Cheukting/mathqa huggingface dataset:
Question (physics): the amounts of time that three secretaries worked on a special project are in the ratio of 2 to 3 to 5 . if they worked a combined total of 90 hours , how many hours did the secretary who worked the longest spend on the project ?
Options: a ) 80 , b ) 70 , c ) 56 , d ) 45 , e ) 14
Rationale: "10 x = 90 = > x = 9 therefore the secretary who worked the longest spent 9 x 5 = 45 hours on the project option ( c )"
Answer: c
Question (physics): one train is travelling 45 kmph and other is at 10 meters a second . ratio of the speed of the two trains is ?
Options: a ) 3 : 3 , b ) 5 : 7 , c ) 5 : 4 , d ) 7 : 2 , e ) 8 : 5
Rationale: c 5 : 4 45 * 5 / 18 = 10 25 : 20 = > 5 : 4
Answer: c
Question (geometry): in the xy - plane , a triangle has vertices ( 00 ) , ( 40 ) and ( 410 ) . if a point ( a , b ) is selected at random from the triangular region , what is the probability that a - b > 0 ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 2 / 5
Rationale: the area of the right triangle is ( 1 / 2 ) * 4 * 10 = 20 . only the points ( a , b ) below the line y = x satisfy a - b > 0 . the part of the triangle which is below the line y = x has an area of ( 1 / 2 ) ( 4 ) ( 4 ) = 8 . p ( a - b > 0 ) = 8 / 20 = 2 / 5 the answer is e .
Answer: e
Question (physics): a train 150 m long takes 6 sec to cross a man walking at 5 kmph in a direction opposite to that of the train . find the speed of the train ?
Options: a ) 75 kmph , b ) 85 kmph , c ) 95 kmph , d ) 105 kmph , e ) 115 kmph
Rationale: let the speed of the train be x kmph speed of the train relative to man = x + 5 = ( x + 5 ) * 5 / 18 m / sec 150 / [ ( x + 5 ) * 5 / 18 ] = 6 30 ( x + 5 ) = 2700 x = 85 kmph answer is b
Answer: b
Question (physics): working together , wayne and his son can shovel the entire driveway in 3 hours . if wayne can shovel 6 times as fast as his son can , how many hours would it take for his son to shovel the entire driveway on his own ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 7 , e ) 12
Rationale: w : the time for wyane to do the job s : the time for his son to do the job we have 1 / w + 1 / s = 1 / 6 and w = 6 s then we have 1 / ( 6 * s ) + 1 / s = 1 / 6 < = > 7 / ( 6 * s ) = 1 / 6 < = > s = 7 ans : d
Answer: d
Question (general): the cost of 10 kg of mangos is equal to the cost of 24 kg of rice . the cost of 6 kg of flour equals the cost of 2 kg of rice . the cost of each kg of flour is $ 21 . find the total cost of 4 kg of mangos , 3 kg of rice and 5 kg of flour ?
Options: a ) 347.8 , b ) 987.8 , c ) 877.8 , d ) 898.8 , e ) 667.4
Rationale: "let the costs of each kg of mangos and each kg of rice be $ a and $ r respectively . 10 a = 24 r and 6 * 21 = 2 r a = 12 / 5 r and r = 63 a = 151.2 required total cost = 4 * 151.2 + 3 * 63 + 5 * 21 = 604.8 + 189 + 105 = $ 898.80 d"
Answer: d
Question (physics): how many pieces of 85 cm length can be cut from a rod of 25.5 meters long ?
Options: a ) 50 , b ) 40 , c ) 30 , d ) 20 , e ) 10
Rationale: "number of pieces = 2550 / 85 = 30 the answer is c ."
Answer: c
Question (general): a father is 4 times as old as his son . in 20 years , he ' ll be twice as old . how old are they now ?
Options: a ) 540 , b ) 1040 , c ) 2040 , d ) 1030 , e ) 15,30
Rationale: if f is age of father and s is age of son f = 4 s f + 20 = 2 * ( s + 20 ) 4 s + 20 = 2 s + 40 2 s = 20 s = 10 f = 40 answer : b
Answer: b
Question (general): how many positive integers h less than 10000 are such that the product of their digits is 210 ?
Options: a ) 24 , b ) 30 , c ) 48 , d ) 54 , e ) 72
Rationale: 210 is the answer when 2 , 3 , 5 and 7 are multiplied . 210 can also be arrive using 56 and 7 and 1 , 5 , 6 and 7 . so sum of arrangements of 2357 , 567 and 1567 . this translates to 4 ! + 3 ! + 4 ! , this equals to 24 + 6 + 24 = 54 , d is the answer .
Answer: d
Question (physics): two trains of lengths 156.62 and 100 meters are running on parallel lines with respective speeds of 30 km / hr and 36 km / hr . the time of crossing each other , if they run in the opposite direction is
Options: a ) 322 sec , b ) 14 sec , c ) 11 sec , d ) 13 sec , e ) 34 sec
Rationale: explanation : total distance to be covered = 156.62 + 100 = 256.62 m trains are running in opposite directions , hence relative speed = 30 + 36 = 66 km / hr = 18.33 m / sec time = distance / relative speed = 256.62 / 18.33 sec = 14 sec therefore , the time of crossing each other in the opposite direction is 14 seconds . answer : b
Answer: b
Question (physics): the length of the bridge , which a train 170 meters long and travelling at 45 km / hr can cross in 30 seconds , is ?
Options: a ) 388 , b ) 267 , c ) 205 , d ) 288 , e ) 261
Rationale: "speed = ( 45 * 5 / 18 ) m / sec = ( 25 / 2 ) m / sec . time = 30 sec . let the length of bridge be x meters . then , ( 170 + x ) / 30 = 25 / 2 = = > 2 ( 170 + x ) = 750 = = > x = 205 m . answer : c"
Answer: c
Question (other): on multiplying a number a by 153 , the result obtained was 102325 . however , it is found that both the 2 ' s are wrong . find the correct result .
Options: a ) 104345 , b ) 107375 , c ) 108385 , d ) 109395 , e ) 105355
Rationale: the only thing you actually know about the correct number a is that it is divisible by 153 and has 5 as a factor . you should immediately try to find the factors of 153 and look for them in the options . 153 = 9 * 17 divisibility by 9 is easy to check . only ( d ) satisfies .
Answer: d
Question (gain): andrew purchased 11 kg of grapes at the rate of 98 per kg and 7 kg of mangoes at the rate of 50 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) 1000 , b ) 1055 , c ) 1428 , d ) 1500 , e ) 1080
Rationale: "cost of 11 kg grapes = 98 × 11 = 1078 . cost of 7 kg of mangoes = 50 × 7 = 350 . total cost he has to pay = 1078 + 350 = 1428 c"
Answer: c
Question (other): two numbers are in the ratio of 3 : 4 . if 12 be subtracted from each , they are in the ratio of 9 : 8 . find the numbers ?
Options: a ) 6,9 , b ) 3,8 , c ) 6,7 , d ) 3,5 , e ) 3,4
Rationale: "( 3 x - 12 ) : ( 4 x - 12 ) = 9 : 8 x = 1 = > 3,4 answer : e"
Answer: e
Question (gain): in an election a candidate who gets 60 % of the votes is elected by a majority of 1380 votes . what is the total number of votes polled ?
Options: a ) a ) 4500 , b ) b ) 5200 , c ) c ) 6900 , d ) d ) 7520 , e ) e ) 6000
Rationale: "let the total number of votes polled be x then , votes polled by other candidate = ( 100 - 60 ) % of x = 40 % of x 60 % of x - 40 % of x = 1380 20 x / 100 = 1380 x = 1380 * 100 / 20 = 6900 answer is c"
Answer: c
Question (general): rounded to 3 decimal places , 1.003 ^ 4 =
Options: a ) 1.004 , b ) 1.006 , c ) 1.008 , d ) 1.012 , e ) 1.016
Rationale: as compared to 1 , 0.003 is a very small quantity . thus , we can write ( 1 + 0.003 ) ^ 4 is nearly equal to ( 1 + 4 * 0.003 ) = 1.012 . as the question asks for approximation to three decimal places , the further terms will anyways not come into picture . d .
Answer: d
Question (gain): the banker ' s gain of a certain sum due 2 years hence at 10 % per annum is rs . 24 . what is the present worth ?
Options: a ) rs . 600 , b ) rs . 500 , c ) rs . 400 , d ) rs . 300 , e ) none of these
Rationale: "explanation : t = 2 years r = 10 % td = ( bg × 100 ) / tr = ( 24 × 100 ) / ( 2 × 10 ) = 12 × 10 = rs . 120 td = ( pw × tr ) / 100 ⇒ 120 = ( pw × 2 × 10 ) / 100 ⇒ 1200 = pw × 2 pw = 1200 / 2 = rs . 600 answer : option a"
Answer: a
Question (gain): in a certain pond , 50 fish were caught , tagged , and returned to the pond . a few days later , 50 fish were caught again , of which 2 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what is the approximate number of fish in the pond ?
Options: a ) 400 , b ) 625 , c ) 1,250 , d ) 2,500 , e ) 10,000
Rationale: "total fish = x percentage of second catch = ( 2 / 50 ) * 100 = 4 % so , x * 4 % = 50 x = 1250 answer : c"
Answer: c
Question (other): at a certain restaurant , the ratio of the number of cooks to the number of waiters is 3 to 10 . when 12 more waiters are hired , the ratio of the number of cooks to the number of waiters changes to 3 to 14 . how many cooks does the restaurant have ?
Options: a ) 4 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: "originally there were 3 k cooks and 10 k waiters . 14 k = 10 k + 12 k = 3 there are 9 cooks . the answer is c ."
Answer: c
Question (gain): the profit earned by selling an article for 912 is equal to the loss incurred when the same article is sold for 448 . what should be the sale price of the article for making 50 per cent profit ?
Options: a ) 960 , b ) 1060 , c ) 1,200 , d ) 1020 , e ) none of these
Rationale: "let the profit or loss be x and 912 – x = 448 + x or , x = 464 ⁄ 2 = 232 \ cost price of the article = 912 – x = 448 + x = 680 \ sp of the article = 680 × 150 ⁄ 100 = 1020 answer d"
Answer: d
Question (physics): working individually , julie can peel potatoes in 10 hours and ted can peel potatoes in 8 hours . if julie and ted work together but independently at the task for 4 hours , at which point ted leaves , how many remaining hours will it take julie to complete the task alone ?
Options: a ) 3 / 15 , b ) 2 / 11 , c ) 1 / 4 , d ) 1 / 3 , e ) 1
Rationale: in first 4 hrs ted will finish 4 / 8 = 1 / 2 of work and julie will finish 4 / 10 work so total 1 / 2 + 2 / 5 = 9 / 10 work is finished and 1 - 9 / 10 = 1 / 10 work remaining . now julie will take ( 1 / 10 ) * 10 = 1 hrs to finish it . so answer is e .
Answer: e
Question (physics): x is able to do a piece of work in 8 days and y can do the same work in 12 days . if they can work together for 3 days , what is the fraction of work left ?
Options: a ) 8 / 5 , b ) 6 / 5 , c ) 7 / 5 , d ) 3 / 5 , e ) 4 / 5
Rationale: "explanation : amount of work x can do in 1 day = 1 / 8 amount of work y can do in 1 day = 1 / 12 amount of work x and y can do in 1 day = 1 / 8 + 1 / 12 = 5 / 24 amount of work x and y can together do in 3 days = 3 × ( 5 / 24 ) = 5 / 8 fraction of work left = 1 – 5 / 8 = 3 / 5 answer : option d"
Answer: d
Question (gain): an article is bought for rs . 1450 and sold for rs . 1420 , find the loss percent ?
Options: a ) 2 % , b ) 4 % , c ) 6 % , d ) 8 % , e ) 12 %
Rationale: "1450 - - - - 30 100 - - - - ? = > 2 % answer : a"
Answer: a
Question (other): in a group of 28 junior high school students , 7 take french , 9 take spanish , and 4 take both languages . the students taking both french and spanish are not counted with the 7 taking french or the 10 taking spanish . how many students are not taking either french or spanish ?
Options: a ) 7 , b ) 6 , c ) 9 , d ) 4 , e ) 8
Rationale: "e 8 add 7 + 9 + 4 to get 20 . then subtract 21 from the total students ⇒ 28 – 20 = 8 . answer is e"
Answer: e
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 r 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 r ?
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 * r = 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 / r = 4 / 3 = > 1 / r = ( 8 - 3 ) / 6 = 5 / 6 = > r = 6 / 5 = 1 [ 1 / 5 ] answer b"
Answer: b
Question (physics): if 36 men can do a piece of work in 15 hours , in how many hours will 15 men do it ?
Options: a ) 22 , b ) 36 , c ) 60 , d ) 88 , e ) 72
Rationale: "explanation : let the required no of hours be x . then less men , more hours ( indirect proportion ) \ inline \ fn _ jvn \ therefore 15 : 36 : : 15 : x \ inline \ fn _ jvn \ leftrightarrow ( 15 x x ) = ( 36 x 15 ) \ inline \ fn _ jvn \ leftrightarrow \ inline \ fn _ jvn x = \ frac { 36 \ times 15 } { 15 } = 36 hence , 15 men can do it in 36 hours . answer : b ) 36"
Answer: b
Question (physics): buses a and b start from a common bus stop x . bus a begins to travel in a straight line away from bus b at a constant rate of 60 miles per hour . one hour later , bus b begins to travel in a straight line in the exact opposite direction at a constant rate of 80 miles per hour . if both buses travel indefinitely , what is the positive difference , in minutes , between the amount of time it takes bus b to cover the exact distance that bus a has covered and the amount of time it takes bus b to cover twice the distance that bus a has covered ?
Options: a ) 36 , b ) 72 , c ) 132 , d ) 144 , e ) 180
Rationale: "1 st part : - in 1 hr , bus a covers 30 miles . relative speed of bus abus b is ( 80 - 30 ) = 50 mph . so time required for bus b to cover the exact distance as a is 50 * t = 30 t = 3 / 5 = 36 min 2 nd part 80 * t = 2 d - b has to cover twice the distance 30 * ( t + 1 ) = d - a traveled 1 hr more and has to travel only only d so d / 30 - 2 d / 80 = 1 d = 120 t = 3 hrs = 180 min question asks for + ve difference between part 1 and part 2 in minutes = 180 - 36 = 180 min e"
Answer: e
Question (general): dawson is going with 14 friends on a trip to washington d . c for spring break . airfare and hotel costs a total of $ 13500.00 for the group of 15 friends . how much does each person have to pay for their hotel and airfare ?
Options: a ) $ 900 , b ) $ 800 , c ) $ 850 , d ) $ 950 , e ) $ 920
Rationale: answer = a the total cost of the trip ( $ 13500.00 ) divided by 15 equals $ 900.00 .
Answer: a
Question (general): the batting average of a particular batsman is 60 runs in 46 innings . if the difference in his highest and lowest score is 190 runs and his average excluding these two innings is 58 runs , find his highest score .
Options: a ) 179 , b ) 367 , c ) 269 , d ) 177 , e ) 199
Rationale: "explanation : total runs scored by the batsman = 60 * 46 = 2760 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2760 â € “ 2552 = 208 runs . let the highest score be x , hence the lowest score = x â € “ 190 x + ( x - 190 ) = 208 2 x = 398 x = 199 runs answer : e"
Answer: e
Question (physics): the point a and point b is 30 miles apart , the point b and point c is 25 miles apart . a car travels from point a to point b in 30 min and point b to point c in 40 min . what is the average speed of the car ?
Options: a ) 34.15 , b ) 40.35 , c ) 47.14 , d ) 50.12 , e ) 56.66
Rationale: average speed = total distance covered / total time taken = 55 miles / 70 min = 0.79 miles / min = 47.14 miles / hour answer : c
Answer: c
Question (general): 0.009 / x = 0.025 . find the value of x
Options: a ) 0.0003 , b ) 0.36 , c ) 0.3 , d ) 36 , e ) 90
Rationale: "x = 0.009 / 0.36 = 0.25 answer : c"
Answer: c
Question (gain): at the moment there are 54210 tagged birds in a certain wildlife refuge . if exactly 30 percent of all birds in the refuge are tagged , what percent of the untagged birds must be tagged so that half of all birds in the refuge are tagged ?
Options: a ) 66.67 , b ) 66 , c ) 67 , d ) 65.99 , e ) 67.26
Rationale: all birds = 54210 currently tagged = 54210 * 30 / 100 = 16263 so untagged birds = 54210 - 16263 = 37947 half of all birds = 27105 the number of birds to be tagged to make half of all birds tagged = 27105 - 16263 = 10842 so now the question remains - 10842 is how much percentage of untagged birds ( 16263 ) = 10842 * 100 / 16263 = 66.67 answer ( a )
Answer: a
Question (physics): find the cost of fencing around a circular field of diameter 70 m at the rate of rs . 1 a meter ?
Options: a ) 288 , b ) 132 , c ) 220 , d ) 592 , e ) 261
Rationale: "2 * 22 / 7 * 35 = 220 220 * 1 = rs . 220 answer : c"
Answer: c
Question (geometry): the area of a square is equal to four times the area of a rectangle of dimensions 25 cm * 16 cm . what is the perimeter of the square ?
Options: a ) 80 cm , b ) 100 cm , c ) 120 cm , d ) 140 cm , e ) 160 cm
Rationale: "area of the square = s * s = 4 ( 25 * 16 ) = > s * s = 2 * 2 * 5 * 5 * 4 * 4 = > s = 2 * 5 * 4 = 40 cm perimeter of the square = 4 * 40 = 160 cm . answer : e"
Answer: e
Question (physics): a train takes 10 sec to pass a signal post and covers a distance of 10 km in 15 min . find the length of train ?
Options: a ) 100.1 m , b ) 223.1 m , c ) 111.1 m , d ) 120.3 m , e ) 133.4 m
Rationale: explanation : we know , speed = distance / time speed = 10 / 50 x 60 = 40 x 5 / 18 m / sec = 11.1 m / sec length of train = ( speed x time ) = ( 11.11 x 10 ) = 111.1 m answer is c
Answer: c
Question (other): an amount of money is to be distributed among faruk , vasim and ranjith in the ratio 3 : 5 : 6 . if vasims share is rs . 1500 , what is the difference between faruk ' s and ranjith ' s shares ?
Options: a ) s 1200 , b ) s 1500 , c ) s 1600 , d ) s 1900 , e ) s 900
Rationale: explanation : let p = faruk , q = vasim , r = ranjith let p = 3 x , q = 5 x and r = 6 x . then , 5 x = 1500 ? x = 300 . p = 900 , q = 1500 and r = 1800 . hence , ( r - p ) = ( 1800 - 900 ) = 900 answer : e
Answer: e
Question (gain): a farmer spent $ 34 on feed for chickens and goats . he spent 40 % money on chicken feed , which he bought at a 20 % discount off the full price , and spent the rest on goat feed , which he bought at full price . if the farmer had paid full price for both the chicken feed and the goat feed , what amount would he have spent on the chicken feed and goat feed combined ?
Options: a ) $ 37.40 , b ) $ 38.50 , c ) $ 39.20 , d ) $ 39.50 , e ) $ 40.60
Rationale: "a farmer spent 40 % money on chicken feed , so he spent 0.4 * $ 34 = $ 13.6 on chicken feed , thus he spent the remaining 34 - 13.6 = $ 20.4 on goat feed . now , since he bought chicken feed at a 20 % discount then the original price of it was x * 0.8 = $ 13.6 - - > x = $ 17 . therefore if the farmer had paid full price for both the chicken feed and the goat feed , then he would he have spent 17 + 20.4 = $ 37.4 . answer : a ."
Answer: a
Question (general): a sum of rs . 312 was divided among 100 boys and girls in such a way that each boy gets rs . 3.60 and each girl rs . 2.40 .
Options: a ) 45 , b ) 49 , c ) 52 , d ) 60 , e ) 74
Rationale: let number of boys = x then number of girls = ( 100 - x ) 3.60 x + 2.40 ( 100 - x ) = 312 ¡ ê 1.2 x = 312 - 240 = 72 ¡ ê x = 60 answer : d
Answer: d
Question (general): according to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . how many 6 - ounce cans of the concentrate are required to prepare 200 6 - ounce servings of orange juice ?
Options: a ) 25 , b ) 34 , c ) 50 , d ) 67 , e ) 50
Rationale: "orange juice concentrate : water : : 1 : 3 total quantity of orange juice = 200 * 6 = 1200 oz so orange juice concentrate : water : : 300 oz : 900 oz no . of 6 oz can = 300 oz / 6 oz = 50 answer e , 50 cans"
Answer: e
Question (general): if the average ( arithmetic mean ) of a and b is 30 and the average of b and c is 60 , what is the value of c − a ?
Options: a ) 25 , b ) 60 , c ) 90 , d ) 140 , e ) it can not be determined from the information given .
Rationale: - ( a + b = 60 ) b + c = 120 c - a = 60 b . 60
Answer: b
Question (gain): on june 1 a bicycle dealer noted that the number of bicycles in stock had decreased by 4 for each of the past 5 months . if the stock continues to decrease at the same rate for the rest of the year , how many fewer bicycles will be in stock on november 1 than were in stock on january 1 ?
Options: a ) 8 , b ) 12 , c ) 40 , d ) 32 , e ) 36
Rationale: "jan 1 = c feb 1 = c - 4 march 1 = c - 8 april 1 = c - 12 may 1 = c - 16 june 1 = c - 20 july 1 = c - 24 aug 1 = c - 28 sept 1 = c - 32 oct 1 = c - 36 nov 1 = c - 40 difference between stock on november 1 than were in stock on january 1 will be - c - ( c - 40 ) = 40 hence answer will be ( c )"
Answer: c
Question (general): what is the minimum percentage increase in the mean of set f { - 4 , - 1 , 0 , 6 , 9 } if its two smallest elements are replaced with two different primes ?
Options: a ) 25 % , b ) 50 % , c ) 75 % , d ) 100 % , e ) 200 %
Rationale: mean of f is ( - 4 - 1 + 0 + 6 + 9 ) / 5 = 2 ; in order the increase to be minimal we should replace two smallest elements of f , which are - 4 and - 1 , with two smallest primes , which are 2 and 3 . hence our new set will be { 2 , 3 , 0 , 6 , 9 } - - > new mean is ( 2 + 3 + 0 + 6 + 9 ) / 5 = 4 . percent increase = ( 4 - 2 ) / 2 * 100 = 100 % . answer : d .
Answer: d
Question (geometry): the volumes of two cones are in the ratio 1 : 12 and the radii of the cones are in the ratio of 1 : 3 . what is the ratio of their heights ?
Options: a ) a ) 3 : 4
b ) b ) 2 : 7
c ) c ) 2 : 2
d ) d ) 2 : 1
e ) e ) 2 : 9
Rationale: the volume of the cone = ( 1 / 3 ) π r 2 h only radius ( r ) and height ( h ) are varying . hence , ( 1 / 3 ) π may be ignored . v 1 / v 2 = r 12 h 1 / r 22 h 2 = > 1 / 12 = ( 1 ) 2 h 1 / ( 3 ) 2 h 2 = > h 1 / h 2 = 3 / 4 i . e . h 1 : h 2 = 3 : 4 answer : a
Answer: a
Question (gain): two numbers are 35 % and 42 % are less than a third number . how much percent is the second number less than the first ?
Options: a ) 11.769 % , b ) 10.769 % , c ) 12.769 % , d ) 11.69 % , e ) 11.89 %
Rationale: "explanation : i ii iii 65 58 100 65 - - - - - - - - 7 100 - - - - - - ? = > 10.769 % answer b"
Answer: b
Question (physics): john and roger can finish the work 24 days if they work together . they worked together for 16 days and then roger left . john finished the remaining work in another 16 days . in how many days john alone can finish the work ?
Options: a ) 30 days , b ) 48 days , c ) 70 days , d ) 80 days , e ) 90 days
Rationale: amount of work done by john and roger in 1 day = 1 / 24 amount of work done by john and roger in 16 days = 16 ã — ( 1 / 24 ) = 2 / 3 remaining work â € “ 1 â € “ 2 / 3 = 1 / 3 john completes 1 / 3 work in 16 days amount of work john can do in 1 day = ( 1 / 3 ) / 16 = 1 / 48 = > john can complete the work in 48 days answer : b
Answer: b
Question (physics): there are 43 stations between ernakulam and chennai . how many second class tickets have to be printed , so that a passenger can travel from one station to any other station ?
Options: a ) 1980 , b ) 1920 , c ) 1990 , d ) 1890 , e ) 1900
Rationale: "the total number of stations = 45 from 45 stations we have to choose any two stations and the direction of travel ( ernakulam to chennai is different from chennai to ernakulam ) in 45 p 2 ways . 45 p 2 = 45 * 44 = 870 answer : a"
Answer: a
Question (other): if x and y are sets of integers , x # y denotes the set of integers that belong to set x or set y , but not both . if x consists of 12 integers , y consists of 18 integers , and 6 of the integers are in both x and y , then x # y consists of how many integers ?
Options: a ) 6 , b ) 16 , c ) 18 , d ) 30 , e ) 174
Rationale: "the number of integers that belong to set x only is 12 - 6 = 6 ; the number of integers that belong to set y only is 18 - 6 = 12 ; the number of integers that belong to set x or set y , but not both is 6 + 12 = 18 . answer : c ."
Answer: c
Question (general): when a certain tree was first planted , it was 4 feet tall , and the height of the tree increased by a constant amount each year for the next 6 years . at the end of the 6 th year , the tree was 1 / 6 taller than it was at the end of the 4 th year . by how many feet did the height of the tree increase each year ?
Options: a ) 3 / 10 , b ) 2 / 5 , c ) 1 / 2 , d ) 2 / 3 , e ) 6 / 5
Rationale: "say , the tree grows by x feet every year . then , 4 + 6 x = ( 1 + 1 / 6 ) ( 4 + 4 x ) or , x = 1 / 2 answer c"
Answer: c
Question (physics): with a uniform speed a car covers the distance in 8 hours . had the speed been increased by 3 km / hr , the same distance could have been covered in 7 1 / 2 hours . what is the distance covered ?
Options: a ) 360 km , b ) 480 km , c ) 278 km , d ) 297 km , e ) 671 km
Rationale: let the distance be x km . then , x / ( 7 1 / 2 ) - x / 8 = 3 2 x / 15 - x / 8 = 3 = > x = 360 km . answer : a
Answer: a