Cheukting/mathqa huggingface dataset:
Question (general): average expenditure of a person for the first 3 days of a week is rs . 350 and for the next 4 days is rs . 420 . average expenditure of the man for the whole week is :
Options: a ) 350 , b ) 370 , c ) 390 , d ) 430 , e ) none
Rationale: "explanation : assumed mean = rs . 350 total excess than assumed mean = 4 × ( rs . 420 - rs . 350 ) = rs . 280 therefore , increase in average expenditure = rs . 280 / 7 = rs . 40 therefore , average expenditure for 7 days = rs . 350 + rs . 40 = rs . 390 correct option : c"
Answer: c
Question (gain): compound interest of rs . 1000 at 10 % per annum for 1 1 / 2 years will be ( interest compounded half yearly ) .
Options: a ) rs . 473 , b ) rs . 374 , c ) rs . 495 , d ) rs . 157 , e ) none of the above
Rationale: "10 % interest per annum will be 5 % interest half yearly for 3 terms ( 1 1 / 2 years ) so compound interest = 3000 [ 1 + ( 5 / 100 ) ] ^ 3 - 1000 = 1000 [ ( 21 / 20 ) ^ 3 - 1 ] = 1000 ( 9261 - 8000 ) / 8000 = 1 * 1261 / 8 = 157 answer : d"
Answer: d
Question (general): 4,25 , 49,121 , 169,289 , 361,529 ,
Options: a ) 149 , b ) 169 , c ) 841 , d ) 920 , e ) 219
Rationale: "29 ^ 2 = 841 because follow sequence of square of the prime numbers answer : c"
Answer: c
Question (general): what will be the vulgar fraction of 0.70
Options: a ) 3 / 5 , b ) 7 / 10 , c ) 3 / 2 , d ) 3 / 7 , e ) 3 / 8
Rationale: "explanation : 0.70 = 70 / 100 = 7 / 10 option b"
Answer: b
Question (physics): susan drove an average speed of 30 miles per hour for the first 40 miles of a trip then at a average speed of 15 miles / hr for the remaining 40 miles of the trip if she made no stops during the trip what was susan ' s avg speed in miles / hr for the entire trip
Options: a ) 35 , b ) 20 , c ) 45 , d ) 50 , e ) 55
Rationale: avg . speed = total distance / total time total distance = 80 miles total time = 40 / 30 + 40 / 15 = 4 avg . speed = 20 . answer - b
Answer: b
Question (general): if 25 % of x is 15 less than 15 % of 1500 , then x is ?
Options: a ) 720 , b ) 750 , c ) 820 , d ) 840 , e ) 860
Rationale: "25 % of x = x / 4 ; 15 % of 1500 = 15 / 100 * 1500 = 225 given that , x / 4 = 225 - 15 = > x / 4 = 210 = > x = 840 . answer : d"
Answer: d
Question (physics): two good train each 250 m long , are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one .
Options: a ) 12 sec , b ) 24 sec , c ) 48 sec , d ) 60 sec , e ) none
Rationale: "sol . relative speed = ( 45 + 30 ) km / hr = ( 75 x 5 / 18 ) m / sec = ( 125 / 6 ) m / sec . distance covered = ( 250 + 250 ) m = 1000 m . required time = ( 500 x 6 / 125 ) sec = 24 sec . answer b"
Answer: b
Question (gain): a is a working partner and b is a sleeping partner in the business . a puts in rs . 3500 and b rs . 1500 , a receives 10 % of the profit for managing the business the rest being divided in proportion of their capitals . out of a total profit of rs . 9600 , money received by a is ?
Options: a ) 1978 , b ) 2707 , c ) 7728 , d ) 7008 , e ) 7291
Rationale: "35 : 15 = > 7 : 3 9600 * 10 / 100 = 960 9600 - 960 = 8640 8640 * 7 / 10 = 6048 + 960 = 7008 answer : d"
Answer: d
Question (general): 45 % of major airline companies equip their planes with wireless internet access . 70 % of major airlines offer passengers free on - board snacks . what is the greatest possible percentage of major airline companies that offer both wireless internet and free on - board snacks ?
Options: a ) 25 % , b ) 35 % , c ) 45 % , d ) 55 % , e ) 65 %
Rationale: "to maximize the percentage of companies offering both , let ' s assume that all 45 % of companies which offer wireless internet also offer snacks . the answer is 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 4725 . what was the number of original inhabitants ?
Options: a ) 5000 , b ) 7000 , c ) 4000 , d ) 8000 , e ) 9000
Rationale: "let the total number of original inhabitants be x . ( 75 / 100 ) * ( 90 / 100 ) * x = 4725 ( 27 / 40 ) * x = 4725 x = 4725 * 40 / 27 = 7000 the answer is b ."
Answer: b
Question (gain): a and b invests rs . 3000 and rs . 6500 respectively in a business . if a doubles his capital after 6 months . in what ratio should a and b divide that year ' s profit ?
Options: a ) 8 : 8 , b ) 9 : 8 , c ) 9 : 6 , d ) 9 : 5 , e ) 9 : 13
Rationale: "( 3 * 6 + 6 * 6 ) : ( 6.5 * 12 ) 54 : 78 = > 9 : 13 answer : e"
Answer: e
Question (physics): if a car went the first third of the distance at 10 kmh , the second third at 24 kmh , and the last third at 48 kmh , what was the average speed of the car for the entire trip ?
Options: a ) 36 kmh , b ) 19 kmh , c ) 42 kmh , d ) 44 kmh , e ) 50 kmh
Rationale: "assume d / 3 = 240 ( this number is convenient because it is divisible by 10 , 24 and 48 ) so : 240 = 10 * t 1 = 24 hrs 240 = 24 * t 2 = 10 hrs 240 = 48 * t 3 = 5 hrs t = t 1 + t 2 + t 3 = 39 hrs d = rt ( 240 * 3 ) = r * 39 r = 19 answer : b"
Answer: b
Question (other): if 70 % of an equal to 40 % of b , then ratio between a and b is ?
Options: a ) 4 : 7 , b ) 4 : 9 , c ) 4 : 2 , d ) 4 : 1 , e ) 4 : 5
Rationale: explanation : 70 a = 40 b a : b = 4 : 7 answer : a
Answer: a
Question (other): a college has classes from 10 : 00 am until 1 : 40 pm . in this duration , there are 5 periods . if 5 minutes are provided between each period to leave one class and enter the next class , how many minutes long is each period ?
Options: a ) 38 min , b ) 41 min , c ) 40 min , d ) 42 min , e ) 52 min
Rationale: the total time is 220 minutes . there are four breaks of five minutes between the classes for a total of 20 minutes . the total class time is 200 minutes . 200 / 5 classes = 40 minutes per class the answer is c .
Answer: c
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 5 points if you must draw exactly 3 “ low ” cards ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: to get a 5 , you need one high and three lows ( you could have had 2 highs and one low , but the constraint is that you must have three low cards ) hlll = 4 ! 3 ! = 4 4 ! is the number of ways you can arrange these four spaces . divide by 3 ! because you you repeat three low cards ans : d
Answer: d
Question (other): john distributes his pencil among his 4 friends rose , mary , ranjan , and rohit in the ratio 1 / 2 : 1 / 3 : 1 / 3 : 1 / 5 . what is the minimum no . of pencils that the person should have ?
Options: a ) 41 , b ) 65 , c ) 70 , d ) 77 , e ) 98
Rationale: rakesh : rahul : ranjan : rohit = 1 / 2 : 1 / 3 : 1 / 3 : 1 / 5 step 1 : at first we need to do is lcm of 2 , 3,3 and 5 is 30 . step 2 : then pencil are distributed in ratio among friends , rakesh = ( 1 / 2 x 30 ) = 15 . rahul = ( 1 / 3 x 30 ) = 10 . ranjan = ( 1 / 3 x 30 ) = 10 . rohit = ( 1 / 5 x 30 ) = 6 . step 3 : total number of pencils are ( 15 x + 10 x + 10 x + 6 x ) = 41 x . for minimum number of pencils x = 1 . the person should have at least 41 pencils . a )
Answer: a
Question (general): the jogging track in a sports complex is 726 meters in circumference . deepak and his wife start from the same point and walk in opposite directions at 4.5 km / hr and 3.75 km / hr respectively . they will meet for the first time in ?
Options: a ) 450 min , b ) 528 min , c ) 610 min , d ) 714 min , e ) 359 min
Rationale: "clearly , the two will meet when they are 726 m apart to be 4.5 + 3.75 = 8.25 km apart , they take 1 hour to be 726 m apart , they take 100 / 825 * 726 / 1000 = 242 / 2750 * 60 = 528 min . answer is b"
Answer: b
Question (other): the marks obtained by vijay and amith are in the ratio 4 : 7 and those obtained by amith and abhishek in the ratio of 3 : 2 . the marks obtained by vijay and abhishek are in the ratio of ?
Options: a ) 6 : 8 , b ) 6 : 1 , c ) 6 : 5 , d ) 6 : 7 , e ) 6 : 3
Rationale: "4 : 7 3 : 2 - - - - - - - 12 : 21 : 14 12 : 14 6 : 7 answer : d"
Answer: d
Question (general): there are , in a certain league , 10 teams , and each team face another team for a total of 10 times . how many games are played in the season ?
Options: a ) 1000 , b ) 450 , c ) 720 , d ) 180 , e ) 400
Rationale: "by using the formula , t [ n ( n - 1 ) / 2 ] , where t = no . of games between two teams and n = total no . of teams , we get : 450 option a ."
Answer: a
Question (general): in 10 years , a will be twice as old 5 as b was 10 years ago . if a is now 8 years older than b , the present age of b is
Options: a ) 35 , b ) 37 , c ) 38 , d ) 41 , e ) 42
Rationale: "explanation : let b ' s age = x years . then , as age = ( x + 8 ) years . ( x + 8 + 10 ) = 2 ( x — 10 ) hence x = 38 . present age of b = 38 years answer : option c"
Answer: c
Question (general): an assembly line produces 36 cogs per hour until an initial order of 60 cogs is completed . the speed of the assembly line is then immediately increased so that it can produce 60 cogs per hour until another 60 cogs are produced . what is the overall average output , in cogs per hour , for the assembly line during this whole time ?
Options: a ) 38 , b ) 40 , c ) 42 , d ) 45 , e ) 50
Rationale: the time to produce the first 60 cogs is 60 / 36 = 5 / 3 hours . the time to produce the next 60 cogs is 60 / 60 = 1 hour . the average output is 120 cogs / ( 8 / 3 ) hours = 45 cogs per hour . the answer is d .
Answer: d
Question (general): if the number is decreased by 5 and divided by 7 the result is 7 . what would be the result if 2 is subtracted and divided by 13 ?
Options: a ) 4 , b ) 7 , c ) 8 , d ) 5 , e ) 3
Rationale: "explanation : let the number be x . then , ( x - 5 ) / 7 = 7 = > x - 5 = 49 x = 54 . : ( x - 2 ) / 13 = ( 54 - 2 ) / 13 = 4 answer : option a"
Answer: a
Question (gain): a ladder 14 feet long is leaning against a wall that is perpendicular to level ground . the bottom of the ladder is 5 feet from the base of the wall . if the top of the ladder slips down 4 feet , how many feet will the bottom of the ladder slip ?
Options: a ) 4 , b ) 5 , c ) 8 , d ) 10.72 , e ) 15
Rationale: "14 ^ 2 - 5 ^ 2 = 171 it means that the height is equal to 13.07 ~ = 13 . since the top of the ladder slips down 4 feet , then the height of the wall = 13 - 4 = 9 the bottom = sqrt ( 14 ^ 2 - 9 ^ 2 ) = sqrt ( 196 - 81 ) = 10.72 ans is d"
Answer: d
Question (gain): find the simple interest on rs . 78000 at 15 ( 2 / 5 ) % per annum for 9 months .
Options: a ) rs . 9009 , b ) rs . 9008 , c ) rs . 9002 , d ) rs . 9202 , e ) rs . 9001
Rationale: "explanation : p = rs . 78000 , r = 77 / 5 % p . a and t = 9 / 12 years = ¾ years therefore , s . i = ( p * r * t ) / 100 = ( 78000 * 77 / 5 * ¾ * 1 / 100 ) = rs . 9009 answer : a"
Answer: a
Question (general): the instructions state that cheryl needs 4 / 9 square yards of one type of material and 2 / 3 square yards of another type of material for a project . she buys exactly that amount . after finishing the project , however , she has 6 / 12 square yards left that she did not use . what is the total amount of square yards of material cheryl used ?
Options: a ) 1 / 12 , b ) 1 / 9 , c ) 2 / 3 , d ) 1 1 / 9 , e ) 4 / 9
Rationale: "total bought = 4 / 9 + 2 / 3 left part 6 / 12 - - - > 2 / 3 so used part 4 / 9 + 2 / 3 - 2 / 3 = 4 / 9 ans e"
Answer: e
Question (general): how many different pairs of positive integers ( a , b ) satisfy the equation 1 / a + 1 / b = 32 / 51 ?
Options: a ) 6 , b ) 3 , c ) 2 , d ) 1 , e ) 0
Rationale: "there is no certain way to solve 2 unknown with 1 equation . the best way is to look at the question and retrospect the most efficient way . in this question , a and b are only positive integers . so that is a big relief . now , we can start with putting a = 1,2 , . . and so on till the time we are confident about one of the options . so , we start with a = 1 , we get b as - ve . out a = 2 , we get b as 6 . yes ( now ( a , b ) = ( 2,6 ) . we can directly see that ( a , b ) = ( 6,2 ) will also satisfy . so we have 2 possible solutions ) a = 3 , we get b as 3 . yes ( now we have 3 possible solutions ) a = 4 , we get b as fraction . out a = 5 , we get b again as some fraction . out a = 6 already taken . we have a , b options left . c , d , e are out . a is 6 . to have 6 as the answer , we will need one more pair like 2,6 and one more solution where a = b . when a = b , we have only 1 solution = 2 . so , one more solution , where a = b is not possible . so , answer will be c ."
Answer: c
Question (general): a , b and c rents a pasture for rs . 870 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should b pay ?
Options: a ) 360 , b ) 227 , c ) 268 , d ) 198 , e ) 176
Rationale: "12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 12 / 29 * 870 = 360 answer : a"
Answer: a
Question (geometry): the surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 6 cm each . the radius of the sphere is
Options: a ) 3 cm , b ) 4 cm , c ) 6 cm , d ) 8 cm , e ) none
Rationale: "solution 4 î r 2 = 2 î 3 x 6 â ‡ ’ r 2 = ( 3 x 6 / 2 ) â ‡ ’ 9 â ‡ ’ r = 3 cm . answer a"
Answer: a
Question (physics): the speed of a railway engine is 96 km per hour when no compartment is attached , and the reduction in speed is directly proportional to the square root of the number of compartments attached . if the speed of the train carried by this engine is 24 km per hour when 9 compartments are attached , the maximum number of compartments that can be carried by the engine is :
Options: a ) 19 , b ) 18 , c ) 16 , d ) 17 , e ) 14
Rationale: "the reduction in speed is directly proportional to the square root of the number of compartments attached doesreductionmean amount subtracted ? or percentage decrease ? there are at least two interpretations , and the wording does not provide a clear interpretation between them . evidently what the question intends is the subtraction interpretation . what is subtracted from the speed is directly proportional to the square root of the number of compartments attached . in other words , if s = speed , and n = number of compartments , then s = 42 - k * sqrt ( n ) wherekis a constant of the proportionality . in general , if a is directly proportional to b , we can write a = k * b and solve for k . if n = 9 , then s = 24 24 = 96 - k * sqrt ( 9 ) = 96 - 3 k k = 24 now , we need to know : what value of n makes s go to zero ? 0 = 96 - 24 * sqrt ( n ) 24 * sqrt ( n ) = 96 sqrt ( n ) = 4 n = 4 ^ 2 = 16 thus , 16 is the maximum number of cars the engine can pull and still move . c"
Answer: c
Question (general): average of money that group of 4 friends pay for rent each month is $ 800 . after one persons rent is increased by 20 % the new mean is $ 870 . what was original rent of friend whose rent is increased ?
Options: a ) 800 , b ) 1400 , c ) 1000 , d ) 1100 , e ) 1200
Rationale: "0.2 x = 4 ( 870 - 800 ) 0.2 x = 280 x = 1400 answer b"
Answer: b
Question (general): if n = 2 ^ 0.3 and n ^ b = 16 , b must equal
Options: a ) 3 / 80 , b ) 3 / 5 , c ) 4 , d ) 5 / 3 , e ) 40 / 3
Rationale: "30 / 100 = 3 / 10 n = 2 ^ 3 / 10 n ^ b = 2 ^ 4 ( 2 ^ 3 / 10 ) ^ b = 2 ^ 4 b = 40 / 3 answer : e"
Answer: e
Question (general): the average mark of the students of a class in a particular exam is 90 . if 3 students whose average mark in that exam is 40 are excluded , the average mark of the remaining will be 95 . find the number of students who wrote the exam ?
Options: a ) 25 , b ) 35 , c ) 23 , d ) 22 , e ) 33
Rationale: "let the number of students who wrote the exam be x . total marks of students = 90 x . total marks of ( x - 3 ) students = 80 ( x - 3 ) 90 x - ( 3 * 40 ) = 95 ( x - 3 ) 165 = 5 x = > x = 33 answer : e"
Answer: e
Question (gain): a survey of employers found that during 1993 employment costs rose 3.5 percent , where employment costs consist of salary costs and fringe - benefit costs . if salary costs rose 3 percent and fringe - benefit costs rose 6.5 percent during 1993 , then fringe - benefit costs represented what percent of employment costs at the beginning of 1993 ?
Options: a ) 16.5 % , b ) 14 % , c ) 35 % , d ) 55 % , e ) 65 %
Rationale: the amount by which employment costs rose is equal to 0.035 ( salary costs + fringe benefit costs ) ; on the other hand the amount by which employment costs rose is equal to 0.03 * salary costs + 0.065 * fringe benefit costs ; so , 35 ( s + f ) = 30 s + 65 f - - > s = 6 f - - > f / s = 1 / 6 - - > f / ( s + f ) = 1 / ( 1 + 6 ) = 1 / 7 = 0.14 . answer : b .
Answer: b
Question (physics): machine a and machine b process the same work at different rates . machine c processes work as fast as machines a and b combined . machine d processes work 3 times as fast as machine c ; machine d ’ s work rate is also exactly 4 times machine b ’ s rate . assume all 4 machines work at fixed unchanging rates . if machine a works alone on a job , it takes 7 hours . if all 4 machines work together on the same job simultaneously , how many minutes will it take all of them to complete it ?
Options: a ) 8 , b ) 21 , c ) 24 , d ) 27 , e ) 30
Rationale: c = a + b d = 3 c = 3 ( a + b ) = 4 b then b = 3 a and c = 4 a the combined rate of the four machines is a + 3 a + 4 a + 12 a = 20 a machine a can complete the work in 420 minutes , so its rate is 1 / 420 of the work per minute . the combined rate is 20 / 420 = 1 / 21 so the work will be completed in 21 minutes . the answer is b .
Answer: b
Question (general): in a company the manager wants to give some gifts to all of the workers . in each block there are about 200 workers are there . the total amount for giving the gifts for all the workers is $ 6000 . the worth of the gift is 2 $ . how many blocks are there in the company ?
Options: a ) 10 , b ) 12 , c ) 18 , d ) 20 , e ) 15
Rationale: "each employee will get a gift worth of = $ 2 total employees = 6000 / 2 = 3000 total blocks = 3000 / 200 = 15 correct option is e"
Answer: e
Question (physics): a 300 meter long train crosses a platform in 48 seconds while it crosses a signal pole in 18 seconds . what is the length of the platform ?
Options: a ) 500 , b ) 289 , c ) 350 , d ) 882 , e ) 281
Rationale: "speed = [ 300 / 18 ] m / sec = 50 / 3 m / sec . let the length of the platform be x meters . then , x + 300 / 48 = 50 / 3 3 ( x + 300 ) = 2400 è x = 500 m . answer : a"
Answer: a
Question (gain): from january 1 , 2015 , to january 1 , 2017 , the number of people enrolled in health maintenance organizations increased by 12 percent . the enrollment on january 1 , 2017 , was 45 million . how many million people , to the nearest million , were enrolled in health maintenance organizations on january 1 , 2015 ?
Options: a ) 38 , b ) 39 , c ) 40 , d ) 41 , e ) 42
Rationale: "soln : - 12 x = 45 - - > 28 / 25 * x = 45 - - > x = 45 * 25 / 28 = 1125 / 28 = ~ 40 answer : c ."
Answer: c
Question (general): what is the average ( arithmetic mean ) of the numbers 100 , 150 , 200 , 200 , 250 , and 300 ?
Options: a ) 100 , b ) 150 , c ) 140 , d ) 200 , e ) 250
Rationale: "{ 100 , 150 , 200 , 200 , 250 , 300 } = { 200 - 100,200 - 50 , 200 , 200,200 + 50,200 + 100 } - - > the average = 200 . answer : d ."
Answer: d
Question (gain): andrew purchased 14 kg of grapes at the rate of 54 per kg and 10 kg of mangoes at the rate of 62 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) 1000 , b ) 1376 , c ) 1456 , d ) 1900 , e ) 1566
Rationale: "cost of 14 kg grapes = 54 × 14 = 756 . cost of 10 kg of mangoes = 62 x 10 = 620 . total cost he has to pay = 756 + 620 = 1376 b"
Answer: b
Question (physics): two trains move in the same direction at speeds 50 kmph and 32 kmph respectively . a man in the slower train observes that 15 seconds elapse before the faster train completely passes by him . what is the length of faster train ?
Options: a ) 100 m , b ) 75 m , c ) 120 m , d ) 50 m , e ) 70 m
Rationale: since both trains move in same direction so : average speed = 50 - 32 = 18 kmph = 5 mps speeed = length of train / time length of train = 5 * 15 = 75 m answer : b
Answer: b
Question (gain): what will be the fraction of 30 %
Options: a ) 1 / 4 , b ) 1 / 5 , c ) 3 / 10 , d ) 1 / 11 , e ) none of above
Rationale: "explanation : it will 30 * 1 / 100 = 3 / 10 option c"
Answer: c
Question (general): jacob is 39 years old . he is 3 times as old as his brother . how old will jacob be when he is twice as old ?
Options: a ) 63 , b ) 64 , c ) 65 , d ) 76 , e ) 67
Rationale: "j = 39 ; j = 3 b ; b = 39 / 3 = 13 ; twice as old so b = 13 ( now ) + ( 13 ) = 26 ; jacob is 39 + 26 = 65 answer : c"
Answer: c
Question (physics): how many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 42 kmph ?
Options: a ) 21.4 sec , b ) 77 sec , c ) 25 sec , d ) 18 sec , e ) 17 sec
Rationale: "d = 100 + 150 = 250 s = 42 * 5 / 18 = 11.7 mps t = 250 / 11.7 = 21.4 sec answer : a"
Answer: a
Question (physics): two cars of length 120 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively . in what time will they be clear of each other from the moment they meet ?
Options: a ) 10 sec , b ) 30 sec , c ) 40 sec , d ) 20 s , e ) 50 sec
Rationale: d relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 120 + 280 = 400 m . the time required = d / s = 400 / 20 = 20 s .
Answer: d
Question (general): a student is ranked 6 th from right and 5 th from left . how many students are there in totality ?
Options: a ) 10 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: "from right 6 , from left 5 total = 6 + 5 - 1 = 10 answer : a"
Answer: a
Question (physics): if 6 men can reap 60 acres of land in 10 days , how many acres of land can 12 men reap in 20 days ?
Options: a ) 120 , b ) 360 , c ) 240 , d ) 182 , e ) 1000
Rationale: "6 men 60 acres 10 days 12 men ? 20 days 60 * 12 / 6 * 20 / 10 60 * 2 * 2 60 * 4 = 240 answer : c"
Answer: c
Question (general): solve for x and check : 15 x = 165
Options: a ) 98 , b ) 165 , c ) 180 , d ) 253 , e ) none of these
Rationale: solution : dividing each side by 15 , we obtain ( 15 x / 15 ) = ( 165 / 15 ) therefore : x = 11 check : 15 x = 165 ( 15 * 11 ) = 165 165 = 165 answer : b
Answer: b
Question (physics): if ram and gohul can do a job in 10 days and 15 days independently . how many days would they take to complete the same job working simultaneously ?
Options: a ) 5 , b ) 8 , c ) 4 , d ) 7 , e ) 6
Rationale: "if total work is x . ram rate of working = x / 10 per day . gohul rate of working = x / 15 per day . rate of work = ( x / 10 ) + ( x / 15 ) = 30 x / 5 x = 6 days answer is option e"
Answer: e
Question (gain): what will be the difference between simple and compound interest at 8 % per annum on a sum of rs . 1000 after 4 years ?
Options: a ) 64.19 , b ) 64.12 , c ) 40.5 , d ) 64.1 , e ) 64.11
Rationale: "s . i . = ( 1000 * 8 * 4 ) / 100 = rs . 320 c . i . = [ 1000 * ( 1 + 8 / 100 ) 4 - 1000 ] = rs . 360.5 difference = ( 360.5 - 320 ) = rs . 40.5 answer : c"
Answer: c
Question (physics): a motorcyclist started riding at highway marker a , drove 120 miles to highway marker b , and then , without pausing , continued to highway marker c , where she stopped . the average speed of the motorcyclist , over the course of the entire trip , was 40 miles per hour . if the ride from marker a to marker b lasted 3 times as many hours as the rest of the ride , and the distance from marker b to marker c was half of the distance from marker a to marker b , what was the average speed , in miles per hour , of the motorcyclist while driving from marker b to marker c ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 67.5
Rationale: "a - b = 120 miles b - c = 60 miles avg speed = 40 miles time taken for a - b 3 t and b - c be t avg speed = ( 120 + 60 ) / total time 40 = 180 / 4 t t = 67.5 b - c = 67.5 mph answer e"
Answer: e