regisss/math_qa huggingface dataset:
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 32 , then how old is b ?
Options: a ) 17 years , b ) 19 years , c ) 29 years , d ) 10 years , e ) 12 years
Rationale: "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 32 5 x = 30 = > x = 6 hence , b ' s age = 2 x = 12 years . answer : e"
Answer: e
Problem: evaluate : 6702.5 + 670.25 + 67.025 + 6.7025 + 0.67025
Options: a ) 7447.14775 , b ) 6981.59775 , c ) 6918.59775 , d ) 6198.59775 , e ) 6891.59775
Rationale: "6702.5 670.25 67.025 6.7025 + 0.67025 - - - - - - - - - - - - - - - 7447.14775 answer is a ."
Answer: a
Problem: a cylindrical can has a radius of 4 centimeters and a height of 24 centimeters . what is the area , in square centimeters , of a rectangular label that completely covers the curved surface of the can without over - lapping ?
Options: a ) 16 pi , b ) 64 pi , c ) 96 pi , d ) 192 pi , e ) 576 pi
Rationale: "they are asking the lateral surface area of the cylinder . the lateral surface area = 2 * pi * r * h = 2 * pi * 4 * 24 = 192 pi answer is d ."
Answer: d
Problem: it is the new year and mandy has made a resolution to lose weight this year . she plans to exercise and do yoga . for exercise she plans to workout at the gym and ride her bicycle in the ratio of 2 : 3 everyday . she will also do yoga in the ratio , yoga : exercise = 2 : 3 . if she rides her bike for 12 minutes , how much time will she spend doing yoga ? ( rounded to minutes )
Options: a ) 10 min . , b ) 41 min . , c ) 17 min . , d ) 23 min . , e ) 20 min .
Rationale: the ratio is 2 : 3 = gym : ride , so ( 12 ) ( 3 / 2 ) = 18 minutes at the gym , and 18 + 12 = 30 minutes exercise , so ( 2 / 3 ) ( 30 ) = 20 minutes yoga . answer : e
Answer: e
Problem: the probability that a man will be alive for 10 more yrs is 3 / 4 & the probability that his wife will alive for 10 more yrs is 3 / 7 . the probability that none of them will be alive for 10 more yrs , is
Options: a ) 1 / 2 , b ) 1 , c ) 1 / 7 , d ) 3 / 4 , e ) 2
Rationale: "sol . required probability = pg . ) x p ( b ) = ( 1 — d x ( 1 — i ) = : x 1 = 1 / 7 ans . ( c )"
Answer: c
Problem: a jar of 264 marbles is divided equally among a group of marble - players . if 2 people join the group , each one would receive 1 marble less . how many people are there in the group today ?
Options: a ) 20 , b ) 21 . , c ) 22 , d ) 23 , e ) 24
Rationale: "only 22 and 24 divide 264 perfectly , assume initially , there are 22 people , , each will get 12 marbles two people join , then 24 will get 11 marble each . hence answer e = 24"
Answer: e
Problem: two numbers are in the ratio 3 : 4 . if the sum of numbers is 63 , find the numbers .
Options: a ) 27 and 36 . , b ) 25 and 30 . , c ) 23 and 44 . , d ) 63 and 12 . , e ) 12 and 36 .
Rationale: "sum of the terms of the ratio = 3 + 4 = 7 sum of numbers = 63 therefore , first number = 3 / 7 × 63 = 27 second number = 4 / 7 × 63 = 36 therefore , the two numbers are 27 and 36 . answer is a"
Answer: a
Problem: a man spends 2 / 5 of his salary on house rent , 3 / 10 of his salary on food , and 1 / 8 of his salary on conveyance . if he has rs 1400 left with him , find his expenditure on food and conveyance
Options: a ) 3200 , b ) 3400 , c ) 3600 , d ) 3800 , e ) 4000
Rationale: "if his salary is x , then x - x * ( 2 / 5 + 3 / 10 + 1 / 8 ) = 1400 x ( 1 - 33 / 40 ) = 1400 x = 1400 * 40 / 7 = rs 8000 expenditure on food and conveyance = 8000 * 3 / 10 + 8000 * 1 / 8 = 2400 + 1000 = 3400 answer : b"
Answer: b
Problem: a certain bus driver is paid a regular rate of $ 14 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 976 in total compensation , how many total hours did he work that week ?
Options: a ) 54 , b ) 51 , c ) 59 , d ) 55 , e ) 52
Rationale: "for 40 hrs = 40 * 14 = 560 excess = 976 - 560 = 416 for extra hours = . 75 ( 14 ) = 10.5 + 14 = 24.5 number of extra hrs = 416 / 24.5 = 18.82 = 19 approx . total hrs = 40 + 19 = 59 answer c 59"
Answer: c
Problem: a cistern has a leak which would empty the cistern in 20 minutes . a tap is turned on which admits 3 liters a minute into the cistern , and it is emptied in 24 minutes . how many liters does the cistern hold ?
Options: a ) 360 , b ) 487 , c ) 481 , d ) 729 , e ) 268
Rationale: "1 / x - 1 / 20 = - 1 / 24 x = 120 120 * 3 = 360 answer : a"
Answer: a
Problem: the ratio of the incomes of a and b is 2 : 3 and the ratio of their expenditure is 1 : 2 . if at the end of the year , each saves $ 500 then the income of a is ?
Options: a ) $ 1000 , b ) $ 1500 , c ) $ 1200 , d ) $ 900 , e ) $ 1100
Rationale: "let the income of a and b be $ 2 x and $ 3 x let their expenditures be $ y and $ 2 y 2 x - y = 500 - - - - - - - 1 ) 3 x - 2 y = 500 - - - - - - - 2 ) from 1 ) and 2 ) x = 500 a ' s income = 2 x = 2 * 500 = $ 1000 answer is a"
Answer: a
Problem: the compound and the simple interests on a certain sum at the same rate of interest for two years are rs . 11730 and rs . 10200 respectively . find the sum
Options: a ) rs . 17037 , b ) rs . 17000 , c ) rs . 17276 , d ) rs . 170287 , e ) rs . 171881
Rationale: explanation : the simple interest for the first year is 10200 / 2 is rs . 5100 and compound interest for first year also is rs . 5100 . the compound interest for second year on rs . 5100 for one year so rate of the interest = ( 100 * 1530 ) / ( 5100 * 1 ) = 30 % p . a . so p = ( 100 * 10200 ) / ( 30 * 2 ) = rs . 17000 answer : b
Answer: b
Problem: the sum of two numbers is 8 and the sum of their squares is 120 . find the product of the two numbers .
Options: a ) 25 , b ) 24 , c ) 23 , d ) 21 , e ) 28
Rationale: let a and b be the two numbers ( a + b ) ^ 2 = a ^ 2 + 2 ab + b ^ 2 given ( a + b ) = 8 a ^ 2 + b ^ 2 = 120 so , 8 ^ 2 = 120 + 2 ab 2 ab = 120 - 64 2 ab = 56 ab = 28 ans e
Answer: e
Problem: if the cost price of 121 chocolates is equal to the selling price of 77 chocolates , the gain percent is :
Options: a ) 56.14 % , b ) 57.44 % , c ) 57.14 % , d ) 56.34 % , e ) 57.87 %
Rationale: "explanation : solution : let c . p . of each chocolate be re . 1 . then , c . p . of 77 chocolates = rs . 77 ; s . p . of 77 chocolates = rs . 121 . . ' . gain % = 44 * 100 / 77 = 57.14 % answer : c"
Answer: c
Problem: a library has an average of 500 visitors on sundays and 140 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is :
Options: a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) 550
Rationale: "explanation : since the month begins with a sunday , so there will be five sundays in the month , required average = ( 500 * 5 + 140 * 25 ) / 30 = 6000 / 30 = 200 answer : b ) 200"
Answer: b
Problem: a man can row his boat with the stream at 6 km / h and against the stream in 4 km / h . the man ' s rate is ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 7
Rationale: "ds = 6 us = 4 s = ? s = ( 6 - 4 ) / 2 = 1 kmph answer : a"
Answer: a
Problem: a man buys 100 lts of liquid which contains 25 % of the liquid and the rest is water . he then mixes it with 90 lts of another mixture with 30 % of liquid . what is the % of water in the new mixture ?
Options: a ) 81 , b ) 75 , c ) 72.63 , d ) 73 , e ) 76
Rationale: 25 % in 100 lts is 25 . so water = 100 - 25 = 75 lts . 30 % of 90 lts = 27 . so water in 2 nd mixture = 90 - 27 = 63 lts . now total quantity = 100 + 90 = 190 lts . total water in it will be 75 + 63 = 138 lts . % of water = ( 100 * 138 ) / 190 = 72.63 answer : c
Answer: c
Problem: a train running at the speed of 60 km / hr crosses a pole in 3 seconds . find the length of the train ?
Options: a ) 150 meter , b ) 170 meter , c ) 156 meter , d ) 168 meter , e ) 50 meter
Rationale: "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 3 = 50 meter answer : e"
Answer: e
Problem: the sale price sarees listed for rs . 750 after successive discount is 20 % and 15 % is ?
Options: a ) 227 , b ) 570 , c ) 342 , d ) 680 , e ) 230
Rationale: "750 * ( 80 / 100 ) * ( 85 / 100 ) = 570 answer : b"
Answer: b
Problem: operation # is defined as adding a randomly selected two digit multiple of 10 to a randomly selected two digit prime number and reducing the result by half . if operation # is repeated 10 times , what is the probability that it will yield at least two integers ?
Options: a ) 0 % , b ) 10 % , c ) 20 % , d ) 30 % , e ) 40 %
Rationale: "any multiple of 10 is even . any two - digit prime number is odd . ( even + odd ) / 2 is not an integer . thus # does not yield an integer at all . therefore p = 0 . answer : a ."
Answer: a
Problem: a room of 8 m 44 cm long and 3 m 50 cm broad is to be paved with square tiles . find the least number of square tiles required to cover the floor .
Options: a ) 73850 , b ) 73805 , c ) 844 , d ) 350 , e ) 2
Rationale: "explanation : area of the room = 844 * 350 sq cm size of largest square tile = h . c . f of 844 cm and 350 cm = 2 cm area of 1 tile = 2 * 2 sq cm no . of tiles required = ( 844 * 350 ) / ( 2 * 2 ) = 73850 answer : a ) 73850"
Answer: a
Problem: a train leaves mumabai at 9 am at a speed of 40 kmph . after one hour , another train leaves mumbai in the same direction as that of the first train at a speed of 45 kmph . when and at what distance from mumbai do the two trains meet ?
Options: a ) 287 , b ) 279 , c ) 270 , d ) 278 , e ) 379
Rationale: "when the second train leaves mumbai the first train covers 40 * 1 = 40 km so , the distance between first train and second train is 40 km at 10.00 am time taken by the trains to meet = distance / relative speed = 40 / ( 45 - 40 ) = 8 hours so , the two trains meet at 6 p . m . the two trains meet 6 * 45 = 270 km away from mumbai . answer : c"
Answer: c
Problem: he average weight of 8 persons increases by 3.5 kg when a new person comes in place of one of them weighing 62 kg . what might be the weight of the new person ?
Options: a ) 75 kg , b ) 55 kg , c ) 45 kg , d ) 85 kg , e ) 90 kg
Rationale: "explanation : total weight increased = ( 8 x 3.5 ) kg = 28 kg . weight of new person = ( 62 + 28 ) kg = 90 kg . answer : e"
Answer: e
Problem: the price of a jacket is reduced by 20 % . during a special sale the price of the jacket is reduced another 25 % . by approximately what percent must the price of the jacket now be increased in order to restore it to its original amount ?
Options: a ) 32.5 , b ) 35 , c ) 48.1 , d ) 65 , e ) 66.67
Rationale: "1 ) let the price of jacket initially be $ 100 . 2 ) then it is decreased by 20 % , therefore bringing down the price to $ 80 . 3 ) again it is further discounted by 25 % , therefore bringing down the price to $ 60 . 4 ) now 60 has to be added byx % in order to equal the original price . 60 + ( x % ) 60 = 100 . solving this eq for x , we get x = 66.67 ans is e ."
Answer: e
Problem: a cylindrical can has a radius of 3 centimeters and a height of 12 centimeters . what is the area , in square centimeters , of a rectangular label that completely covers the curved surface of the can without over - lapping ?
Options: a ) 16 pi , b ) 72 pi , c ) 96 pi , d ) 192 pi , e ) 576 pi
Rationale: "they are asking the lateral surface area of the cylinder . the lateral surface area = 2 * pi * r * h = 2 * pi * 3 * 12 = 72 pi answer is b ."
Answer: b
Problem: a grocer purchased a quantity of bananas at 3 pounds for $ 0.50 and sold the entire quantity at 4 pounds for $ 1.00 . how many pounds did the grocer purchase if the profit from selling the bananas was $ 9.00 ?
Options: a ) 40 , b ) 60 , c ) 90 , d ) 120 , e ) 108
Rationale: "cost price of 1 pound of bananas = 0.5 / 3 = 1 / 6 selling price of 1 pound of bananas = 1 / 4 profit per pound = ( 1 / 4 - 1 / 6 ) = ( 1 / 12 ) total profit is given as 9 ( 1 / 12 ) * x = 9 x = 108 answer : e"
Answer: e
Problem: a man took a loan from a bank at the rate of 11 % p . a . simple interest . after 3 years he had to pay rs . 5400 interest only for the period . the principal amount borrowed by him was :
Options: a ) rs . 16363.64 , b ) rs . 10 , 000.64 , c ) rs . 15 , 000,64 , d ) rs . 21 , 353.64 , e ) none
Rationale: "solution principal = rs . ( 100 x 5400 / 11 x 3 ) = rs . 16363.64 . answer a"
Answer: a
Problem: the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 5 . if the sum of their ages is 98 , what is the difference between the ages of patrick and monica ?
Options: a ) 32 , b ) 48 , c ) 45 , d ) 72 , e ) 18
Rationale: "ages of p and mi = 3 x : 5 x ages of mi and mo = 3 x : 5 x rationalizing their ages . ratio of their ages will be 9 x : 15 x : 25 x sum = 49 x = 98 x = 2 difference if ages of pa and mo = 25 x - 9 x = 16 x = 16 * 2 = 32 answer a"
Answer: a
Problem: three 6 faced dice are thrown together . the probability that exactly two dice show the same number on them is - .
Options: a ) 5 / 12 , b ) 4 / 13 , c ) 5 / 17 , d ) 3 / 12 , e ) 8 / 9
Rationale: "using question number 11 and 12 , we get the probability as 1 - ( 1 / 36 + 5 / 9 ) = 5 / 12 answer a"
Answer: a
Problem: six dots are evenly spaced on the circumference of a circle . how many combinations of three dots can we make from these 6 dots that do not form an equilateral triangle ?
Options: a ) 18
b ) 17
c ) 16
d ) 15
e ) 14
Rationale: the total number of ways we can choose three dots is 6 c 3 = 20 . we can form two equilateral triangles from these six dots . there are 20 - 2 = 18 combinations which do not form an equilateral triangle . the answer is a .
Answer: a
Problem: nd the area of trapezium whose parallel sides are 20 cm and 16 cm long , and the distance between them is 15 cm ?
Options: a ) 270 cm 2 , b ) 275 cm 2 , c ) 280 cm 2 , d ) 285 cm 2 , e ) 290 cm 2
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 16 ) * ( 15 ) = 270 cm 2 answer : a"
Answer: a
Problem: how many positive integer solutions does the equation 2 x + 1 y = 100 have ?
Options: a ) 44 , b ) 33 , c ) 50 , d ) 35 , e ) 14
Rationale: "formula : ( constant ) / ( lcm of two nos ) = 100 / ( 2 * 1 ) = 50 answer : c"
Answer: c
Problem: if all the 6 are replaced by 9 , then the algebraic sum of all the numbers from 1 to 100 ( both inclusive ) varies by how much ?
Options: a ) 330 , b ) 360 , c ) 380 , d ) 400 , e ) 420
Rationale: "unit place increased by 3 . so 6 , 16,26 , . . . . 96 . total 10 * 3 = 30 increased . ten ' s place increased by 30 . so 60,61 , . . . 69 . total 10 * 30 = 300 increased . so total varies = 300 + 30 = 330 . answer : a"
Answer: a
Problem: a train 130 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train . find the speed of the train .
Options: a ) 45 kmph , b ) 50 kmph , c ) 55 kmph , d ) 60 kmph , e ) 73 kmph
Rationale: "explanation : let the speed of the train be x kmph . speed of the train relative to man = ( x + 5 ) kmph = ( x + 5 ) × 5 / 18 m / sec . therefore 130 / ( ( x + 5 ) × 5 / 18 ) = 6 < = > 30 ( x + 5 ) = 2340 < = > x = 73 speed of the train is 73 kmph . answer : option e"
Answer: e
Problem: sale of rs 6835 , rs . 9927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs , 6700 ?
Options: a ) 4966 , b ) 6191 , c ) 2877 , d ) 2676 , e ) 1881
Rationale: "total sale for 5 months = rs . ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs . 34009 . required sale = rs . [ ( 6700 x 6 ) - 34009 ] = rs . ( 40200 - 34009 ) = rs . 6191 answer : b"
Answer: b
Problem: find the average of all prime numbers between 10 and 40
Options: a ) 15.6 , b ) 22.5 , c ) 18.6 , d ) 32.2 , e ) 26.9
Rationale: "prime numbers between 10 and 40 are 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 required average = ( 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 ) / 8 = 180 / 8 = 22.5 answer is b"
Answer: b
Problem: if y is 80 % greater than x , than x is what % less than y ?
Options: a ) 20 , b ) 25 , c ) 33 1 / 3 , d ) 44 4 / 9 , e ) 80
Rationale: "let x = 100 so y = 180 we want percentage change . so , ( 100 - 180 ) / 180 = - 44.44 % = 44 4 / 9 % lesser than y . hence option ( d ) ."
Answer: d
Problem: how many miles is 150 km ?
Options: a ) 91.5 miles , b ) 92.75 miles , c ) 93.75 miles , d ) 94.5 miles , e ) 95.75 miles
Rationale: "93.75 miles 150 / 1.6 answer : c"
Answer: c
Problem: every disk in a bag is either blue , yellow or green . the ratio of blue disks to yellow disks to green disks in this bag is 3 : 7 : 8 . if the total number of disks in the bag is 108 , how many more green disks than blue disks are in the bag ?
Options: a ) 25 , b ) 28 , c ) 30 , d ) 35 , e ) 40
Rationale: "let b : y : g = 3 x : 7 x : 8 x . 3 x + 7 x + 8 x = 18 x = 108 - - > x = 6 . g - b = 8 x - 3 x = 5 x = 30 . the answer is c ."
Answer: c
Problem: a room is 7 meters 20 centimeters in length and 4 meters 32 centimeters in width . find the least number of square tiles of equal size required to cover the entire floor of the room .
Options: a ) 10 , b ) 15 , c ) 17 , d ) 19 , e ) 21
Rationale: "let us calculate both the length and width of the room in centimeters . length = 7 meters and 20 centimeters = 720 cm width = 4 meters and 32 centimeters = 432 cm as we want the least number of square tiles required , it means the length of each square tile should be as large as possible . further , the length of each square tile should be a factor of both the length and width of the room . hence , the length of each square tile will be equal to the hcf of the length and width of the room = hcf of 720 and 432 = 144 thus , the number of square tiles required = ( 720 x 432 ) / ( 144 x 144 ) = 5 x 3 = 15 answer : b"
Answer: b
Problem: a number is greater than 3 but less than 8 . also the number is greater than 6 but less than 10 . what is the number ?
Options: a ) 5 , b ) 7 , c ) 6 , d ) 8 , e ) 9
Rationale: b 7
Answer: b
Problem: efrida and frazer who live 13 miles apart , meet at a restaurant that is directly north of efrida ' s home and directly east of frazer ' s home . if the restaurant is two miles closer to efrida ' s home , than to frazer ' s home , how many miles is the restaurant from frazer ' s home ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 10 , e ) 11
Rationale: "it ' s a simple geometry problem . look at the diagram below : answer : e ."
Answer: e
Problem: a cistern is filled by a tap in 8 1 / 2 hours . due to leak in the bottom of the cistern , it takes half an hour longer to fill the cistern . if the cistern is full how many hours will it take the leak to empty it ?
Options: a ) 133 , b ) 143 , c ) 153 , d ) 163 , e ) 173
Rationale: "filling rate - leak rate = net rate 1 / 8.5 - leak rate = 1 / 9 leak rate = 2 / 17 - 1 / 9 = 1 / 153 the answer is c ."
Answer: c
Problem: nicky and cristina are running a race . since cristina is faster than nicky , she gives him a 54 meter head start . if cristina runs at a pace of 5 meters per second and nicky runs at a pace of only 3 meters per second , how many seconds will nicky have run before cristina catches up to him ?
Options: a ) 15 seconds , b ) 18 seconds , c ) 25 seconds , d ) 27 seconds , e ) 45 seconds
Rationale: "used pluging in method say t is the time for cristina to catch up with nicky , the equation will be as under : for nicky = n = 3 * t + 54 for cristina = c = 5 * t @ t = 27 , n = 135 c = 135 right answer ans : d"
Answer: d
Problem: susan can type 10 pages in 5 minutes . mary can type 5 pages in 10 minutes . working together , how many pages can they type in 30 minutes ?
Options: a ) 15 , b ) 20 , c ) 25 , d ) 65 , e ) 75
Rationale: susan can type 2 pages in 1 min mary can type 0.5 pages in 1 min so , both of them work together they type 2.5 pages in 1 min so , in 30 min they type ( 30 * 2.5 ) = 75 pages answer : e
Answer: e
Problem: ( 178 % of 1265 ) ÷ 5.96 = ?
Options: a ) 125 , b ) 175 , c ) 225 , d ) 375 , e ) 524
Rationale: explanation : ? = ( 178 x 1265 / 100 ) ÷ 6 = 2250 / 600 = 375 answer : option d
Answer: d
Problem: at the faculty of aerospace engineering , 312 students study random - processing methods , 234 students study scramjet rocket engines and 112 students study them both . if every student in the faculty has to study one of the two subjects , how many students are there in the faculty of aerospace engineering ?
Options: a ) 430 , b ) 434 , c ) 438 , d ) 444 , e ) 446
Rationale: "312 + 234 - 112 ( since 112 is counted twice ) = 434 b is the answer"
Answer: b
Problem: there are 399 doctors and nurses in a hospital . if the ratio of the doctors to the nurses is 8 : 11 , then how many nurses are there in the hospital ?
Options: a ) 152 , b ) 209 , c ) 57 , d ) 231 , e ) 181
Rationale: "given , the ratio of the doctors to the nurses is 8 : 11 number of nurses = 11 / 19 x 399 = 231 answer : d"
Answer: d
Problem: after spending rs . 5000 on rent , rs . 1500 on milk , rs . 4500 on groceries , rs . 2500 on childrens education rs . 2000 on petrol and rs . 6100 on miscellaneous expenses , mr . kishore saved 10 % of his monthly salary . how much did he save in rs . ?
Options: a ) 2160 , b ) 2350 , c ) 2000 , d ) 2300 , e ) 2400
Rationale: "explanation : total exp = 5000 + 1500 + 4500 + 2500 + 2000 + 6100 = 21600 exp in % = 100 - 10 = 90 % , 21600 = 90 % saving = 10 % = 21600 x 10 / 90 = rs . 2400 answer : e"
Answer: e
Problem: a train 825 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 90 seconds . the speed of the train is :
Options: a ) 33 , b ) 27 , c ) 27 , d ) 50 , e ) 81
Rationale: "speed of the train relative to man = ( 125 / 10 ) m / sec = ( 25 / 2 ) m / sec . [ ( 25 / 2 ) * ( 18 / 5 ) ] km / hr = 45 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 45 = = > x = 50 km / hr . answer : d"
Answer: d
Problem: in a hostel , the number of students decreased by 10 % and the price of food increased by 20 % over the previous year . if each student consumes the same amount of food then by how much should the consumption of food be cut short by every student , so that the total cost of the food remains the same as that of the previous year ?
Options: a ) 19 % , b ) 15 % , c ) 25 % , d ) 40 % , e ) 7.4 %
Rationale: "cost of food ( c ) = food consumed per student ( f ) * number of students ( n ) * price of food ( p ) originally , c = fnp when number of students decrease by 8 % , and the price of food increases by 20 % , c = f ( new ) * ( 0.9 n ) * ( 1.2 p ) = > f ( new ) = f / ( 0.9 * 1.2 ) = > f ( new ) = 0.9259 f therefore the new cost of food must be 92.59 % of the old cost , or the cost of food must decrease by 7.4 % ( option e )"
Answer: e
Problem: the time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 63 kmph , find the speed of the stream ?
Options: a ) 15 , b ) 19 , c ) 14 , d ) 21 , e ) 16
Rationale: "the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 63 / 3 = 21 kmph . answer : d"
Answer: d
Problem: if the sales tax reduced from 3 1 / 2 % to 3 1 / 3 % , then what difference does it make to a person who purchases an article with market price of rs . 6600 ?
Options: a ) 11 , b ) 13 , c ) 14 , d ) 18 , e ) 10
Rationale: "required difference = [ 3 ½ % of rs . 6600 ] – [ 3 1 / 3 % of rs . 6600 ] = [ ( 7 / 20 - ( 10 / 3 ) ] % of rs . 6600 = 1 / 6 % of rs . 6600 = rs . [ ( 1 / 6 ) 8 ( 1 / 100 ) * 6600 ] = rs . 11 . answer is a ."
Answer: a
Problem: working alone at its constant rate , machine a produces x boxes in 10 minutes and working alone at its constant rate , machine b produces 2 x boxes in 5 minutes . how many minutes does it take machines a and b , working simultaneously at their respective constant rates , to produce 7 x boxes ?
Options: a ) 3 minutes , b ) 4 minutes , c ) 5 minutes , d ) 14 minutes , e ) 12 minutes
Rationale: "rate = work / time given rate of machine a = x / 10 min machine b produces 2 x boxes in 5 min hence , machine b produces 4 x boxes in 10 min . rate of machine b = 4 x / 10 we need tofind the combined time that machines a and b , working simultaneouslytakeat their respective constant rates let ' s first find the combined rate of machine a and b rate of machine a = x / 10 min + rate of machine b = 4 x / 10 = 5 x / 10 now combine time = combine work needs to be done / combine rate = 7 x / 5 x * 10 = 14 min ans : d"
Answer: d
Problem: in a shop , the profit is 320 % of the cost . if the cost increases by 25 % but the selling price remains constant , approximately what percentage of the selling price is the profit ?
Options: a ) 70 % , b ) 50 % , c ) 100 % , d ) 60 % , e ) 55 %
Rationale: "cp . = rs . 100 . = > profit = rs . 320 , s . p . = rs . 420 . new c . p . = 125 % of rs . 100 = rs . 125 new s . p . = rs . 420 . profit = rs . ( 420 - 125 ) = rs . 295 . req = ( 295 / 420 * 100 ) = = > 70 % answer a"
Answer: a
Problem: 2 trains in same direction at 50 km / hr , 32 km / hr . a man in slower train observes 15 sec elapse before the faster train completely passed by him what is length of faster train ?
Options: a ) 65 meters , b ) 75 meters , c ) 85 meters , d ) 95 meters , e ) 55 meters
Rationale: relative speed = 18 k / hr = 5 m / sec distance covered = length of faster train = 5 * 15 = 75 meters answer : b
Answer: b
Problem: lionel left his house and walked towards walt ' s house , 48 miles away . four hours later , walt left his house and ran towards lionel ' s house . if lionel ' s speed was 2 miles per hour and walt ' s 6 miles per hour , how many miles had lionel walked when he met walt ?
Options: a ) 12 , b ) 18 , c ) 20 , d ) 24 , e ) 28
Rationale: "in the first 4 hours lionel at the rate of 2 miles per hour covered distance = rate * time = 4 * 2 = 8 miles . so , the distance between him and walt was 48 - 8 = 40 miles when walt left his house . now , their combined rate to cover this distance was 2 + 6 = 8 miles per hour , hence they will meet ( they will cover that distance ) in time = distance / rate = 40 / 8 = 5 hours . total time that lionel was walking is 4 + 5 = 9 hours , which means that he covered in that time interval distance = rate * time = 2 * 9 = 18 miles . answer : b ."
Answer: b
Problem: x and y started a business by investing rs . 36000 and rs . 42000 respectively after 4 months z joined in the business with an investment of rs . 48000 , then find share of z in the profit of rs . 13860 ?
Options: a ) 4032 , b ) 4000 , c ) 3250 , d ) 3825 , e ) 3985
Rationale: "ratio of investment , as investments is for different time . investment x number of units of time . ratio of investments x : y : z = 36000 : 42000 : 48000 = > 6 : 7 : 8 . x = 6 x 12 months = 72 , y = 7 x 12 = 84 , z = 8 x 8 = 64 = > 18 : 21 : 16 . ratio of investments = > x : y : z = 18 : 21 : 16 . investment ratio = profit sharing ratio . z = 13860 ã — 16 / 55 = rs . 4032 . share of z in the profit is rs . 4032 . option a"
Answer: a
Problem: a cyclist traveled for two days . on the second day the cyclist traveled 3 hours longer and at an average speed 10 mile per hour slower than she traveled on the first day . if during the two days she traveled a total of 280 miles and spent a total of 12 hours traveling , what was her average speed on the second day ?
Options: a ) 5 mph , b ) 10 mph , c ) 20 mph , d ) 30 mph , e ) 40 mph
Rationale: "solution : d = 280 mi t = 12 hrs day 1 time = t 1 day 2 time = t 2 t 2 - t 1 = 4 hrs - - - - - ( i ) t 1 + t 2 = 12 hrs - - - - - ( ii ) adding i and ii , t 2 = 8 hrs and t 1 = 4 hrs day 1 rate = r 1 day 2 rate = r 2 r 1 - r 2 = 10 mph i . e . r 1 = 10 + r 2 280 = 8 r 2 + 4 r 1 i . e . 280 = 8 r 2 + 4 ( 10 + r 2 ) i . e . r 2 = 20 mph answer : b"
Answer: b