimum possible value of xy is - 4 × 8 = - 32 - 32 + 24 = - 8 answer : b"
Answer: b
Question (general): the difference between a two - digit number and the number obtained by interchanging the two digits is 63 . which is the smaller of the two numbers ?
Options: a ) 29 , b ) 70 , c ) 92 , d ) can not be determined , e ) none of these
Rationale: "explanation : let the ten ' s digit be x and units digit by y . then , ( 10 x + y ) - ( 10 y + x ) = 63 9 ( x - y ) = 63 x - y = 7 thus , none of the numbers can be determined . answer is d"
Answer: d
Question (physics): a man started driving at a constant speed , from the site of a blast , the moment he heard the blast . he heard a second blast after a time of 30 mins and 12 seconds . if the second blast occurred exactly 30 mins after the first , how many meters was he from the site when he heard the second blast ? ( speed of sound = 330 m / s )
Options: a ) 3120 , b ) 3330 , c ) 3540 , d ) 3750 , e ) 3960
Rationale: "the distance the sound traveled to the man is 12 * 330 = 3960 meters the answer is e ."
Answer: e
Question (general): how many positive integers less than 5,000 are evenly divisible by neither 13 nor 21 ?
Options: a ) 4,514 , b ) 4,475 , c ) 4,521 , d ) 4,428 , e ) 4,349
Rationale: "integers less than 5000 divisible by 13 5000 / 13 = 333 . something , so 333 integers less than 5000 divisible by 21 5000 / 21 = 238 . # # , so 238 we have double counted some , so take lcm of 13 and 21 = 105 and divide by 5000 , we get 47 . so all numbers divisible by 13 and 21 = 333 + 238 - 47 = 524 now subtract that from 4999 . 4999 - 524 = 4349 answer e ."
Answer: e
Question (physics): a train leaves delhi at 9 a . m . at a speed of 30 kmph . another train leaves at 2 p . m . at a speed of 40 kmph on the same day and in the same direction . how far from delhi , will the two trains meet ?
Options: a ) 900 km , b ) 800 km , c ) 600 km , d ) 690 km , e ) 609 km
Rationale: explanation : d = 30 * 5 = 150 rs = 40 – 30 = 10 t = 150 / 10 = 15 d = 40 * 15 = 600 km answer : option c
Answer: c
Question (general): what is difference between biggest and smallest fraction among 2 / 5 , 3 / 4 , 4 / 5 and 5 / 6
Options: a ) 2 / 5 , b ) 3 / 5 , c ) 1 / 6 , d ) 1 / 7 , e ) none of these
Rationale: "explanation : 2 / 5 = . 4 , 3 / 4 = . 75 , 4 / 5 = . 8 and 5 / 6 = . 833 so biggest is 5 / 6 and smallest is 2 / 5 their difference is 5 / 6 - 2 / 5 = 13 / 30 option e"
Answer: e
Question (gain): a 5 % stock yields 10 % . the market value of the stock is :
Options: a ) rs . 56 , b ) rs . 55 , c ) rs . 50 , d ) rs . 90 , e ) rs . 75
Rationale: "explanation : for an income of rs . 10 , investment = rs . 100 . for an income of rs 5 , investment = rs . 100 / 10 x 5 = rs 50 market value of rs . 100 stock = rs . 50 answer is c"
Answer: c
Question (physics): a train 120 m long passes a man , running at 6 kmph in the direction opposite to that of the train , in 6 seconds . the speed of the train is
Options: a ) 54 kmph , b ) 60 kmph , c ) 66 kmph , d ) 72 kmph , e ) 82 kmph
Rationale: "speed of train relative to man : 120 / 6 * 18 / 5 km / hr = 72 km / hr let speed of train = x therefore x + 6 = 72 x = 72 - 6 x = 66 km / hr answer : c"
Answer: c
Question (physics): every day daniel drives 64 miles back from work . on sunday , daniel drove all the way back from work at a constant speed of x miles per hour . on monday , daniel drove the first 32 miles back from work at ( 2 x ) miles per hour , and the rest of the way at ( x / 2 ) miles per hour . the time it took daniel to drive back from work on monday is longer than the time it took him to drive back from work on sunday by what percent ?
Options: a ) 15 % , b ) 25 % , c ) 35 % , d ) 45 % , e ) 55 %
Rationale: "let ' s test x = 4 . . . . on sunday , daniel drove 64 miles at 4 miles / hour . d = ( r ) ( t ) 64 = ( 4 ) ( t ) 64 / 4 = 16 = t it takes 16 hours to drive home on monday , daniel drove the first 32 miles at ( 2 ) ( 4 ) = 8 miles / hour and the rest of the way ( 32 miles ) at 4 / 2 = 2 miles / hour d = ( r ) ( t ) 32 = ( 8 ) ( t ) 32 / 8 = 4 = t it takes 4 hours for the first part d = ( r ) ( t ) 32 = ( 2 ) ( t ) 32 / 2 = 16 = t it takes 16 hours for the second part total time to drive home on monday = 4 + 16 = 20 hours we ' re asked by what percent 20 hours is greater than 16 hours . 20 / 16 = 1.25 , so it is 25 % greater . b"
Answer: b
Question (geometry): the diagonal of a rhombus are 25 m and 50 m . its area is :
Options: a ) 900 , b ) 800 , c ) 700 , d ) 625 , e ) 650
Rationale: "area of the rhombus = 1 / 2 d 1 d 2 = ( 1 / 2 ã — 25 ã — 50 ) cm ( power ) 2 = 25 ã — 25 = 625 cm ( power ) 2 answer is d ."
Answer: d
Question (geometry): what is the angle between the hands of a clock when time is 10 : 20 ?
Options: a ) 90 deg , b ) 75 deg , c ) 45 deg , d ) 15 deg , e ) 30 deg
Rationale: "angle between two hands = 20 h - 11 / 2 m = 20 * 10 - 20 * 11 / 2 = 200 - 110 = 90 deg answer : a"
Answer: a
Question (geometry): the diameter of a cylindrical tin is 14 cm and height is 5 cm . find the volume of the cylinder ?
Options: a ) 230 , b ) 141 , c ) 66 , d ) 245 , e ) 21
Rationale: "r = 7 h = 5 π * 7 * 7 * 5 = 45 π cc answer : d"
Answer: d
Question (physics): if 40 men take 15 days to to complete a job , in how many days can 25 men finish that work ?
Options: a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28
Rationale: ans . 24 days
Answer: a
Question (physics): it takes printer a 4 more minutes more than printer b to print 40 pages . working together , the two printers can print 50 pages in 6 minutes . how long will it take printer a to print 160 pages ?
Options: a ) 12 , b ) 18 , c ) 48 , d ) 20 , e ) 30
Rationale: if it takes 4 more minutes for a to print 40 pages than it takes b , it takes 5 more minutes for a to print 50 pages than it takes b . thus if b is the number of minutes than b takes to print 50 pages , we can write : 1 / b + 1 / ( b + 5 ) = 1 / 6 ( since in 1 minute , they print 1 / 6 th of the 50 page job ) 6 ( 2 b + 5 ) = b ( b + 5 ) b ^ 2 - 7 b - 30 = 0 ( b - 10 ) ( b + 3 ) = 0 b = 10 thus it takes a 15 minutes to print 50 pages and 15 * 160 / 50 = 48 minutes to print 160 pages ( answer c )
Answer: c
Question (physics): find the cost of fencing around a circular field of diameter 22 m at the rate of rs . 3 a meter ?
Options: a ) 288 , b ) 132 , c ) 772 , d ) 207.3 , e ) 261
Rationale: "2 * 22 / 7 * 11 = 69.1 69.1 * 3 = rs . 207.3 answer : d"
Answer: d
Question (general): there are 6 people in the elevator . their average weight is 156 lbs . another person enters the elevator , and increases the average weight to 151 lbs . what is the weight of the 7 th person .
Options: a ) 121 , b ) 168 , c ) 189 , d ) 190 , e ) 200
Rationale: solution average of 7 people after the last one enters = 151 . â ˆ ´ required weight = ( 7 x 151 ) - ( 6 x 156 ) = 1057 - 936 = 121 . answer a
Answer: a
Question (general): each child has 2 pencils and 13 skittles . if there are 15 children , how many pencils are there in total ?
Options: a ) 30 , b ) 12 , c ) 18 , d ) 22 , e ) 08
Rationale: 2 * 15 = 30 . answer is a .
Answer: a
Question (general): if a certain number x is divided by 62 , the reminder is 7 . what is the reminder when x + 11 is divided by 31 ?
Options: a ) 3 , b ) 5 , c ) 18 , d ) 6 , e ) 8
Rationale: x can be written as 62 k + 7 or x = 7 , 69,131 , etc . x + 11 = 62 k + 7 + 11 = 62 k + 18 or x + 11 = 18 , 80,142 etc . when divided by 31 , we will get the remainder 18 . c
Answer: c
Question (general): if 7 ^ w is a factor of the product of the integers from 1 to 100 , inclusive , what is the largest value of w ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: so the question just means that we have to find all the multiples w of 7 between 1 to 100 so there are 14 multiples of 7 ( 7 - 98 ) but 49 and 98 contain two 7 ' s as factors so we have to add 14 + 2 = 16 e
Answer: e
Question (general): a women purchased 3 towels @ rs . 100 each , 5 towels @ rs . 150 each and two towels at a certain rate which is now slipped off from his memory . but she remembers that the average price of the towels was rs . 145 . find the unknown rate of two towels ?
Options: a ) a ) 400 , b ) b ) 450 , c ) c ) 500 , d ) d ) 550 , e ) e ) 600
Rationale: "10 * 145 = 1450 3 * 100 + 5 * 150 = 1050 1450 – 1050 = 400 a"
Answer: a
Question (physics): if 2 pipes take an hour to fill a tank , then how long should 8 pipes take to fill the same tank ?
Options: a ) 20 min , b ) 10 min , c ) 15 min , d ) 25 min , e ) 30 min
Rationale: if 2 pipes take an hour to fill a tank , then 8 pipes will take 2 * 60 / 8 = 15 mins to dig a ditch of the same type . answer : c
Answer: c
Question (general): there are 6 chess amateurs playing in villa ' s chess club tournament . if each chess amateur plays with exactly 4 other amateurs , what is the total number of chess games possible to be played in the tournament ?
Options: a ) 10 , b ) 20 , c ) 40 , d ) 60 , e ) 12
Rationale: method 2 : each person is one participant of 4 games . so there are in all 4 * 6 = 24 instances of one participant games . but each game has 2 participants so total number of games = 24 / 2 = 12 e
Answer: e
Question (gain): a jar full of whisky contains 30 % alcohol . a part of this whisky is replaced by another containg 19 % alcohol and now the percentage of alcohol was found to be 26 % . what quantity of whisky is replaced ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 2 / 5 , d ) 3 / 5 , e ) 4 / 5
Rationale: "let us assume the total original amount of whiskey = 10 ml - - - > 4 ml alcohol and 6 ml non - alcohol . let x ml be the amount removed - - - > total alcohol left = 4 - 0.4 x new quantity of whiskey added = x ml out of which 0.19 is the alcohol . thus , the final quantity of alcohol = 4 - 0.4 x + 0.19 x - - - - > ( 4 - 0.21 x ) / 10 = 0.26 - - - > x = 20 / 3 ml . per the question , you need to find the x ml removed as a ratio of the initial volume - - - > ( 20 / 3 ) / 10 = 1 / 3 . hence , a is the correct answer ."
Answer: a
Question (physics): worker a takes 4 hours to do a job . worker b takes 10 hours to do the same job . how long it take both a & b , working together but independently , to do the same job ?
Options: a ) 20 / 9 , b ) 40 / 9 , c ) 40 / 14 , d ) 60 / 9 , e ) 80 / 9
Rationale: one day work of a = 1 / 4 one day work of b = 1 / 10 so one day work of a and b together = 1 / 4 + 1 / 10 = 14 / 40 so total days required = 40 / 14 answer : c
Answer: c
Question (physics): express a speed of 30 kmph in meters per second ?
Options: a ) 10 mps , b ) 8 mps , c ) 9 mps , d ) 7 mps , e ) 12 mps
Rationale: "30 * 5 / 18 = 8 mps answer : b"
Answer: b
Question (general): in a maths test , students were asked to find 5 / 16 of a certain number . one of the students by mistake found 5 / 6 th of that number and his answer was 100 more than the correct answer . find the number .
Options: a ) 192 , b ) 280 , c ) 384 , d ) 400 , e ) 500
Rationale: "explanation : let the number be x . 5 * x / 6 = 5 * x / 16 + 100 25 * x / 48 = 100 x = 192 answer a"
Answer: a
Question (physics): a boat running up stram takes 6 hours to cover a certain distance , while it takes 9 hours to cover the same distance running down stream . what is the ratio between the speed of the boat and the speed of water current respectively ?
Options: a ) 2 : 3 , b ) 5 : 1 , c ) 4 : 5 , d ) 7 : 1 , e ) 8 : 1
Rationale: "explanation : let speed of boat is x km / h and speed stream is y km / hr 6 ( x + y ) = 9 ( x - y ) 6 x + 6 y = 9 x - 9 y 15 y = 3 x 5 y = x x / y = 5 / 1 5 : 1 answer : option b"
Answer: b
Question (gain): the cost price of a radio is rs . 1900 and it was sold for rs . 1330 , find the loss % ?
Options: a ) 18 % , b ) 31 % , c ) 30 % , d ) 45 % , e ) 12 %
Rationale: "1900 - - - - 570 100 - - - - ? = > 30 % answer : c"
Answer: c
Question (physics): someone on a skateboard is traveling 13 miles per hour . how many feet does she travel in 25 seconds ? ( 1 mile = 5280 feet )
Options: a ) 476.75 ft , b ) 450 ft , c ) 480 ft , d ) 490 ft , e ) 500 ft
Rationale: "per second = > 13 * 5280 ft / 60 * 60 = 19.07 ft 25 seconds = > 19.07 * 25 = 476.75 ft answer : a"
Answer: a
Question (general): there are 4 more women than there are men on a local co - ed softball team . if there are a total of 14 players on the team , what is the ratio of men to women ?
Options: a ) 10 / 16 , b ) 6 / 16 , c ) 4 / 16 , d ) 6 / 10 , e ) 5 / 9
Rationale: "w = m + 4 w + m = 14 m + 4 + m = 14 2 m = 10 m = 5 w = 9 ratio : 5 : 9 ans : e"
Answer: e