Cheukting/mathqa huggingface dataset:
Question (general): if x / y = 2 / 7 , then ( x + y ) / ( x - y ) = ?
Options: a ) 5 , b ) 1 / 5 , c ) - 1 / 6 , d ) - 9 / 5 , e ) - 5
Rationale: "any x and y satisfying x / y = 2 / 7 should give the same value for ( x + y ) / ( x - y ) . say x = 2 and y = 7 , then ( x + y ) / ( x - y ) = ( 2 + 7 ) / ( 2 - 7 ) = - 9 / 5 . answer : d ."
Answer: d
Question (physics): two goods trains each 500 m long are running in opposite directions on parallel tracks . their speeds are 70 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 ) 22 , b ) 36 , c ) 48 , d ) 99 , e ) 23
Rationale: "relative speed = 70 + 30 = 100 km / hr . 100 * 5 / 18 = 250 / 9 m / sec . distance covered = 500 + 500 = 1000 m . required time = 1000 * 9 / 250 = 36 sec answer : b"
Answer: b
Question (physics): p works 25 % more efficiently than q and q works 50 % more efficiently than r . to complete a certain project , p alone takes 50 days less than q alone . if , in this project p alone works for 60 days and then q alone works for 140 days , in how many days can r alone complete the remaining work ?
Options: a ) 50 days , b ) 102.7 days , c ) 100 days , d ) 150 days , e ) 80 days
Rationale: "p works 25 % more efficiently than q : something that takes q 5 days , takes p 4 days q works 50 % more efficiently than r : something that takes r 7.5 days , takes q 5 days p alone takes 50 days less than q : for every 4 days p works , q has to work an extra day . hence p alone can do it in 200 days and q alone in 250 days and hence r alone in 390 days p works for 60 days - - > 60 / 200 work done = > 30 % q works for 140 days - - > 140 / 250 work done = > 56 % 260 % work left . . . r alone will take 26 % * 395 = 102.7 days answer is ( b )"
Answer: b
Question (physics): a train 560 m in length crosses a telegraph post in 16 seconds . the speed of the train is ?
Options: a ) 126 kmph , b ) 77 kmph , c ) 54 kmph , d ) 71 kmph , e ) 88 kmph
Rationale: "s = 560 / 16 * 18 / 5 = 126 kmph answer : a"
Answer: a
Question (gain): a man invests rs . 3,000 at the rate of 5 % per annum . how much more should he invest at the rate of 8 % , so that he can earn a total of 6 % per annum ?
Options: a ) rs . 1200 , b ) rs . 1300 , c ) rs . 1500 , d ) rs . 2000 , e ) none of these
Rationale: "explanation : interest on rs . 3000 at 5 % per annum = ( 3000 × 5 × 1 ) / 100 = rs . 150 let his additional investment at 8 % = x interest on rs . x at 8 % per annum = ( x × 8 × 1 ) / 100 = 2 x / 25 . to earn 6 % per annum for the total , interest = ( 3000 + x ) × 6 × 1 / 100 . = > 150 + 2 x / 25 = ( 3000 + x ) × 6 × 1 / 100 . = > 15000 + 8 x = ( 3000 + x ) × 6 . = > 15000 + 8 x = 18000 + 6 x . = > 2 x = 3000 . = > x = 1500 . answer : c"
Answer: c
Question (physics): k is 50 % faster than l . if l starts at 9 a . m . and k starts at 10 a . m . l travels at a speed of 50 km / hr . if l and k are 300 kms apart , the time when they meet when they travel in opposite direction is ?
Options: a ) 12 pm , b ) 22 pm , c ) 72 pm , d ) 92 pm , e ) 23 pm
Rationale: explanation : let ' t ' be the time after which they met since l starts . given k is 50 % faster than l 50 t + 1.5 * 50 ( t - 1 ) = 300 50 t + 75 t = 300 + 75 t = 375 / 125 = 3 hrs past the time that l starts so they meet at ( 9 + 3 ) hrs = 12 : 00 noon . answer : a
Answer: a
Question (other): how many prime numbers between 1 and 100 are factors of 10010 ?
Options: a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1
Rationale: "factor of 10010 = 2 * 5 * 7 * 11 * 13 - - - 5 prime numbers a"
Answer: a
Question (other): one lady has 2 children , one of her child is boy , what is the probability of having both are boys
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) 3 / 4
Rationale: n ( s ) = one of her child is boy out of 2 children = bb , bg = 2 n ( e ) = both are boys = bb = 1 so p = n ( e ) / n ( s ) = 1 / 2 answer : a
Answer: a
Question (gain): 7 / 10 of the population of the country of venezia lives in montague province , while the rest lives in capulet province . in the upcoming election , 80 % of montague residents support romeo , while 70 % of capulet residents support juliet ; each resident of venezia supports exactly one of these two candidates . rounded if necessary to the nearest percent , the probability that a juliet supporter chosen at random resides in capulet is
Options: a ) 28 % , b ) 41 % , c ) 60 % , d ) 72 % , e ) 78 %
Rationale: "total population = 100 ( assume ) . 7 / 10 * 100 = 70 people from montague . 3 / 10 * 100 = 30 people from capulet . 0.2 * 70 = 14 people from montague support juliet . 0.7 * 30 = 21 people from capulet support juliet . the probability that a juliet supporter chosen at random resides in capulet is 21 / ( 14 + 21 ) = ~ 60 . answer : c"
Answer: c
Question (physics): car a runs at the speed of 58 km / hr & reaches its destination in 8 hr . car b runs at the speed of 70 km / h & reaches its destination in 4 h . what is the respective ratio of distances covered by car a & car b ?
Options: a ) 11 : 6 , b ) 12 : 7 , c ) 29 : 18 , d ) 15 : 6 , e ) 13 : 6
Rationale: "sol . distance travelled by car a = 58 ã — 8 = 464 km distance travelled by car b = 70 ã — 4 = 280 km ratio = 464 / 280 = 29 : 18 c"
Answer: c
Question (general): for any positive integer n , the sum of the first n positive integers equals n ( n + 1 ) / 2 . what is the sum y of all the even integers between 99 and 301 ?
Options: a ) 10,100 , b ) 20,200 , c ) 22,650 , d ) 40,200 , e ) 45,150
Rationale: "i would solve it in a different way . first of all , total number of even integers between 99 and 301 are , ( 301 - 99 ) / 2 = 202 / 2 = 101 average = ( 301 + 99 ) / 2 = 400 / 2 = 200 sum y = average * total count = 200 * 101 = 20,200 answer is b"
Answer: b
Question (general): in what ratio p : q should the mixture p of milk and water in the ratio of 4 : 1 be mixed with another mixture q of milk and water in the ratio 2 : 3 so that the resultant mixture contains equal quantities of milk and water ?
Options: a ) 1 : 3 , b ) 2 : 3 , c ) 1 : 4 , d ) 3 : 4 , e ) 3 : 5
Rationale: "( 4 / 5 ) * p + ( 2 / 5 ) * q = ( 1 / 5 ) * p + ( 3 / 5 ) * q 3 p = q p / q = 1 / 3 the answer is a ."
Answer: a
Question (general): if n is an integer and 101 n ^ 2 is less than or equal to 12100 , what is the greatest possible value of n ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "101 * n ^ 2 < = 12100 n ^ 2 < = 12100 / 101 which will be less than 121 since 12100 / 100 = 121 which is the square of 9 next closest value of n where n ^ 2 < = 121 is 10 ans d"
Answer: d
Question (physics): how many minutes is it before 12 noon if 20 minutes ago it was 3 times as many minutes after 9 am ?
Options: a ) 40 , b ) 39 , c ) 42 , d ) 55 , e ) 29
Rationale: a 40 minutes , or 11.20 am
Answer: a
Question (other): a bag holds 4 red marbles and 5 green marbles . if you removed two randomly selected marbles from the bag , without replacement , what is the probability that both would be red ?
Options: a ) 1 / 10 , b ) 1 / 6 , c ) 3 / 10 , d ) 2 / 5 , e ) 1 / 4
Rationale: "probability of selecting first red marble = 4 / 9 probability of selecting second red marble without replacement = 3 / 8 final probability = 4 / 9 * 3 / 8 = 1 / 6 the correct answer is b ."
Answer: b
Question (physics): the sum of four consecutive even numbers is 140 . what would be the smallest number ?
Options: a ) 32 , b ) 88 , c ) 70 , d ) 123 , e ) 12
Rationale: "let the four consecutive even numbers be 2 ( x - 2 ) , 2 ( x - 1 ) , 2 x , 2 ( x + 1 ) their sum = 8 x - 4 = 140 = > x = 18 smallest number is : 2 ( x - 2 ) = 32 answer : a"
Answer: a
Question (general): a number is doubled and 15 is added . if the resultant is multiplied by 5 , it becomes 125 . what is that number ?
Options: a ) 5 , b ) 10 , c ) 8 , d ) none of these , e ) can not be determined
Rationale: "solution let the number be x . then , 5 ( 2 x + 15 ) ‹ = › 125 ‹ = › 2 x + 15 = 25 ‹ = › 2 x = 10 x = 5 . answer d"
Answer: d
Question (physics): a train is 360 meter long is running at a speed of 75 km / hour . in what time will it pass a bridge of 140 meter length ?
Options: a ) 87 , b ) 69 , c ) 40 , d ) 72 , e ) 24
Rationale: "speed = 75 km / hr = 75 * ( 5 / 18 ) m / sec = 125 / 6 m / sec total distance = 360 + 140 = 500 meter time = distance / speed = 500 * ( 6 / 125 ) = 24 seconds answer : e"
Answer: e
Question (general): if k ^ 3 is divisible by 120 , what is the least possible value of integer k ?
Options: a ) 15 , b ) 30 , c ) 60 , d ) 90 , e ) 120
Rationale: "k ^ 3 = 120 * x = 2 ^ 3 * 3 * 5 * x the factors of k must at minimum include 2 * 3 * 5 = 30 . the answer is b ."
Answer: b
Question (gain): population of a city in 20004 was 1000000 . if in 2005 there isan increment of 20 % , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45 % , then find the population of city atthe end of the year 2007
Options: a ) 1131000 , b ) 979923 , c ) 980241 , d ) 2356677 , e ) 1083875
Rationale: "required population = p ( 1 + r 1 / 100 ) ( 1 - r 2 / 100 ) ( 1 + r 3 / 100 ) = p ( 1 + 20 / 100 ) ( 1 - 35 / 100 ) ( 1 + 45 / 100 ) = 1131000 a"
Answer: a
Question (general): sony and johnny caught 40 fishes . sony caught 4 times as many as johnny . how many fishes did johnny catch ?
Options: a ) 12 , b ) 16 , c ) 34 , d ) 38 , e ) 8
Rationale: s + j = 40 s = 4 * j j = 8 answer : e
Answer: e
Question (general): two digits in brother ' s age are the same as the digit in the sister ' s age , but in reverse order . in 20 9 years brother will be twice as old as sister will be then . what is the difference in their current age ?
Options: a ) 34 , b ) 50 , c ) 32 , d ) 28 , e ) 45
Rationale: brother ' s age = 10 x + y so sister ' s age = 10 y + x . . after 29 years , 10 x + y + 29 = 2 * ( 10 y + x + 29 ) . . . . so 29 + 19 y = 8 x . . . check for odd values of y , y = 1 satisfies the eqn with x = 6 . . . so ages are 61 and 16 and ans as found correctly by u is e . . 45
Answer: e
Question (general): a man owns 1 / 3 of market reserch beauro buzness , and sells 3 / 5 of his shares for 2000 rs , what is the value of buzness ?
Options: a ) 40000 , b ) 60000 , c ) 10000 , d ) 25000 , e ) 50000
Rationale: "if value of business = x total sell ( 1 x / 3 ) ( 3 / 5 ) = 2000 - > x = 10000 answer : c"
Answer: c
Question (general): a contest will consist of n questions , each of which is to be answered eithertrueorfalse . anyone who answers all n questions correctly will be a winner . what is the least value of n for which the probability is less than 1 / 100 that a person who randomly guesses the answer to each question will be a winner ?
Options: a ) 5 , b ) 10 , c ) 50 , d ) 100 , e ) 1000
Rationale: "a contest will consist of n questions , each of which is to be answered eithertrueorfalse . anyone who answers all n questions correctly will be a winner . what is the least value of n for which the probability is less than 1 / 1000 that a person who randomly guesses the answer to each question will be a winner ? a . 5 b . 10 c . 50 d . 100 e . 1000 soln : ans is b probability that one question is answered right is 1 / 2 . now for minimum number of questions needed to take probability less than 1 / 1000 is = > ( 1 / 2 ) ^ n < 1 / 100 n = 50 satisfies this . c"
Answer: c
Question (physics): 15 binders can bind 1400 books in 21 days . how many binders will be required to bind 1600 books in 20 days ?
Options: a ) 14 , b ) 18 , c ) 24 , d ) 28 , e ) none of these
Rationale: "binders books days 15 1400 21 x 1600 20 x / 15 = ( 1600 / 1400 ) * ( 21 / 20 ) = > x = 18 answer : b"
Answer: b
Question (general): what is the smallest number which when increased by 3 is divisible by 18 , 70 , 100 and 84 ?
Options: a ) 5307 , b ) 5647 , c ) 5927 , d ) 6297 , e ) 6557
Rationale: "when increased by 3 , the number must include at least 2 ^ 2 * 3 ^ 2 * 5 ^ 2 * 7 = 6300 the answer is d ."
Answer: d
Question (other): find the compound ratio of ( 1 : 2 ) , ( 1 : 3 ) and ( 3 : 5 ) is
Options: a ) 1 : 10 , b ) 2 : 3 , c ) 3 : 4 , d ) 4 : 5 , e ) 3 : 2
Rationale: "required ratio = 1 / 2 * 1 / 3 * 3 / 5 = 1 / 10 = 1 : 10 answer is a"
Answer: a
Question (general): the arithmetic mean and standard deviation of a certain normal distribution are 16.5 and 1.5 , respectively . what value is exactly 2 standard deviations less than the mean ?
Options: a ) 10.5 , b ) 11 , c ) 11.5 , d ) 12 , e ) 13.5
Rationale: "the value which isexactlytwo sd less than the mean is : mean - 2 * sd = 16.5 - 2 * 1.5 = 13.5 . answer : e ."
Answer: e
Question (general): find the value of 3 / 11 × [ ( 1 + 1 / 3 ) ( 1 + 1 / 4 ) … … … … . ( 1 + 1 / 120 ) ] is ?
Options: a ) 11 , b ) 12 , c ) 14 , d ) 15 , e ) 16
Rationale: "3 / 11 × [ ( 1 + 1 / 3 ) ( 1 + 1 / 4 ) . . . . . . . ( 1 + 1 / 120 ) ] 3 / 11 × [ 4 / 3 + 5 / 4 × . . . . . . . . 121 / 120 ] 3 / 11 × 4 / 3 × 5 / 4 × . . . . 121 / 120 121 / 11 = 11 . a )"
Answer: a
Question (physics): two cars are driving towards one another . the first car is traveling at a speed of 120 km / h , which is 28 % faster than the second car . if the distance between the cars is 855 km , how long will it takes the cars to meet ( in hours ) ?
Options: a ) 2.5 . , b ) 3 . , c ) 3.5 , d ) 4 . , e ) 4.5 .
Rationale: let s be the speed of the slower car . then the speed of the faster is 1.28 s 1.28 s = 120 s = 120 / 1.28 cumulative speed / rate = s + 1.28 s = 2.28 s time taken to meet = 855 / 2.28 s = 855 / 213.75 = 4 hrs answer : d
Answer: d
Question (general): according to the directions on a packet of smoothie mix , 1 3 - ounce packet of smoothie mix is to be combined with 10 ounces of water to make a smoothie . how many 3 - ounce packets of smoothie mix are required to prepare 150 12 - ounce smoothies ?
Options: a ) 120 , b ) 150 , c ) 180 , d ) 240 , e ) 600
Rationale: "this question was n ' t particularly grueling , but i think it ' s the first where i had the opportunity to solve it via theory andinspectionthat many on this board suggest as strategy on the gmat . it actually came to me by accident . basically , if we thought that the 3 packets of powder were included in the 12 ounces of water , that would mean we would need 150 packets of smoothie mix ( along with 12 ( 150 ) ounces of water for a total of 150 packets . however , we know , after a more careful reading of the stimulus , that the 3 ounces are not included in the 12 ounces . as such , the answer has to be less than 150 packets , since 150 would be too much powder considering you already have 150 ( 12 ) ounces of water and need less packets than water to make a smoothie . as such , the only answer less than 150 is 120 , a . does this make sense ? or am i way off base ? b"
Answer: b
Question (general): which fraction should be added to : 1 / ( 2 ã — 3 ) + 1 / ( 3 ã — 4 ) + 1 / ( 4 ã — 5 ) + . . . . . . . + 1 / ( 23 ã — 24 ) so that the result is equal to 1 ?
Options: a ) 7 / 24 , b ) 11 / 24 , c ) 13 / 24 , d ) 17 / 24 , e ) 19 / 24
Rationale: the given expression = 1 / ( 2 ã — 3 ) + 1 / ( 3 ã — 4 ) + 1 / ( 4 ã — 5 ) + . . . . . . + 1 / ( 23 ã — 24 ) = ( 1 / 2 - 1 / 3 ) + ( 1 / 3 - 1 / 4 ) + ( 1 / 4 - 1 / 5 ) + . . . . . . . . . . + ( 1 / 23 - 1 / 24 ) = 1 / 2 - 1 / 24 = 11 / 24 thus , the fraction we should add = 1 - 11 / 24 = 13 / 24 the answer is c .
Answer: c
Question (gain): of the land owned by a farmer , 90 percent was cleared for planting . of the cleared land , 80 percent was planted with barley and 10 percent of the cleared land was planted with potato . if the remaining 90 acres of cleared land was planted with tomato , how many acres did the farmer own ?
Options: a ) 850 , b ) 950 , c ) 1025 , d ) 975 , e ) 1000
Rationale: 80 % of 90 % = 72 % , 10 % 0 f 90 % = 9 % so the remaining 90 - 72 - 9 = 9 % = 90 acres or 10 % of 90 % = 9 % - - > 90 / 9 * 100 = 1000 acres answer ( e )
Answer: e
Question (general): what is the remainder when 14,452 × 15,652 × 16,781 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "only the unit ' s digit of the product will decide the remainder when divided by 5 . hence , 2 * 2 * 1 = will give units digit as 4 so , whatever be the number , if it ends in 4 , the remainder after dividing with 5 will be 4 . optione"
Answer: e
Question (general): if 4 xz + yw = 6 and xw + yz = 12 , what is the value of the expression ( 2 x + y ) ( 2 z + w ) ?
Options: a ) 9 . , b ) 30 . , c ) 15 . , d ) 16 . , e ) 18 .
Rationale: "( 2 x + y ) * ( 2 z + w ) = 6 + 2 ( 12 ) = 30 answer : b"
Answer: b
Question (general): if one positive integer is greater than another positive integer by 3 , and the difference of their cubes is 63 , what is their sum ?
Options: a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1
Rationale: 1 ^ 3 = 1 2 ^ 3 = 8 3 ^ 3 = 27 4 ^ 3 = 64 the two numbers are 1 and 4 . the answer is a .
Answer: a
Question (gain): in a recent election , geoff received 0.5 percent of the 5,000 votes cast . to win the election , a candidate needed to receive more than x % of the vote . if geoff needed exactly 2,571 more votes to win the election , what is the value of x ?
Options: a ) 50 , b ) 54 , c ) 52 , d ) 60 , e ) 63
Rationale: "word problems are tricky in somehow more than other problem because you have the additional step to translate . breaking the problem : geoff how many votes he receives ? ? 25 votes he needs 2571 more votes so : 25 + 2571 = 2596 now what ' s the problem wants ? ? a x % . . . . . . . . 2596 is what % of total votes 5000 . . . . . . . . translating : 2596 = x / 100 * 5000 - - - x = 52 % . . . . . . . . . . c"
Answer: c
Question (physics): a bus trip of 360 miles would have taken 1 hour less if the average speed v for the trip had been greater by 5 miles per hour . what was the average speed v , in miles per hour , for the trip ?
Options: a ) 35 , b ) 40 , c ) 45 , d ) 50 , e ) 55
Rationale: "the time is the distance / speed . the time difference is 1 hour . 360 / v - 360 / ( v + 5 ) = 1 360 ( v + 5 ) - 360 v = ( v ) ( v + 5 ) 1800 = ( v ) ( v + 5 ) 40 * 45 = ( v ) ( v + 5 ) v = 40 mph the answer is b ."
Answer: b
Question (geometry): the area of sector of a circle whose radius is 12 metro and whose angle at the center is 41 ° is ?
Options: a ) 49 m 2 , b ) 50 m 2 , c ) 51.5 m 2 , d ) 53 m 2 , e ) 59 m 2
Rationale: "41 / 360 * 22 / 7 * 12 * 12 = 51.5 m 2 answer : c"
Answer: c
Question (gain): 10 % of employees are women with fair hair . 40 % of fair - haired employees are women . what percent of employees have fair hair ?
Options: a ) 25 , b ) 30 , c ) 50 , d ) 55 , e ) 60
Rationale: "i came up with ( a ) 25 think of 100 people total : from the first fact , 10 of these are women with fair hair . from the second fact , these 10 women make up 40 % of the total fair haired population . we can then make a ratio of 60 : 40 fair haired men to fair haired women . this means that ( 60 / 40 ) * 10 equals the number of fair haired men , which is 15 men with fair hair . add this 15 to the 10 women and get 25 fair haired men and women out of 100 total men and women . 25 % a"
Answer: a
Question (geometry): a rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn , one parallel to the length and the other parallel to the breadth . what is the cost of traveling the two roads at rs . 3 per sq m ?
Options: a ) rs . 3919
b ) rs . 3910
c ) rs . 3997
d ) rs . 3900
e ) rs . 3902
Rationale: area = ( l + b – d ) d ( 80 + 60 – 10 ) 10 = > 1300 m 2 1300 * 3 = rs . 3900 answer : d
Answer: d
Question (physics): it takes 50 identical printing machines 8 hours to print 500,000 posters . how long would it take 40 of these machines to print the same total ?
Options: a ) 10 hr , b ) 12 hr , c ) 12 hr 24 min , d ) 12 hr , 40 min , e ) 13 hr , 20 min
Rationale: "50 machines finish the job in 8 hours . we do not have to take care of the 500 ' 000 posters , it does not matter . 40 machines means , 20 % less of capacity and therefore 20 % longer to work for a certain job . 8 * 1.2 = 9 hr , 36 min answer a . . hi reto , since you are looking time for 40 machines it is 25 % less so will take 25 % more . . ans 8 * 1.25 = 10 hrs . . a )"
Answer: a
Question (gain): a man bought 40 shares of rs . 60 at 5 discount , the rate of dividend being 1212 % the rate of interest obtained is
Options: a ) 13.64 % , b ) 15.5 % , c ) 14 % , d ) 14.25 % , e ) 14.95 %
Rationale: explanation : face value of a share = rs . 60 he bought each share at rs . 60 - rs . 5 = rs . 55 number of shares = 40 dividend = 12 1 / 2 % = 25 / 2 % dividend per share = 60 × 25 / 2 × 100 = rs . 7.5 total dividend = ( 40 × 7.5 ) ie , he got a dividend of ( 40 × 7.5 ) for an investment of rs . ( 40 × 55 ) interest obtained = 40 × 7.5 × 100 / 40 × 55 = 13.64 % answer : option a
Answer: a
Question (geometry): a equilateral triangle having one side 5 m . in this triangle there is a square of side 2 m . calculate the percentage of area outside square in that triangle .
Options: a ) 68
b ) 54
c ) 63.04
d ) 62
e ) 60
Rationale: area of triangle = â ˆ š 3 a 2 / 4 . = 1.732 * 25 / 4 = 10.825 m 2 . area of square = 2 * 2 = 4 m 2 . rest area after square = 10.825 - 4 = 6.825 m 2 . % rest area after square = 6.825 / 10.825 * 100 = 63.04 % answer c
Answer: c
Question (general): the average of numbers 0.54204 , 0.54203 , 0.54202 and 0.54201 is ?
Options: a ) 0.54202 , b ) 0.54204 , c ) 0.542022 , d ) 0.542025 , e ) none
Rationale: "answer average = ( 0.54204 + 0.54203 + 0.54202 + 0.54201 ) / 4 = 2.1681 / 4 = 0.542025 correct option : d"
Answer: d
Question (general): 0.007 x 0.45 = ?
Options: a ) 0.00315 , b ) 0.0315 , c ) 0.315 , d ) 0.0351 , e ) none of them
Rationale: "7 x 45 = 315 sum of decimal places = 5 therefore , 0.007 x 0.45 = 0.00315 answer is a ."
Answer: a
Question (gain): one fourth of one third of two fifth of a number is 15 . what will be 40 % of that number
Options: a ) 140 , b ) 150 , c ) 180 , d ) 200 , e ) 220
Rationale: "explanation : ( 1 / 4 ) * ( 1 / 3 ) * ( 2 / 5 ) * x = 15 then x = 15 * 30 = 450 40 % of 450 = 180 answer : option c"
Answer: c
Question (gain): a certain candy manufacturer reduced the weight of candy bar m by 25 percent buy left the price unchanged . what was the resulting percent increase in the price per ounce of candy bar m ?
Options: a ) 20 , b ) 30 , c ) 34 , d ) 35 , e ) 33.33
Rationale: "assume 1 oz candy cost $ 1 before . now price remain same $ 1 but weight of candy reduces to 0.75 oz new price of candy = 1 / 0.75 = 1.3333 price increase 33.33 % e"
Answer: e
Question (other): apple costs l rupees per kilogram for first 30 kgs and q rupees per kilogram for each additional kilogram . if the price of 33 kilograms is 11.67 and for 36 kgs of apples is 12.48 then the cost of first 10 kgs of apples is
Options: a ) 3.69 , b ) 3.66 , c ) 3.6 , d ) 3.62 , e ) 3.61
Rationale: "ans : by framing equations we get 30 l + 3 q = 11.67 30 l + 6 q = 12.48 eliminate q by multiplying the first equation by 2 and subtracting second equation from the first then we get l = 0.362 cost of 10 kgs of apples = 0.362 x 10 = 3.62 answer : d"
Answer: d
Question (general): every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 76800 ?
Options: a ) 81000 , b ) 97200 , c ) 27772 , d ) 29889 , e ) 22312
Rationale: 76800 * 9 / 8 * 9 / 8 = 97200 . answer : b
Answer: b
Question (physics): a walks at 30 kmph and 30 hours after his start , b cycles after him at 48 kmph . how far from the start does b catch up with a ?
Options: a ) 1200 km , b ) 1500 km , c ) 2000 km , d ) 2400 km , e ) 3600 km
Rationale: "suppose after x km from the start b catches up with a . then , the difference in the time taken by a to cover x km and that taken by b to cover x km is 30 hours . x / 30 - x / 48 = 30 x = 2400 km answer is d"
Answer: d
Question (general): kamal obtained 96 , 65 , 82 , 67 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 65 , b ) 69 , c ) 72 , d ) 79 , e ) none
Rationale: "sol . average = 96 + 65 + 82 + 67 + 85 / 5 ) = ( 395 / 5 ) = 79 . answer d"
Answer: d