Cheukting/mathqa huggingface dataset:
Question (gain): a man buys 54 pens at marked price of 46 pens from a whole seller . if he sells these pens giving a discount of 1 % , what is the profit percent ?
Options: a ) 7.6 % , b ) 7.7 % , c ) 16.21 % , d ) 13.6 % , e ) 7.8 %
Rationale: "explanation : let marked price be re . 1 each c . p . of 54 pens = rs . 46 s . p . of 54 pens = 99 % of rs . 54 = rs . 53.46 profit % = ( profit / c . p . ) x 100 profit % = ( 7.46 / 46 ) x 100 = 16.21 % answer : c"
Answer: c
Question (physics): find the area of a cuboid of length 15 cm , breadth 10 cm . and height 16 cm .
Options: a ) 2400 cm cube , b ) 2410 cm cube , c ) 2420 cm cube , d ) 2430 cm cube , e ) 2480 cm cube
Rationale: "area of a cuboid = lxbxh = 15 cm x 10 cm x 16 cm = 2400 cm cube answer : a"
Answer: a
Question (physics): a can do a piece of work in 15 days . a does the work for 5 days only and leaves the job . b does the remaining work in 6 days . in how many days b alone can do the work ?
Options: a ) 5 days , b ) 7 days , c ) 12 days , d ) 9 days , e ) 10 days
Rationale: "explanation : a ’ s 5 day work = 5 * 1 / 15 = 1 / 3 remaining work = 1 - 1 / 3 = 2 / 3 b completes 2 / 3 work in 6 days b alone can do in x days 2 / 3 * x = 6 x = 9 days answer : option d"
Answer: d
Question (general): the sum of first n consecutive odd integers is n ^ 2 . what is the sum of all odd integers between 15 and 41 inclusive .
Options: a ) 351 , b ) 392 , c ) 410 , d ) 424 , e ) 450
Rationale: "we ' re dealing with a sequence of consecutive odd integers : 15 to 41 , inclusive . we ' re asked for the sum of this group . 1 ) start with the sum of the smallest and the biggest : 15 + 41 = 56 2 ) now look at the ' next smallest ' and the ' next biggest ' : 17 + 39 = 56 now we have proof that there is no middle term . we have 7 bunches of 56 . 7 ( 56 ) = 392 b"
Answer: b
Question (gain): the cost price of a radio is rs . 1800 and it was sold for rs . 1430 , find the loss % ?
Options: a ) 18 % , b ) 20.5 % , c ) 30 % , d ) 45 % , e ) 12 %
Rationale: "1800 - - - - 370 100 - - - - ? = > 20.5 % answer : b"
Answer: b
Question (physics): when working alone , painter w can paint a room in 2 hours , and working alone , painter x can paint the same room in z hours . when the two painters work together and independently , they can paint the room in 3 / 4 of an hour . what is the value of z ?
Options: a ) 3 / 4 , b ) 1 [ 1 / 5 ] , c ) 1 [ 2 / 5 ] , d ) 1 [ 3 / 4 ] , e ) 2
Rationale: "rate * time = work let painter w ' s rate be w and painter x ' s rate be x r * t = work w * 2 = 1 ( if the work done is same throughout the question then the work done can be taken as 1 ) = > w = 1 / 2 x * z = 1 = > x = 1 / z when they both work together then their rates get added up combined rate = ( w + x ) r * t = work ( w + x ) * 3 / 4 = 1 = > w + x = 4 / 3 = > 1 / 2 + 1 / z = 4 / 3 = > 1 / z = ( 8 - 3 ) / 6 = 5 / 6 = > z = 6 / 5 = 1 [ 1 / 5 ] answer b"
Answer: b
Question (physics): a work crew of 6 men takes 8 days to complete one - half of a job . if 9 men are then added to the crew and the men continue to work at the same rate , how many days will it take the enlarged crew to do the rest of the job ?
Options: a ) 2 , b ) 3 , c ) 3 1 / 5 , d ) 4 , e ) 4 4 / 5
Rationale: "suppose 1 man can do work in x days . . so 4 men will do in . . 6 / x = 1 / 8 * 1 / 2 as half job is done x = 96 now 9 more are added then 15 / 96 = 1 / 2 * 1 / d for remaining half job d = 3 1 / 5 number of days c"
Answer: c
Question (general): what is the dividend . divisor 17 , the quotient is 8 and the remainder is 5
Options: a ) a ) 145 , b ) b ) 141 , c ) c ) 150 , d ) d ) 153 , e ) e ) 158
Rationale: "d = d * q + r d = 17 * 8 + 5 d = 136 + 5 d = 141 answer : b"
Answer: b
Question (physics): a searchlight on top of the watch - tower makes 3 revolutions per minute . what is the probability that a man appearing near the tower will stay in the dark for at least 15 seconds ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4
Rationale: "3 revolutions per minute = 1 revolution every 20 seconds so no matter what anybody appearing at the tower can not stay in the dark for more than 20 seconds . this will be our total number of possibilities i . e the denominator . p ( man in dark for at least 15 seconds ) = 1 - p ( man in dark for max of 15 seconds ) = 1 - 15 / 20 = 1 - 3 / 4 = 1 / 4 or the other way would be : p ( man in dark for at least 5 seconds ) is like saying he can be in dark for 5 , 6,7 . . . all the way to 20 seconds because that is the max . in this approach it would be 5 / 20 seconds = 1 / 4 . answer is a"
Answer: a
Question (physics): john and amanda stand at opposite ends of a straight road and start running towards each other at the same moment . their rates are randomly selected in advance so that john runs at a constant rate of 3 , 4 , or 5 miles per hour and amanda runs at a constant rate of 3 , 4 , 5 , 6 , or 7 miles per hour . what is the probability that john has traveled farther than amanda by the time they meet ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 5 , d ) 2 / 15 , e ) 4 / 15
Rationale: john will run farther if he runs at 5 mph and amanda runs at 4 mph or 3 mph . in this case , p ( john runs farther ) = 1 / 3 * 2 / 5 = 2 / 15 john will run farther if he runs at 4 mph and amanda runs at 3 mph . in this case , p ( john runs farther ) = 1 / 3 * 1 / 5 = 1 / 15 p ( john runs farther ) = 2 / 15 + 1 / 15 = 3 / 15 = 1 / 5 the answer is c .
Answer: c
Question (general): the average of numbers 0.64205 , 0.64203 , 0.64202 and 0.64201 is ?
Options: a ) 0.64202 , b ) 0.64204 , c ) 0.642022 , d ) 0.642028 , e ) none
Rationale: "answer average = ( 0.64205 + 0.64203 + 0.64202 + 0.64201 ) / 4 = 2.56811 / 4 = 0.642028 correct option : d"
Answer: d
Question (physics): two bullet train s 140 m and 210 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time ( in seconds ) which they take to cross each other , is :
Options: a ) 15.8 sec . , b ) 12.6 sec . , c ) 11.8 sec . , d ) 10.8 sec . , e ) 08.8 sec .
Rationale: "relative speed = ( 60 + 40 ) km / hr = 100 x 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = ( 140 + 210 ) m = 350 m . required time = 350 x 9 / 250 = 54 / 5 = 12.6 sec . answer b"
Answer: b
Question (general): 4 friends are pooling their money for pizza . emma has 8 dollars . daya has 25 % more money than emma , jeff has 2 / 5 of the money daya has , and brenda has 4 more dollars than jeff . how much money does brenda have ?
Options: a ) 14 , b ) 6 , c ) 7 , d ) 8 , e ) 10
Rationale: d 8 emma has 8 dollars . daya has 25 % more dollars than emma . daya = 8 + 8 x 25 % = 8 + 8 x . 25 = 8 + 2 = 10 jeff has 2 / 5 of what daya has . = 10 x 2 / 5 = 4 brenda has 4 more dollars than jeff . = 4 + 4 = 8 brenda has 8 dollars . the correct answer is d .
Answer: d
Question (gain): in one alloy there is 12 % chromium while in another alloy it is 8 % . 35 kg of the first alloy was melted together with 40 kg of the second one to form a third alloy . find the percentage of chromium in the new alloy .
Options: a ) 8.8 % , b ) 9.75 % , c ) 9.2 % , d ) 8.6 % , e ) 8.4 %
Rationale: "the amount of chromium in the new 35 + 45 = 80 kg alloy is 0.12 * 35 + 0.08 * 45 = 7.8 kg , so the percentage is 7.8 / 80 * 100 = 9.75 % . answer : b ."
Answer: b
Question (general): mike took a taxi to the airport and paid $ 2.50 to start plus $ 0.25 per mile . annie took a different route to the airport and paid $ 2.50 plus $ 5.00 in bridge toll fees plus $ 0.25 per mile . if each was charged exactly the same amount , and annie ' s ride was 26 miles , how many miles was mike ' s ride ?
Options: a ) 20 , b ) 30 , c ) 36 , d ) 46 , e ) 54
Rationale: "the cost of annie ' s ride was 2.5 + 5 + ( 0.25 * 26 ) = $ 14 let x be the distance of mike ' s ride . the cost of mike ' s ride is 2.5 + ( 0.25 * x ) = 14 0.25 * x = 11.5 x = 46 miles the answer is d ."
Answer: d
Question (gain): fox jeans regularly sell for $ 15 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 8.91 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discount rates is 22 percent , what is the discount rate on pony jeans ?
Options: a ) 9 % , b ) 10 % , c ) 11 % , d ) 12 % , e ) 15 %
Rationale: "let x be the discount on pony jeans . then 0.22 - x is the discount on fox jeans . 3 ( 0.22 - x ) ( 15 ) + 2 x ( 18 ) = 8.91 9.9 - 45 x + 36 x = 8.91 9 x = 0.99 x = 0.11 the answer is c ."
Answer: c
Question (gain): find the simple interest on $ 10000 at 4 % per annum for 12 months ?
Options: a ) $ 400 , b ) $ 500 , c ) $ 650 , d ) $ 710 , e ) $ 1000
Rationale: "p = $ 10000 r = 4 % t = 12 / 12 years = 1 year s . i . = p * r * t / 100 = 10000 * 4 * 1 / 100 = $ 400 answer is a"
Answer: a
Question (physics): 50 men took a dip in a water tank 40 m long and 20 m broad on a religious day . if the average displacement of water by a man is 3 m 3 , then the rise in the water level in the tank will be :
Options: a ) 20 cm , b ) 25 cm , c ) 35 cm , d ) 18.75 cm , e ) none of these
Rationale: "explanation : total volume of water displaced = ( 3 x 50 ) m 3 = 150 m 3 rise in water level = 150 / 40 ã — 20 = 0.1875 m = 18.75 cm answer : d"
Answer: d
Question (physics): a contractor undertakes to built a walls in 50 days . he employs 40 peoples for the same . however after 25 days he finds that only 40 % of the work is complete . how many more man need to be employed to complete the work in time ?
Options: a ) 60 , b ) 30 , c ) 35 , d ) 20 , e ) none of these
Rationale: "40 men complete 0.4 work in 25 days . applying the work rule , m 1 × d 1 × w 2 = m 2 × d 2 × w 1 we have , 40 × 25 × 0.6 = m 2 × 25 × 0.4 or m 2 = 40 × 25 × 0.6 / 25 × 0.4 = 60 men answera"
Answer: a
Question (general): the average weight of 6 person ' s increases by 4.5 kg when a new person comes in place of one of them weighing 75 kg . what might be the weight of the new person ?
Options: a ) 160 kg , b ) 175 kg , c ) 180 kg , d ) 102 kg , e ) 190 kg
Rationale: "total weight increased = ( 6 x 4.5 ) kg = 27 kg . weight of new person = ( 75 + 27 ) kg = 102 kg option d"
Answer: d
Question (physics): a thief goes away with a santro car at a speed of 40 kmph . the theft has been discovered after half an hour and the owner sets off in a bike at 60 kmph when will the owner over take the thief from the start ?
Options: a ) a ) 2 , b ) b ) 5 , c ) c ) 7 , d ) d ) 5 , e ) e ) 1
Rationale: "explanation : | - - - - - - - - - - - 20 - - - - - - - - - - - - - - - - - - - - | 60 40 d = 20 rs = 60 – 40 = 20 t = 20 / 10 = 1 hours answer : option e"
Answer: e
Question (gain): sandy buys an old scooter for $ 900 and spends $ 300 on its repairs . if sandy sells the scooter for $ 1500 , what is the gain percent ?
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 30 %
Rationale: "selling price / total cost = 1500 / 1200 = 1.25 the gain percent is 25 % . the answer is d ."
Answer: d
Question (general): a , b , c , d , e are the 5 electronic shops in the naza market , which have 20 , 30 , 60 , 80 and 50 t . v . sets with them respectively , then the average number of t . v . sets in each shop is
Options: a ) 24 , b ) 48 , c ) 50 , d ) 60 , e ) none
Rationale: answer average number of t . v . sets = ( 20 + 30 + 60 + 80 + 50 ) / 5 = 48 correct option : b
Answer: b
Question (general): a no . when divided by 281 gives a remainder 160 , what remainder will be obtainedby dividingthe same no . 21 ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: "281 + 160 = 441 / 21 = 21 ( remainder ) a"
Answer: a
Question (geometry): in the rectangular coordinate system , points ( 16 , 0 ) and ( – 16 , 0 ) both lie on circle c . what is the maximum possible value of the radius of c ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 16 , e ) none of the above
Rationale: "d it takes 3 distinct points to define a circle . only 2 are given here . the two points essentially identify a single chord of the circle c . since no other information is provided , however , the radius of the circle can essentially be anything . all this information tell us is that the radius isgreater 16 d"
Answer: d
Question (physics): the speed of a railway engine is 74 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 ) 49 , b ) 18 , c ) 16 , d ) 17 , e ) 19
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 = 74 - 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 = 74 - k * sqrt ( 9 ) = 74 - 3 k k = 16.67 now , we need to know : what value of n makes s go to zero ? 0 = 74 - 16.67 * sqrt ( n ) 16.67 * sqrt ( n ) = 74 sqrt ( n ) = 4.44 n = 4.44 ^ 2 > 19 with 20 compartments , the train does not budge . therefore , it would budge if there were one fewer cars . thus , 19 is the maximum number of cars the engine can pull and still move . e"
Answer: e
Question (general): the sum of even numbers between 1 and 31 is
Options: a ) 16 , b ) 128 , c ) 240 , d ) 512 , e ) none
Rationale: "solution required numbers are 2 , 4 , 6 , . . 30 . this is an a . p containing 15 terms . required sum = n / 2 ( first term + last term ) ‹ = › 15 / 2 ( 2 + 30 ) ‹ = › 240 . answer c"
Answer: c
Question (general): find value for x from below equation ? x + 1 = - 3
Options: a ) 1 , b ) - 4 , c ) - 1 , d ) 2 , e ) 3
Rationale: "1 . subtract 1 from both sides : x + 1 - 1 = - 3 - 1 2 . simplify both sides : x = - 4 b"
Answer: b
Question (general): if the average ( arithmetic mean ) of a and b is 45 and the average of b and c is 50 , what is the value of c â ˆ ’ a ?
Options: a ) 25 , b ) 10 , c ) 90 , d ) 14 , e ) it can not be determined from the information given
Rationale: "the arithmetic mean of a and b = ( a + b ) / 2 = 45 - - a + b = 90 - - 1 similarly for b + c = 100 - - 2 subtracting 1 from 2 we have c - a = 10 ; answer : b"
Answer: b
Question (gain): a certain plant was 11 feet long on the day it was plantedthe length grows by a constant amount everyday ( inc . the first day it was planted ) . if this plant grew by 30 % b / w the 4 th day and 10 th day after it was planted , how many feet per day does the plant grow
Options: a ) a ) 2 , b ) b ) 4.5 , c ) c ) 0.69 , d ) d ) 5.5 , e ) e ) 3
Rationale: if the plant is 11 feet tall when it is planted , it will be 11 + k feet tall at the end of the day ( where k is the constant length it grows by every day ) . similarly , at the end of the 4 th day the plant must be 11 + 4 k feet tall and at the end of the 10 th day it must be 11 + 10 k feet tall . therefore 6 k = 0.3 ( 11 + 4 k ) = > k = 0.69 therefore the plant grows by 0.69 feet every day . option ( c )
Answer: c
Question (general): 6,61 , 212,507 , _ ?
Options: a ) 974 , b ) 994 , c ) 954 , d ) 845 , e ) 754
Rationale: "( 2 ) 3 - 2 = 6 ( 4 ) ^ 3 - 3 = 61 ( 6 ) ^ 3 - 4 = 212 ( 8 ) ^ 3 - 5 = 507 ( 10 ) ^ 3 - 6 = 994 answer : b"
Answer: b
Question (physics): john and steve are speed walkers in a race . john is 14 meters behind steve when he begins his final push . john blazes to the finish at a pace of 4.2 m / s , while steve maintains a blistering 3.7 m / s speed . if john finishes the race 2 meters ahead of steve , how long was john ’ s final push ?
Options: a ) 13 seconds , b ) 17 seconds , c ) 26 seconds , d ) 32 seconds , e ) 51 seconds
Rationale: "let t be the time that john spent for his final push . thus , per the question , 4.2 t = 3.7 t + 14 + 2 - - - > 0.5 t = 16 - - - > t = 32 seconds . d is the correct answer ."
Answer: d
Question (general): the average age of an adult class is 40 years . 12 new students with an avg age of 32 years join the class . therefore decreasing theaverage by 4 year . find what was theoriginal strength of class ?
Options: a ) 11 , b ) 12 , c ) 17 , d ) 19 , e ) 21
Rationale: "let original strength = y then , 40 y + 12 x 32 = ( y + 12 ) x 36 ⇒ 40 y + 384 = 36 y + 432 ⇒ 4 y = 48 ∴ y = 12 b"
Answer: b
Question (gain): running at the same constant rate , 5 identical machines can produce a total of 270 bottles per minute . at this rate , how many bottles could 10 such machines produce in 4 minutes ?
Options: a ) 648 , b ) 1,800 , c ) 2,160 , d ) 10,800 , e ) 64,800
Rationale: "5 machines produce 270 bottles per minute ; 1 machine produces 270 / 5 = 54 bottles per minute ; 10 machines produce 54 * 10 = 540 bottles per minute ; in 4 minutes 10 machines produce 540 * 4 = 2,160 bottles . answer : c ."
Answer: c
Question (physics): the radius of the wheel of a bus is 100 cms and the speed of the bus is 66 km / h , then the r . p . m . ( revolutions per minutes ) of the wheel is
Options: a ) 175 , b ) 250 , c ) 300 , d ) 330 , e ) none of these
Rationale: "radius of the wheel of bus = 100 cm . then , circumference of wheel = 2 ï € r = 200 ï € = 628.57 cm distance covered by bus in 1 minute = 66 â  „ 60 ã — 1000 ã — 100 cms distance covered by one revolution of wheel = circumference of wheel = 440 cm â ˆ ´ revolutions per minute = 6600000 / 60 ã — 628.57 = 175 answer a"
Answer: a
Question (geometry): what is the smallest positive integer x , such that 1944 x is a perfect cube ?
Options: a ) 4 , b ) 3 , c ) 8 , d ) 12 , e ) 18
Rationale: "take out the factors of 1944 that will come 2 ^ 3 * 3 ^ 3 * 3 ^ 2 . for perfect cube you need every no . raise to the power 3 . for 1944 to be a perfect cube , need 1 3 that means = 3 b is the answer ."
Answer: b
Question (general): if n is an integer and 101 n ^ 2 is less than or equal to 6400 , what is the greatest possible value of n ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: 101 * n ^ 2 < = 6400 n ^ 2 < = 6400 / 101 which will be less than 81 since 6400 / 100 = 64 which is the square of 9 next closest value of n where n ^ 2 < = 64 is 7 ans 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
Rationale: "answer let the number be n . then , ( n / 5 ) + 5 = ( n / 4 ) - 5 ⇒ ( n / 4 ) - ( n / 5 ) = 10 ⇒ ( 5 n - 4 n ) / 20 = 10 ∴ n = 200 option : c"
Answer: c
Question (physics): a train 360 m long runs with a speed of 45 km / hr . what time will it take to pass a platform of 390 m long ?
Options: a ) 38 sec , b ) 35 sec , c ) 44 sec , d ) 40 sec , e ) 60 sec
Rationale: "explanation : speed = 45 km / hr = 45 × ( 10 / 36 ) m / s = 150 / 12 = 50 / 4 = 25 / 2 m / s total distance = length of the train + length of the platform = 360 + 390 = 750 meter time taken to cross the platform = 750 / ( 25 / 2 ) = 750 × 2 / 25 = 60 seconds answer : option e"
Answer: e
Question (general): a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets rs . 500 more than d , what is a ' s share ?
Options: a ) rs . 2500 , b ) rs . 1000 , c ) rs . 1500 , d ) rs . 2000 , e ) none
Rationale: sol . let the shares of a , b , c and d be rs . 5 x , rs . 2 x , rs . 4 x and rs . 3 x respectively . then , 4 x - 3 x = 500 ⇔ x = 500 . ∴ a ' s share = rs . 5 x = rs . ( 5 x 500 ) = rs . 2500 . answer a
Answer: a
Question (other): a certain high school has 500 students . of these students , 50 are taking music , 20 are taking art , and 10 are taking both music and art . how many students are taking neither music nor art ?
Options: a ) 430 , b ) 440 , c ) 450 , d ) 460 , e ) 470
Rationale: "we ' re given a series of facts to work with : 1 ) a certain high school has 500 students . 2 ) of these students : x are taking music , y are taking art , and z are taking both music and art . we ' re asked how many students are taking neither music nor art ? let ' s test x = 50 y = 20 z = 10 so , we have 50 students taking music , 20 taking art and 10 taking both music and art . 40 student taking just music 10 student taking just art 10 student taking both music and art total = 60 students we ' re asked for the total number of students who are taking neither course . that is 500 - 60 = 440 . b"
Answer: b
Question (other): praveen starts business with rs . 3920 and after 5 months , hari joins with praveen as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is hari ’ s contribution in the capital ?
Options: a ) s . 10080 , b ) s . 8000 , c ) s . 8500 , d ) s . 9000 , e ) s . 6000
Rationale: "let hari ’ s capital be rs . x . then , 3920 * 12 / 7 x = 2 / 3 = > 14 x = 141120 = > x = 10080 . answer : a"
Answer: a
Question (general): the ratio between b and y is 7 / 9 ; b and y are increased by 4 , what is the ratio between the new values of b and y ?
Options: a ) 7 / 9 , b ) 14 / 9 , c ) 7 / 18 , d ) 11 / 13 , e ) it can not be determined
Rationale: ratio = 7 k / 9 k = 7 / 9 , 14 / 18 , etc . b and y are increased by 4 - - > ( 7 k + 4 ) / ( 9 k + 4 ) new ratio can be 11 / 13 , 18 / 22 , etc . answer : e
Answer: e
Question (gain): the difference between simple interest and compound interest on rs . 1200 for one year at 10 % per annum reckoned half yearly is
Options: a ) 2 , b ) 7 , c ) 3 , d ) 0 , e ) 8
Rationale: "explanation : s . i = rs . ( 1200 x 10 x 1 / 100 ) = rs . 120 . c . i = rs [ ( 1200 x 1 + 5 / 100 ) ² - 1200 ] = rs . 123 . difference = rs . [ 123 - 120 ] = rs . 3 . answer : b"
Answer: b
Question (physics): a woman can do a piece of work in 40 days . man is 25 % more efficient than woman . in how many days a man can do the same piece of work ?
Options: a ) 32 days , b ) 36 days , c ) 38 days , d ) 40 days , e ) 53 days
Rationale: the ratio of the efficiencies of a woman and man = 100 : 125 = 4 : 5 the ratio of the days taken by woman and man to finish the work = 5 : 4 woman takes 32 days to finish the work . = > 5 parts = 40 the number of days taken by man to finish the work = 4 parts = 40 / 5 x 4 = 32 days a
Answer: a
Question (general): if a ^ 2 + b ^ 2 = 144 and ab ≠ 0 , then the greatest possible value for b is between
Options: a ) 16 and 13 , b ) 12 and 3 , c ) 11 and 4 , d ) 10 and 5 , e ) 9 and 6
Rationale: since a ≠ 0 , greatest possible value for b will be less than 12 but closer to it . so it lies between 11 and 12 answer : b
Answer: b
Question (other): the ratio between the present ages of a and b is 3.5 : 3 respectively . the ratio between a ' s age 4 years ago and b ' s age 4 years hence is 1 : 1 . what is the ratio between a ' s age 4 years hence and b ' s age 4 years ago ?
Options: a ) 14 : 4 , b ) 13 : 0 , c ) 15 : 11 , d ) 13 : 12 , e ) 13 : 17
Rationale: "let the present ages of a and b be 3.5 x and 3 x years respectively . then , ( 3.5 x - 4 ) / ( 3 x + 4 ) = 1 / 1 0.5 x = 8 = > x = 16 required ratio = ( 5 x + 4 ) : ( 3 x - 4 ) = 60 : 44 = 15 : 11 . answer : c"
Answer: c
Question (physics): ram , who is half as efficient as krish , will take 21 days to complete a task if he worked alone . if ram and krish worked together , how long will they take to complete the task ?
Options: a ) 16 days , b ) 12 days , c ) 8 days , d ) 7 days , e ) 18 days
Rationale: "number of days taken by ram to complete task = 21 since ram is half as efficient as krish , amount of work done by krish in 1 day = amount of work done by ram in 2 days if total work done by ram in 24 days is 21 w amount of work done by ram in 1 day = w amount of work done by krish in 1 day = 2 w total amount of work done by krish and ram in a day = 3 w total amount of time needed by krish and ram to complete task = 21 w / 3 w = 7 days answer d"
Answer: d