Cheukting/mathqa huggingface dataset:
Question (general): if 20 machine can finish a job in 36 days , then how many more machines would be needed to finish the job in one - third less time ?
Options: a ) a . 4 , b ) b . 8 , c ) c . 10 , d ) d . 12 , e ) e . 16
Rationale: "you might think of this in a management context - we can use the principle of ' person - hours ' to solve any problem where we have identical workers . so , using simpler numbers , suppose you know that 6 identical employees , working simultaneously , would finish a job in 5 hours . then that job requires 6 * 5 = 30 total hours of person - work . if instead you wanted the job done in 3 hours , you ' d assign 30 / 3 = 10 employees to do the job , because you want to get a total of 30 hours of work from the employees . we can solve this problem identically . if 20 machines ( identical ones , i assume ) work simultaneously for 36 days , they will do a total of 20 * 36 machine - days of work . so the job requires 20 * 36 days of machine work in total . we instead want the job done in 1 / 3 less time , so in 24 days . so we ' ll need 20 * 36 / 24 = 30 machines , or 10 additional machines . c"
Answer: c
Question (gain): suganya and suriya are partners in a business . suganya invests rs . 38,000 for 8 months and suriya invests rs . 40,000 for 10 months . out of a profit of rs . 31,570 . suganya ' s share is
Options: a ) rs . 1435 , b ) rs . 12,628 , c ) rs . 1685 , d ) rs . 18,942 , e ) none
Rationale: "solution ratio of their shares = ( 35000 ã — 8 ) : ( 42000 ã — 10 ) = 2 : 44 . suganya ' s share = rs . ( 31570 ã — 2 / 44 ) = rs . 1435 . answer a"
Answer: a
Question (gain): suresh started a business , investing rs . 18000 . after 3 months and 4 months respectively , rohan and sudhir joined him with capitals of 12000 and 9000 . at the end of the year the total profit was rs . 3795 . what is the difference between rohan ’ s and sudhir ’ s share in the profit ?
Options: a ) s . 345 , b ) s . 350 , c ) s . 352 , d ) s . 362 , e ) s . 368
Rationale: "suresh : rohan : sudhir ratio of their investments = 18000 × 12 : 12000 × 9 : 9000 × 8 = 6 : 3 : 2 the difference between rohan ’ s and sudhir ’ s share = 1 share : . i . e . = rs . 3795 × 1 / 11 = rs . 345 . a"
Answer: a
Question (general): for each 6 - month period during a light bulb ' s life span , the odds of it not burning out from over - use are half what they were in the previous 6 - month period . if the odds of a light bulb burning out during the first 6 - month period following its purchase are 1 / 3 , what are the odds of it burning out during the period from 6 months to 1 year following its purchase ?
Options: a ) 5 / 27 , b ) 2 / 9 , c ) 1 / 3 , d ) 4 / 9 , e ) 2 / 3
Rationale: "probability of not burning out during the first 6 months 1 - 1 / 3 = 2 / 3 probability of not burning out during the next 6 months 2 / 3 / 2 = 1 / 3 , hence probability of burning out 1 - 1 / 3 = 2 / 3 . probability of burning out during the period from 6 months to 1 year = probability of not burning out in first 6 months * probability of burning out in next 6 months = 2 / 3 * 2 / 3 = 4 / 9 answer : d ."
Answer: d
Question (general): a grocer has a sale of rs . 5921 , rs . 5468 , rs . 5568 , rs . 6088 and rs . 6433 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 5900 ?
Options: a ) 4902 , b ) 4922 , c ) 5922 , d ) 5924 , e ) 5928
Rationale: "total sale for 5 months = rs . ( 5921 + 5468 + 5568 + 6088 + 6433 ) = rs . 29478 . required sale = rs . [ ( 5900 x 6 ) - 29478 ] = rs . ( 35400 - 29478 ) = rs . 5922 . answer : c"
Answer: c
Question (general): if x is real , find the maximum value of the expression - 2 x ^ 2 + 3 x + 5 .
Options: a ) 2.145 , b ) 6.125 , c ) 8.725 , d ) 11.885 , e ) 13.485
Rationale: "this is an equation of a downward facing parabola . the maximum value is the top point of the parabola . - 2 x ^ 2 + 3 x + 5 = ( - 2 x + 5 ) ( x + 1 ) the roots are 5 / 2 and - 1 . the maximum value must be when x is halfway between these two points . x = 0.75 the maximum value is - 2 ( 0.75 ) ^ 2 + 3 ( 0.75 ) + 5 = 6.125 the answer is b ."
Answer: b
Question (general): nelly made a part payment of $ 875 toward buying a brand new refrigerator , which represents 25 % of the total cost of the refrigerator , how much remains to be paid ?
Options: a ) $ 2225 , b ) $ 2782 , c ) $ 1625 , d ) $ 2629 , e ) $ 2625
Rationale: explanation : let ' s start with what the total price of the refrigerator would be . if 25 % is equal to $ 875 then 100 % equals $ x . we just have to multiply $ 875 by 4 to get total amount = $ 3500 . out of this amount we then need to deduct the amount already paid which was $ 875 so we have $ 3500 - $ 875 = $ 2625 answer : option e
Answer: e
Question (gain): 16 is what % of 90 ?
Options: a ) 16 , b ) 17.78 , c ) 17 , d ) 18.5 , e ) 18.23
Rationale: we assume that 90 is 100 % assume ' x ' is value we looking for here , 90 = 100 % and x % = 16 therefore , 100 / x = 90 / 16 100 / x = 5.625 x = 17.78 b
Answer: b
Question (physics): amar takes as much time in running 12 meters as a car takes in covering 45 meters . what will be the distance covered by amar during the time the car covers 1.4 km ?
Options: a ) 700 m , b ) 500 m , c ) 373 m , d ) 356 m , e ) 640 m
Rationale: "distance covered by amar = 12 / 45 ( 1.4 km ) = 4 / 15 ( 1400 ) = 373 m answer : c"
Answer: c
Question (general): how many 2 digit number contain number 3 ?
Options: a ) 18 , b ) 28 , c ) 38 , d ) 68 , e ) 58
Rationale: "total 2 digit no . = 9 * 10 * = 90 not containing 3 = 8 * 9 = 72 total 2 digit number contain 3 = 90 - 72 = 18 answer : a"
Answer: a
Question (geometry): the side of a square is increased by 15 % then how much % does its area increases ?
Options: a ) 52.65
b ) 56.25
c ) 50.75
d ) 32.25
e ) 52.75
Rationale: a = 100 a 2 = 10000 a = 115 a 2 = 13225 - - - - - - - - - - - - - - - - 10000 - - - - - - - - - 3225 100 - - - - - - - ? = > 32.25 % answer : d
Answer: d
Question (physics): marla starts running around a circular track at the same time nick starts walking around the same circular track . marla completes 28 laps around the track per hour and nick completes 13 laps around the track per hour . how many minutes after marla and nick begin moving will marla have completed 4 more laps around the track than nick ?
Options: a ) 5 , b ) 8 , c ) 12 , d ) 16 , e ) 20
Rationale: "maria ' s rate - 28 laps per hour - - > 28 / 60 laps / min nick ' s rate - 13 laps per hour - - > 13 / 60 laps / min lets set equations : 28 / 60 * t = 4 ( since maria had to run 4 laps before nick would start ) 13 / 60 * t = 0 ( hick has just started and has n ' t run any lap yet ) ( 28 / 60 - 13 / 60 ) * t = 4 - 0 ( since nick was chasing maria ) t = 16 min needed maria to run 4 laps answer : d"
Answer: d
Question (gain): a , b and c invested rs . 6300 , rs . 4200 and rs . 10500 respectively , in a partnership business . find the share of a in profit of rs . 14200 after a year ?
Options: a ) 3630 , b ) 9232 , c ) 4260 , d ) 2387 , e ) 2813
Rationale: "6300 : 4200 : 10500 3 : 2 : 5 3 / 10 * 14200 = 4260 answer : c"
Answer: c
Question (probability): three coins are tossed . find the probability of at most 2 tails ?
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 2 / 3 , d ) 7 / 8 , e ) 3 / 8
Rationale: "n ( s ) = 2 ^ 3 = 8 let e is the event of getting at most 2 tails n ( e ) = hhh , tth , htt , tht , hht , hth , thh = 7 p ( e ) = n ( e ) / n ( s ) = 7 / 8 ans - d"
Answer: d
Question (general): when a certain number x is divided by 63 , the remainder is 25 . what is the remainder when x is divided by 8 ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "when a certain number x is divided by 63 , the remainder is 25 . what is the remainder when x is divided by 8 ? putting a value say x = 255 we get remainder as 25 when divided by 63 . when 25 divided by 8 we get 1 as remainder . a is the answer ."
Answer: a
Question (general): the average of 25 results is 8 . the average of first 12 of them is 14 and that of last 12 is 17 . find the 13 result ?
Options: a ) 52 , b ) 68 , c ) 78 , d ) 92 , e ) 65
Rationale: "13 th result = sum of 25 results - sum of 24 results 18 * 25 - 14 * 12 + 17 * 12 = 78 answer is d"
Answer: d
Question (general): 5.02 can be expressed in terms of percentage as
Options: a ) 5.02 % , b ) 50.2 % , c ) 209 % , d ) 502 % , e ) none of these
Rationale: "explanation : while calculation in terms of percentage we need to multiply by 100 , so 5.02 * 100 = 502 answer : option d"
Answer: d
Question (gain): x and y invested in a business . they earned some profit which they divided in the ratio of 1 : 2 . if x invested rs . 20,000 . the amount invested by y is
Options: a ) rs . 45,000 , b ) rs . 40,000 , c ) rs . 60,000 , d ) rs . 80,000 , e ) none
Rationale: "solution suppose y invested rs . y then , 20000 / y = 1 / 2 â € ¹ = â € º y = ( 20000 ã — 2 / 1 ) . â € ¹ = â € º y = 40000 . answer b"
Answer: b
Question (physics): sari and ken climb up a mountain . at night , they camp together . on the day they are supposed to reach the summit , sari wakes up at 05 : 00 and starts climbing at a constant pace . ken starts climbing only at 07 : 00 , when sari is already 700 meters ahead of him . nevertheless , ken climbs at a constant pace of 500 meters per hour , and reaches the summit before sari . if sari is 50 meters behind ken when he reaches the summit , at what time did ken reach the summit ?
Options: a ) 13 : 00 , b ) 13 : 30 , c ) 14 : 00 , d ) 15 : 00 , e ) 12 : 00
Rationale: "both sari and ken climb in the same direction . speed of sari = 700 / 2 = 350 meters / hr ( since she covers 700 meters in 2 hrs ) speed of ken = 500 meters / hr at 8 : 00 , distance between ken and sari is 700 meters . ken needs to cover this and another 50 meters . time he will take = total distance to be covered / relative speed = ( 700 + 50 ) / ( 500 - 350 ) = 5 hrs starting from 7 : 00 , in 5 hrs , the time will be 12 : 00 answer ( e )"
Answer: e
Question (general): the mean of 50 observations was 36 . it was found later that an observation 48 was wrongly taken as 23 . the corrected new mean is ?
Options: a ) 36.6 , b ) 36.1 , c ) 36.5 , d ) 36.2 , e ) 36.9
Rationale: "correct sum = ( 36 * 50 + 48 - 23 ) = 1825 . correct mean = 1825 / 50 = 36.5 answer : c"
Answer: c
Question (general): it takes 3 workers a total of 12 hours to build a giant machine with each worker working at the same rate . if 4 workers start to build the machine at 11 : 00 am , and one extra worker per hour is added beginning at 3 : 00 pm , at what time will the machine be complete ?
Options: a ) 5 : 30 , b ) 5 : 45 , c ) 6 : 00 , d ) 6 : 15 , e ) 6 : 30
Rationale: "3 workers build 1 / 12 of a machine in one hour . 1 worker builds 1 / 36 of a machine in one hour . in the first 4 hours , 4 workers build 4 * ( 1 / 36 ) * 4 = 16 / 36 of a machine from 3 : 00 to 4 : 00 , 5 workers build another 5 / 36 . the total is 21 / 36 . from 4 : 00 to 5 : 00 , 6 workers build another 6 / 36 . the total is 27 / 36 . from 5 : 00 to 6 : 00 , 7 workers build another 7 / 36 . the total is 34 / 36 . to build another 2 / 36 , 8 workers need ( 2 / 8 ) * 60 minutes which is 15 minutes . the machine is complete at 6 : 15 . the answer is d ."
Answer: d
Question (general): buffalo gives 4 liter milk , cow gives ( 1 / 2 ) liter milk and goat gives 1 / 4 liter milk . you have to get 20 liter milk by 20 animals . what is the number of cows ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: "assume number of respective animals are x , y , z . x + y + z = 20 - - - ( 1 ) as the total number of animal has to be 20 amt of milk will be 4 x + ( 1 / 2 ) y + ( 1 / 4 ) z = 20 - - - ( 2 ) solving equation 1 and 2 we get 15 x + y = 60 - - - - ( 3 ) since buffalo gives 4 litre and total milk is 20 , x < 5 but from eq 3 , x can not be more than 4 ; further if x = 1 or 2 ; y > 20 . . . not possible , since total animal is 20 thus , x = 3 , y = 15 , z = 2 15 cows answer : d"
Answer: d
Question (general): claire has a total of 80 pets consisting of gerbils and hamsters only . one - quarter of the gerbils are male , and one - third of the hamsters are male . if there are 25 males altogether , how many gerbils does claire have ?
Options: a ) 39 , b ) 50 , c ) 54 , d ) 57 , e ) 36
Rationale: "g + h = 80 . . . 1 ; g / 4 + h / 3 = 25 . . . . 2 or 3 g + 4 h = 25 * 12 = 300 g = 80 - h or 3 ( 80 - h ) + 4 h = 300 h = 300 - 240 = 60 then g = 96 - 60 = 36 e"
Answer: e
Question (physics): a , band c can do a piece of work in 11 days , 45 days and 55 days respectively , working alone . how soon can the work be done if a is assisted by band c on alternate days ?
Options: a ) 7 days , b ) 8 days , c ) 9 days , d ) 10 days , e ) 11 days
Rationale: "( a + b ) ' s 1 day ' s work = 1 / 11 + 1 / 45 = 56 / 495 ( a + c ) ' s 1 day ' s work = 1 / 11 + 1 / 55 = 6 / 55 work done in 2 day ' s = 56 / 495 + 6 / 55 = 2 / 9 2 / 9 th work done in 2 days work done = 9 / 2 * 2 = 9 days answer : c"
Answer: c
Question (physics): 15 people can write 90 book in 20 days working 7 hour a day . then in how many day 240 can be written by 72 people ?
Options: a ) 240 / 9 , b ) 309 / 28 , c ) 100 / 9 , d ) 200 / 9 , e ) 339 / 26
Rationale: "work per day epr hour per person = 90 / ( 20 * 7 * 15 ) / / eq - 1 people = 72 ; let suppose day = p ; per day work for 8 hours acc . to condition work per day epr hour per person = 240 / ( p * 7 * 72 ) / / eq - 2 eq - 1 = = eq - 2 ; p = 100 / 9 answer : c"
Answer: c
Question (general): a number , x is chosen at random from the set of positive integers less than 10 . what is the probability that ( 7 / x ) > x ?
Options: a ) 1 / 5 , b ) 7 / 9 , c ) 1 / 3 , d ) 2 / 3 , e ) 2 / 9
Rationale: "number x has to be chosen from numbers 1 - 9 ( 7 / x ) > x = > 7 > x ^ 2 = > x ^ 2 - 7 < 0 x can have 2 values only 1 , 2 therefore , probability = 2 / 9 answer e"
Answer: e
Question (general): a factory producing tennis balls stores them in either big boxes , 25 balls per box , or small boxes , with 17 balls per box . if 94 freshly manufactured balls are to be stored , what is the least number of balls that can be left unboxed ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "there is no way to store 94 balls without leftovers : 94 − 0 ∗ 25 = 94 - 94 − 2 ∗ 25 = 44 , 94 − 3 ∗ 25 = 19 are not divisible by 17 . 93 balls can be stored successfully : 93 − 1 ∗ 25 = 68 is divisible by 17 . thus , 93 = 1 ∗ 25 + 4 ∗ 17 and we need 1 big box and 4 small boxes . answer : b"
Answer: b
Question (general): what is x if x + 3 y = 33 and y = 10 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "substitute y by 10 in x + 3 y = 33 x + 3 ( 10 ) = 33 x + 30 = 33 if we substitute x by 3 in x + 30 = 33 , we have 3 + 30 = 33 . hence x = 3 correct answer c"
Answer: c
Question (gain): a shopkeeper sold 50 articles at the cost price of 60 articles . then find the profit % or lost %
Options: a ) 20 % , b ) 22 % , c ) 25 % , d ) 30 % , e ) 35 %
Rationale: "here 50 articles selling price = 60 articles cost price so the difference = 60 - 50 = 10 % of profit = 10 * 100 / 50 = 20 % correct option is a"
Answer: a
Question (gain): the owner of a furniture shop charges his customer 20 % more than the cost price . if a customer paid rs . 3000 for a computer table , then what was the cost price of the computer table ?
Options: a ) 2500 , b ) 2772 , c ) 1991 , d ) 6725 , e ) 2099
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 3000 ( 100 / 120 ) = rs . 2500 . answer : a"
Answer: a
Question (physics): suresh can complete a job in 15 hours . ashutosh alone can complete the same job in 20 hours . suresh works for 9 hours and then the remaining job is completed by ashutosh . how many hours will it take ashutosh to complete the remaining job alone ?
Options: a ) 4 , b ) 5 , c ) 8 , d ) 12 , e ) none of these
Rationale: the part of job that suresh completes in 9 hours = 9 â  „ 15 = 3 â  „ 5 remaining job = 1 - 3 â  „ 5 = 2 â  „ 5 remaining job can be done by ashutosh in 2 â  „ 5 ã — 20 = 8 hours answer c
Answer: c
Question (gain): sonika deposited rs . 9000 which amounted to rs . 10200 after 3 years at simple interest . had the interest been 2 % more . she would get how much ?
Options: a ) 9680 , b ) 2277 , c ) 2999 , d ) 10700 , e ) 10740
Rationale: "( 9000 * 3 * 2 ) / 100 = 540 10200 - - - - - - - - 10740 answer : e"
Answer: e
Question (general): jerry ’ s average ( arithmetic mean ) score on the first 3 of 4 tests is 85 . if jerry wants to raise his average by 3 points , what score must he earn on the fourth test ?
Options: a ) 97 , b ) 89 , c ) 90 , d ) 93 , e ) 95
Rationale: "total score on 3 tests = 85 * 3 = 255 jerry wants the average to be = 88 hence total score on 4 tests should be = 88 * 4 = 352 score required on the fourth test = 352 - 255 = 97 option a"
Answer: a
Question (general): a card game called “ high - low ” divides a deck of 52 playing cards into 2 types , “ high ” cards and “ low ” cards . there are an equal number of “ high ” cards and “ low ” cards in the deck and “ high ” cards are worth 2 points , while “ low ” cards are worth 1 point . if you draw cards one at a time , how many ways can you draw “ high ” and “ low ” cards to earn 4 points if you must draw exactly 2 “ low ” cards ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "great question ravih . this is a permutations problem ( order matters ) with repeating elements . given thatlowcards are worth 1 pt andhigh cards 2 pts , and you must draw 3 low cards , we know that you must also draw 1 high card . the formula for permutations problems with repeating elements isn ! / a ! b ! . . . where n represents the number of elements in the group and a , b , etc . represent the number of times that repeating elements are repeated . here there are 4 elements and thelowcard is repeated 3 times . as a result , the formula is : 3 ! / 2 ! which represents ( 3 * 2 * 1 ) / ( 2 * 1 ) which simplifies to just 4 , giving you answer c ."
Answer: c
Question (physics): calculate how much time could be saved if the train would run at its usual speed , given that it ran at 4 / 9 of its own speed and got to its destination in 13 hours ?
Options: a ) 1.22 hrs , b ) 2.22 hrs , c ) 5.22 hrs , d ) 6.22 hrs , e ) 7.22 hrs
Rationale: "new speed = 4 / 9 of usual speed new time = 4 / 9 of usual time 4 / 9 of usual time = 13 hrs usual time = 13 * 4 / 9 = 5.78 hrs time saved = 13 - 5.78 = 7.22 hrs answer is e"
Answer: e
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 15.3 years . the ration of the number of boys to the number of girls in the class is ?
Options: a ) 5 : 6 , b ) 2 : 3 , c ) 2 : 5 , d ) 2 : 1 , e ) 2 : 4
Rationale: "let the ratio be k : 1 . then , k * 16.4 + 1 * 15.3 = ( k + 1 ) * 15.8 = ( 16.4 - 15.8 ) k = ( 15.8 - 15.3 ) = k = 0.5 / 0.6 = 5 / 6 required ratio = 5 / 6 : 1 = 5 : 6 . answer : a"
Answer: a
Question (physics): a boy is travelling from his home to school at 6 km / hr and reached 7 min late . next day he travelled at 12 km / hr and reached 8 min early . distance between home and school ?
Options: a ) 2 km , b ) 3 km , c ) 4 km , d ) 5 km , e ) 6 km
Rationale: "let the distance be x t 1 = x / 6 hr t 2 = x / 12 hr difference in time = 7 + 8 = 15 = 1 / 4 hr x / 6 - x / 12 = 1 / 4 x / 12 = 1 / 4 x = 3 km answer is b"
Answer: b
Question (physics): 44 cubic centimetres of silver is drawn into a wire 1 mm in diameter . the length of the wire in metres will be :
Options: a ) 56 m , b ) 88 m , c ) 120 m , d ) 137 m , e ) none
Rationale: "sol . let the length of the wire b h . radius = 1 / 2 mm = 1 / 20 cm . then , 22 / 7 * 1 / 20 * 1 / 20 * h = 44 ⇔ = [ 44 * 20 * 20 * 7 / 22 ] = 5600 cm = 56 m . answer a"
Answer: a
Question (physics): a boat can travel with a speed of 24 km / hr in still water . if the speed of the stream is 4 km / hr , find the time taken by the boat to go 84 km downstream
Options: a ) 3 hours , b ) 4 hours , c ) 5 hours , d ) 6 hours , e ) 7 hours
Rationale: "explanation : speed of the boat in still water = 24 km / hr speed of the stream = 4 km / hr speed downstream = ( 22 + 5 ) = 28 km / hr distance travelled downstream = 84 km time taken = distance / speed = 84 / 28 = 3 hours answer : option a"
Answer: a
Question (other): if 75 % of a boys answered the first question on a certain test correctly , 55 % answered the second question on the test correctly , and 20 % answered neither of the questions correctly , what % answered both correctly ?
Options: a ) 10 % , b ) ( 8 ) 20 % , c ) 50 % , d ) 60 % , e ) 65 %
Rationale: { total } = { first } + { second } - { both } + { neither } 100 % = 75 % + 55 % - { both } + 20 % - - > { both } = 50 % . answer : c
Answer: c
Question (general): the sum of ages of 5 children born at the intervals of 3 years each is 50 years . find out the age of the youngest child ?
Options: a ) 9 , b ) 8 , c ) 7 , d ) 6 , e ) 4
Rationale: let the age of the youngest child = x then , the ages of 5 children can be written as x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 50 ⇒ 5 x + 30 = 50 ⇒ 5 x = 20 ⇒ x = 205 = 4 answer is e .
Answer: e
Question (geometry): if the volume of two cubes are in the ratio 27 : 8 , the ratio of their edges is :
Options: a ) 3 : 1 , b ) 3 : 2 , c ) 3 : 5 , d ) 3 : 7 , e ) none of these
Rationale: "explanation : let the edges be a and b of two cubes , then a 3 / b 3 = 27 / 8 = > ( a / b ) 3 = ( 3 / 2 ) 3 a / b = 3 / 2 = > a : b = 3 : 2 option b"
Answer: b
Question (general): a trained covered x km at 40 kmph and another 2 x km at 20 kmph . find the average speed of the train in covering the entire 6 x km .
Options: a ) 40 kmph , b ) 45 kmph , c ) 48 kmph , d ) 50 kmph , e ) 55 kmph
Rationale: "total time taken = x / 40 + 2 x / 20 hours = 5 x / 40 = x / 8 hours average speed = 6 x / ( x / 8 ) = 48 kmph answer : c"
Answer: c
Question (gain): mary works in a restaurant a maximum of 45 hours . for the first 20 hours , she is paid $ 8 per hour . for each overtime hour , she is paid at a rate which is 25 % higher than her regular rate . how much mary can earn in a week ?
Options: a ) 300 , b ) 420 , c ) 410 , d ) 320 , e ) 400
Rationale: "mary receives $ 8 ( 20 ) = $ 160 for the first 20 hours . for the 25 overtime hours , she receives $ 8 ( 0.25 ) + $ 8 = $ 10 per hour , that is $ 10 ( 25 ) = $ 250 . the total amount is $ 160 + $ 250 = $ 410 answer c 410 ."
Answer: c
Question (gain): a 20 % stock yielding 8 % is quoted at ?
Options: a ) 165 , b ) 170 , c ) 250 , d ) 180 , e ) 185
Rationale: "assume that face value = rs . 100 as it is not given to earn rs . 8 , money invested = rs . 100 to earn rs . 20 , money invested = 100 × 20 / 8 = rs . 250 ie , market value of the stock = rs . 250 answer is c ."
Answer: c
Question (physics): two stations a and b are 110 km apart on a straight line . one train starts from a at 9 a . m . and travels towards b at 20 kmph . another train starts from b at 8 a . m . and travels towards a at a speed of 25 kmph . at what time will they meet ?
Options: a ) 11 , b ) 10 , c ) 8 , d ) 12 , e ) 15
Rationale: "suppose they meet x hours after 9 a . m . distance covered by a in x hours = 20 x km . distance covered by b in ( x - 1 ) hours = 25 ( x - 1 ) km . therefore 20 x + 25 ( x - 1 ) = 110 45 x = 135 x = 3 . so , they meet at 12 a . m . answer : d"
Answer: d
Question (physics): annie and sam set out together on bicycles traveling at 15 and 12 km per hour respectively . after 40 minutes , annie stops to fix a flat tire . if it takes annie 25 minutes to fix the flat tire and sam continues to ride during this time , how many minutes will it take annie to catch up with sam assuming that annie resumes riding at 15 km per hour ?
Options: a ) 20 , b ) 40 , c ) 60 , d ) 80 , e ) 100
Rationale: "annie gains 3 km per hour ( or 1 km every 20 minutes ) on sam . after 40 minutes annie is 2 km ahead . sam rides 1 km every 5 minutes . in the next 25 minutes , sam rides 5 km so sam will be 3 km ahead . it will take annie 60 minutes to catch sam . the answer is c ."
Answer: c
Question (general): if 5 a = 3125 , then the value of 5 ( a - 3 ) is
Options: a ) 25 , b ) 50 , c ) 250 , d ) 300 , e ) none
Rationale: "sol . 5 a = 3125 = 5 a = 55 a = 5 . 5 ( 1 - 3 ) = 5 ( 5 - 3 ) = 5 ( 2 ) = 25 . answer a"
Answer: a