Cheukting/mathqa huggingface dataset:
Question (general): if 13 = 13 w / ( 1 - w ) , then ( 5 w ) 2 =
Options: a ) 1 / 4 , b ) 5 , c ) 1 , d ) 2 , e ) 3
Rationale: "13 - 13 w = 13 w 26 w = 13 w = 1 / 2 5 w = 5 / 2 5 w * 2 = 5 / 2 * 2 = 5 answer : b"
Answer: b
Question (physics): two trains of length 100 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively . in what time will they be clear of each other from the moment they meet ?
Options: a ) 10 sec , b ) 32 sec , c ) 82 sec , d ) 20 sec , e ) 19 sec
Rationale: "relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 100 + 280 = 380 m . the time required = d / s = 380 / 20 = 19 sec . answer : e"
Answer: e
Question (geometry): the ratio of radius of a circle and the side of a square is 2 : 9 . find the ratio of their areas :
Options: a ) 2 : 1 , b ) 4 : 7 , c ) 8 : 77 , d ) 4 : 81 , e ) none
Rationale: "radius / side = 2 / 9 â ‡ ’ area of circle / area of square = 4 / 81 answer : d"
Answer: d
Question (physics): if 12 men can reap 120 acres of land in 36 days , how many acres of land can 24 men reap in 62 days ?
Options: a ) 266.5 , b ) 413.3 , c ) 425.8 , d ) 189.3 , e ) 249.6
Rationale: "12 men 120 acres 36 days 24 men ? 62 days 120 * 24 / 12 * 62 / 36 120 * 2 * 31 / 18 240 * 1.72 = 413.3 answer : b"
Answer: b
Question (general): evaluate : 10010 - 12 * 3 * 2 = ?
Options: a ) 30002 , b ) 70002 , c ) 50002 , d ) 90002 , e ) 10002
Rationale: "according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 10010 - 12 * 3 * 2 = 10010 - 8 = 10002 correct answer e"
Answer: e
Question (physics): a car travels at a speed of 10 miles per hour . how far will it travel in 5 hours ?
Options: a ) 50 miles , b ) 62 miles , c ) 325 miles , d ) 70 miles , e ) 20 miles
Rationale: "during each hour , the car travels 65 miles . for 5 hours it will travel 10 + 10 + 10 + 10 + 10 = 5 * 10 = 50 miles correct answer a"
Answer: a
Question (physics): if 42 men do a work in 25 days , in how many days will 50 men do it ?
Options: a ) 23 , b ) 22 , c ) 19 , d ) 20 , e ) 21
Rationale: "42 * 25 = 50 * x x = 21 days answer : e"
Answer: e
Question (general): find large number from below question the difference of two numbers is 1345 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder
Options: a ) 1235 , b ) 1345 , c ) 1678 , d ) 1767 , e ) 1611
Rationale: let the smaller number be x . then larger number = ( x + 1345 ) . x + 1345 = 6 x + 15 5 x = 1330 x = 266 large number = 266 + 1345 = 1611 e
Answer: e
Question (general): company s produces two kinds of stereos : basic and deluxe . of the stereos produced by company s last month , 2 / 3 were basic and the rest were deluxe . if it takes 9 / 5 as many hours to produce a deluxe stereo as it does to produce a basic stereo , then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos ?
Options: a ) 7 / 17 , b ) 14 / 31 , c ) 7 / 15 , d ) 17 / 35 , e ) 9 / 19
Rationale: "# of basic stereos was 2 / 3 of total and # of deluxe stereos was 1 / 3 of total , let ' s assume total = 15 , then basic = 10 and deluxe = 5 . now , if time needed to produce one deluxe stereo is 1 unit than time needed to produce one basic stereo would be 9 / 5 units . total time for basic would be 10 * 1 = 10 and total time for deluxe would be 5 * 9 / 5 = 9 - - > total time for both of them would be 10 + 9 = 19 - - > deluxe / total = 9 / 19 . answer : e ."
Answer: e
Question (physics): a train 250 meters long completely crosses a 300 meters long bridge in 45 seconds . what is the speed of the train is ?
Options: a ) 32 , b ) 28 , c ) 29 , d ) 44 , e ) 21
Rationale: "s = ( 250 + 300 ) / 45 = 550 / 45 * 18 / 5 = 44 answer : d"
Answer: d
Question (gain): the salaries of a and b together amount to $ 500 . a spends 90 % of his salary and b , 80 % of his . if now , their savings are the same , what is a ' s salary ?
Options: a ) $ 50 , b ) $ 150 , c ) $ 69 , d ) $ 34 , e ) $ 52
Rationale: "let a ' s salary is x b ' s salary = 500 - x ( 100 - 90 ) % of x = ( 100 - 80 ) % of ( 500 - x ) x = $ 34 ( approximately ) answer is d"
Answer: d
Question (general): if there are 10 peanuts in a box and mary puts 8 more peanuts inside , how many peanuts are in the box ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 18
Rationale: "10 + 8 = 18 correct answer is e ) 18"
Answer: e
Question (general): how many positive integers less than 1960 are such that the product of their digits is 10 .
Options: a ) 220 , b ) 230 , c ) 280 , d ) 220 , e ) 240
Rationale: "1960 is divisible by 10 ( or 2 * 5 ) = 196 196 is divisible by 4 = > 49 49 = 7 * 7 hence 1960 is divisible by 2 , 4,5 , 7 , 7 if there were only one 7 , i . e if the problem were 280 c"
Answer: c
Question (general): the average runs of a cricket player of 10 innings was 32 . how many runs must he makes ih his next innings so as to increase his average of runs by 4 ?
Options: a ) 2 , b ) 4 , c ) 70 , d ) 76 , e ) none
Rationale: "sol . average after 11 innings = 36 . therefore required numbert of runs = ( 36 × 11 ) – ( 32 × 10 ) = 396 - 320 = 76 . answer d"
Answer: d
Question (physics): an outlet pipe can empty 2 / 3 of a cistern in 16 minutes . in 4 minutes , what part of the cistern will be emptied ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 6 , e ) 1 / 8
Rationale: "4 / 16 * 2 / 3 = 1 / 6 the answer is d ."
Answer: d
Question (general): the average monthly income of p and q is rs . 5050 . the average monthly income of q and r is rs . 6250 and the average monthly income of p and r is rs . 5200 . the monthly income of p is ?
Options: a ) rs . 3000 , b ) rs . 4000 , c ) rs . 5000 , d ) rs . 6000 , e ) rs . 7000
Rationale: "let p , q and r represent their respective monthly incomes . then , we have : p + q = ( 5050 x 2 ) = 10100 . . . . ( i ) q + r = ( 6250 x 2 ) = 12500 . . . . ( ii ) p + r = ( 5200 x 2 ) = 10400 . . . . ( iii ) adding ( i ) , ( ii ) and ( iii ) , we get : 2 ( p + q + r ) = 33000 or p + q + r = 16500 . . . . ( iv ) subtracting ( ii ) from ( iv ) , we get p = 4000 . p ' s monthly income = rs . 4000 . b )"
Answer: b
Question (geometry): a rectangular wall is covered entirely with two kinds of decorative tiles : regular and jumbo . 1 / 3 of the tiles are jumbo tiles , which have a length three times that of regular tiles and have the same ratio of length to width as the regular tiles . if regular tiles cover 60 square feet of the wall , and no tiles overlap , what is the area of the entire wall ?
Options: a ) 160
b ) 240
c ) 330
d ) 440
e ) 560
Rationale: the number of jumbo tiles = x . the number of regular tiles = 2 x . assume the ratio of the dimensions of a regular tile is a : a - - > area = a ^ 2 . the dimensions of a jumbo tile is 3 a : 3 a - - > area = 9 a ^ 2 . the area of regular tiles = 2 x * a ^ 2 = 60 . the area of jumbo tiles = x * 9 a ^ 2 = 4.5 ( 2 x * a ^ 2 ) = 4.5 * 60 = 270 . total area = 60 + 270 = 330 . answer : c .
Answer: c
Question (other): in a group of 26 junior high school students , 7 take french , 10 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 ) 5 , d ) 4 , e ) 8
Rationale: "c 5 add 7 + 10 + 4 to get 21 . then subtract 21 from the total students ⇒ 26 – 21 = 5 . answer is c"
Answer: c
Question (general): a mixture contains alcohol and water in the ratio 4 : 3 . if 8 litres of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture
Options: a ) 15 litres , b ) 10 litres , c ) 30 litres , d ) 22 litres , e ) 16 litres
Rationale: "let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 4 x / ( 3 x + 8 ) = 4 / 5 20 x = 4 ( 3 x + 8 ) 8 x = 32 x = 4 quantity of alcohol = ( 4 x 4 ) litres = 16 litres . answer is e ."
Answer: e
Question (general): what is the sum of the multiples of 4 between 19 and 130 inclusive ?
Options: a ) 2012 , b ) 2044 , c ) 2060 , d ) 2072 , e ) 2080
Rationale: "the fastest way in an ap is to find the average and multiply with total integers . . between 19 and 130 , the smallest multiple of 4 is 20 and largest = 128 . . average = ( 20 + 128 ) / 2 = 148 / 2 = 74 . total numbers = ( 128 - 20 ) / 4 + 1 = 27 + 1 = 28 . . sum = 28 * 74 = 2072 ans d"
Answer: d
Question (gain): a certain article of clothing was discounted during a special sale to 3 / 4 of its original retail price . when the clothing did n ' t sell , it was discounted even further to 2 / 5 of its original retail price during a second sale . by what percent did the price of this article of clothing decrease from the first sale to the second sale ?
Options: a ) 50 % , b ) 33.33 % , c ) 25 % , d ) 46.66 % , e ) 12.5 %
Rationale: say the original retail price of the item was $ 200 . the price after the first sale = 3 / 4 * $ 200 = $ 150 . the price after the second sale = 2 / 5 * $ 200 = $ 80 . the percent change from the first sale to the second = ( 150 - 80 ) / 150 = 1 / 3 = 46.66 % . answer : d .
Answer: d
Question (physics): bruce and anne can clean their house in 4 hours working together at their respective constant rates . if anne ’ s speed were doubled , they could clean their house in 3 hours working at their respective rates . how many hours does it currently take anne to clean the house on her own ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 12 , e ) 14
Rationale: "lets suppose anne and bruce take a and b hrs working separately so in 1 hour they can together finish 1 / a + 1 / b portion of the work which equals 1 / 4 ( as the work is completed in 4 hours ) after anne doubles her rate of work the portion completed by the both is 1 / a + 2 / b which is equal to 1 / 3 ( as the work is completed in 3 hours ) solving these 2 equations we can find b as 12 answer : d"
Answer: d
Question (general): if p and q are prime numbers , how many divisors does the product p ^ 3 * q ^ 6 have ?
Options: a ) 9 , b ) 12 , c ) 18 , d ) 28 , e ) 363
Rationale: ", p ^ 2 , p ^ 3 and q , q ^ 1 , q ^ 2 . . . . q ^ 6 together essentially there are 18 different combinations you can make ( 3 x 6 ) also you have to include the different combinations the p and q exponents can be a divisor . there are 3 different p exponents and 6 different q exponents : p , p ^ 2 , p ^ 3 , q , q ^ 2 , q ^ 3 . . . q ^ 6 also add 1 since ` ` 1 ' ' can also be a divisor . 18 + 3 + 6 + 1 = 28 , answer : d"
Answer: d
Question (gain): two men started from the same place walk at the rate of 10 kmph and 12 kmph respectively . what time will they take to be 10 km apart , if they walk in the same direction ?
Options: a ) 5 hours , b ) 6 hours , c ) 8 hours , d ) 10 hours , e ) 12 hours
Rationale: "to be 2 km apart they take 1 hour to be 10 km apart they take = 1 / 2 * 10 = 5 hours answer is a"
Answer: a
Question (general): the rate of interest on a sum of money is 3 % p . a . for the first 3 years , 4 % p . a . for the next 4 years , and 5 % for the period beyond 7 years . if the s . i , occurred on the sum for the total period of 8 years is rs . 540 / - , the sum is
Options: a ) 1,200 , b ) 1,800 , c ) 2,100 , d ) 2,250 , e ) 2,540
Rationale: "explanation : i 1 = ( p x 3 x 3 ) / 100 = p / 11 i 2 = ( p x 4 x 4 ) / 100 = 4 p / 25 i 3 = ( p x 1 x 5 ) / 100 = p / 20 p / 11 + 4 p / 25 + p / 20 = 540 30 p / 100 = 540 p = 1800 answer : option b"
Answer: b
Question (general): in a renowned city , the average birth rate is 6 people every two seconds and the death rate is 2 people every two seconds . estimate the size of the population net increase that occurs in one day .
Options: a ) 32,300 , b ) 172,800 , c ) 468,830 , d ) 338,200 , e ) 259,200
Rationale: "every 2 seconds , 4 persons are added ( 6 - 2 ) . every second 2 persons are added . in a day 24 hrs = 24 * 60 minutes = 24 * 60 * 60 = 86400 seconds . 86400 * 2 = 172800 option b is the answer ."
Answer: b
Question (general): for every x , the action [ x ] is defined : [ x ] is the greatest integer less than or equal to x . what is the value of [ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.3 ] - 6.6 ?
Options: a ) 12.6 . , b ) 15.8 . , c ) 14.4 . , d ) 16.2 . , e ) 16.4 .
Rationale: "[ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.3 ] - 6.6 = 6 * 0 + 2 * 7.2 + 8 - 6.6 = 0 + 14.4 + 1.4 15.8 answer b"
Answer: b
Question (physics): a car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 300 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ?
Options: a ) 300 , b ) 320 , c ) 330 , d ) 340 , e ) 290
Rationale: "answer a 300 * t = 1 km = > t = 1 / 360 km / h v * ( t + 2 / 3600 ) = 1 v ( 1 / 360 + 2 / 3600 ) = 1 = > v = 300 km / h"
Answer: a
Question (other): in a group of 25 , 13 can speak latin , 15 can speak french , and 6 do n ' t speak either . how many of these speak both latin and french ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 8
Rationale: let no . of persons who speeks booth latin and french = x so , no . of persons who speeks only latin = 13 - x no . of persons who speeks only french = 15 - x no . of persons who speeks dont speek any lag = 6 therefore ( 13 - x ) + ( 15 - x ) + x + 6 = 25 34 - x = 25 x = 9 answer : a
Answer: a
Question (physics): a train of length 250 m crosses a bridge of length 120 m in 20 seconds . what is the speed of train ?
Options: a ) 33 , b ) 27 , c ) 66.6 , d ) 22 , e ) 72
Rationale: "sol : ( length of train + length of bridge ) = speed of train x time ( 250 + 120 ) = 20 x speed speed = 370 / 20 = 18.5 m / s = 66.6 km / h answer = c"
Answer: c
Question (general): a survey of n people in the town of eros found that 50 % of them preferred brand a . another survey of 150 people in the town of angie found that 60 % preferred brand a . in total , 55 % of all the people surveyed together preferred brand a . what is the total number of people surveyed ?
Options: a ) 50 , b ) 100 , c ) 150 , d ) 300 , e ) 250
Rationale: "it is simply a weighted average question . since the given average of 50 % and 60 % is 55 % ( right in the middle ) , it means the number of people surveyed in eros ( n ) is same as the number of people surveyed in angie . so n = 150 total = 150 + 150 = 300 answer ( d )"
Answer: d
Question (other): in what ratio should a 20 % methyl alcohol solution be mixed with a 50 % methyl alcohol solution so that the resultant solution has 40 % methyl alcohol in it ?
Options: a ) 1 : 3 , b ) 1 : 2 , c ) 2 : 3 , d ) 2 : 1 , e ) 3 : 1
Rationale: two things to remember : - 1 ) the ratio of quantity mixed to get an average is related to the ratio of each qty ' s distance from average . 2 ) more the qty of x from that of y , more closer will be average to x . . qty of 20 % / qty of 50 % = ( 50 − 40 ) / ( 40 − 20 ) = 1 / 2 = 1 : 2 answer : b
Answer: b
Question (geometry): each of the 42 points is placed either inside or on the surface of a perfect sphere . if 65 % or fewer of the points touch the surface , what is the maximum number of segments which , if connected from those points to form chords , could be the diameter of the sphere ?
Options: a ) 7 , b ) 11 , c ) 13 , d ) 23 , e ) 38
Rationale: "maximum number of points on the surface is 65 % * 42 = 27.3 . . . or 27 since it has to be an integer now note that if two points form a diameter , they can not be part of any other diameter . so in the best case we can pair up the points we have 27 points , so at best we can form 13 pairs ( 26 ) . so , answer is ( c )"
Answer: c
Question (gain): rs . 800 becomes rs . 956 in 3 years at a certain rate of simple interest . if the rate of interest is increased by 4 % , what amount will rs . 800 become in 3 years .
Options: a ) rupees 1052 , b ) rs 1152 , c ) rs 1252 , d ) rs 1352 , e ) none of these
Rationale: explanation : s . i . = 956 - 800 = rs 156 r = 156 ∗ 100 / 800 ∗ 3 r = 6 1 / 2 % new rate = 6 1 / 2 + 4 = 21 / 2 % new s . i . = 800 × 21 / 2 × 3100 = 252 now amount will be 800 + 252 = 1052 option a
Answer: a
Question (general): in the rectangular coordinate system , if the line x = 8 y + 5 passes through points ( m , n ) and ( m + 2 , n + p ) , what is the value of p ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) 1 / 6
Rationale: "x = 8 y + 5 , and thus y = x / 8 - 5 / 8 the slope is 1 / 8 . the slope of a line through points ( m , n ) and ( m + 2 , n + p ) is ( n + p - n ) / ( m + 2 - m ) = p / 2 p / 2 = 1 / 8 and thus p = 1 / 4 the answer is c ."
Answer: c
Question (physics): a taxi leaves point a 5 hours after a bus left the same spot . the bus is traveling 10 mph slower than the taxi . find the speed of the taxi , if it overtakes the bus in three hours .
Options: a ) 20 , b ) 24 , c ) 32 , d ) 16 , e ) 40
Rationale: "let the speed of bus be v - 10 , speed of taxi be v the bus travelled a total of 8 hrs and taxi a total of 3 hrs . hence 8 * ( v - 10 ) = 3 v 8 v - 80 = 3 v 5 v = 80 d"
Answer: d
Question (geometry): the length of a rectangular landscape is 12 times its breadth . there is a playground in it whose area is 1200 square mtr & which is 1 / 4 rd of the total landscape . what is the length of the landscape ?
Options: a ) 90 , b ) 120 , c ) 240 , d ) 180 , e ) 110
Rationale: "sol . x * 12 x = 4 * 1200 x = 20 length = 12 * 20 = 240 c"
Answer: c
Question (general): if x , y , and z are positive real numbers such that x + y - z = 62 , y - z + x = 82 , and z - x + y = 100 , then find the x + y + z value ?
Options: a ) 80 , b ) 91 , c ) 62 , d ) 74 , e ) 82
Rationale: "x + y - z = 62 , - - - - - - 1 ) y - z + x = 82 , - - - - - - 2 ) z - x + y = 100 - - - - - - 3 ) from ( 1 ) & ( 2 ) 2 z = 20 z = 10 from ( 2 ) & ( 3 ) 2 y = 182 y = 91 then x = 62 - 81 = - 19 x + y + z = 82 correct option is e"
Answer: e
Question (physics): how many seconds will a 400 metre long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
Options: a ) 24 , b ) 30 , c ) 40 , d ) 45 , e ) 50
Rationale: "relative speed of the train = 63 - 3 = 60 kmph = 60 * 5 / 18 = 50 / 3 m / sec t = 400 * 3 / 50 = 24 sec answer : a"
Answer: a
Question (physics): a 240 meter long train crosses a man standing on the platform in 4 sec . what is the speed of the train ?
Options: a ) 176 kmph , b ) 108 kmph , c ) 216 kmph , d ) 134 kmph , e ) 161 kmph
Rationale: "s = 240 / 4 * 18 / 5 = 216 kmph answer : c"
Answer: c
Question (gain): the population of a town is 10000 . it decreases annually at the rate of 10 % p . a . what will be its population after 2 years ?
Options: a ) 4300 , b ) 4500 , c ) 8100 , d ) 5230 , e ) 5366
Rationale: "10000 × 90 / 100 × 90 / 100 = 8100 answer : c"
Answer: c
Question (physics): a boat running downstream covers a distance of 10 km in 3 hr while for covering the same distance upstream , it takes 6 hr . what is the speed of the boat ?
Options: a ) 2.5 kmph , b ) 3.5 kmph , c ) 4.5 kmph , d ) 1.5 kmph , e ) 9.5 kmph
Rationale: speed upstream = 10 / 3 speed of boat down stream = 10 / 6 speed of boat = 1 / 2 ( 10 / 3 + 10 / 6 ) = 2.5 kmph answer : a
Answer: a
Question (physics): a fort had provision of food for 150 men for 45 days . after 15 days , 25 men left the fort . the number of days for which the remaining food will last , is :
Options: a ) 36 , b ) 37 1 / 4 , c ) 42 , d ) 54 , e ) 48
Rationale: "after 15 days : 150 men had food for 30 days . suppose 125 men had food for x days . now , less men , more days ( indirect proportion ) therefore 125 : 150 : : 30 : x < = > 125 x x = 150 x 30 = > x = 150 x 30 / 125 = > x = 36 . correct answer is a"
Answer: a
Question (physics): the length of a room is 8 m and width is 4.75 m . what is the cost of paying the floor by slabs at the rate of rs . 900 per sq . metre .
Options: a ) 25650 , b ) 25750 , c ) 26550 , d ) 26750 , e ) 34200
Rationale: "area = 8 × 4.75 sq . metre . cost for 1 sq . metre . = rs . 900 hence total cost = 8 × 4.75 × 900 = 8 × 4275 = rs . 34200 answer is e ."
Answer: e
Question (gain): a person distributed 15 % of his income to his 3 children each . he deposited 30 % of his income to his wife ' s account . he donated 5 % of remaining amount to an orphan house . finally he has $ 40000 . find his total income ?
Options: a ) a ) 452000 , b ) b ) 200000 , c ) c ) 800000 , d ) d ) 500000 , e ) e ) 652000
Rationale: "3 children got = 3 * 15 % = 45 % wife got = 30 % orphan house = 5 % total = 45 + 30 + 5 = 80 % remaining = 100 - 80 = 20 % 20 % = 40000 100 % = 40000 * 100 / 20 = $ 200000 answer is b"
Answer: b
Question (general): the difference between a two - digit number and the number obtained by interchanging the positions of its digits is 81 . what is the difference between the two digits of that number ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: "sol . let the ten ’ s digit be x and unit ’ s digit be y , then , ( 10 x + y ) - ( 10 y + x ) = 81 ⇔ 9 ( x - y ) = 81 ⇔ x - y = 9 answer e"
Answer: e
Question (physics): a and b runs around a circular track . a beats b by one round or 10 minutes . in this race , they had completed 4 rounds . if the race was only of one round , find the a ' s time over the course :
Options: a ) 8.5 min
b ) 7.5 min
c ) 1.5 min
d ) 9.5 min
e ) 4.5 min
Rationale: explanation : b runs around the track in 10 min . i . e , speed of b = 10 min per round a beats b by 1 round time taken by a to complete 4 rounds = time taken by b to complete 3 rounds = 30 min a ' s speed = 30 / 4 min per round = 7.5 min per round hence , if the race is only of one round a ' s time over the course = 7 min 30 sec answer : b
Answer: b
Question (physics): a certain industrial loom weaves 0.127 meters of cloth every second . approximately how many seconds will it take for the loom to weave 15 meters of cloth ?
Options: a ) 114 , b ) 115 , c ) 116 , d ) 117 , e ) 118
Rationale: "let the required number of seconds be x more cloth , more time , ( direct proportion ) hence we can write as ( cloth ) 0.127 : 15 : : 1 : x = > 0.127 * x = 15 = > x = 15 / 0.127 = > x = 118 answer : e"
Answer: e
Question (general): the average marks of a class of 35 students is 45 and that of another class of 55 students is 65 . find the average marks of all the students ?
Options: a ) 52.6 , b ) 52.4 , c ) 52.1 , d ) 57 , e ) 52.9
Rationale: "sum of the marks for the class of 35 students = 35 * 45 = 1575 sum of the marks for the class of 55 students = 55 * 65 = 3575 sum of the marks for the class of 90 students = 1575 + 3575 = 5150 average marks of all the students = 5150 / 90 = 57 . answer : d"
Answer: d
Question (general): a and b together have $ 100 . if 3 / 10 of a ' s amount is equal to 1 / 5 of b ' s amount , how much amount does b have ?
Options: a ) $ 60 , b ) $ 55 , c ) $ 42 , d ) $ 31 , e ) $ 100
Rationale: "3 / 10 a = 1 / 5 b a = 1 / 5 * 10 / 3 b a = 2 / 3 b a / b = 2 / 3 a : b = 2 : 3 b ' s share = 100 * 3 / 5 = $ 60 answer is a"
Answer: a
Question (physics): two cars start from the opposite places of a main road , 150 km apart . first car runs for 30 km and takes a right turn and then runs 15 km . it then turns left and then runs for another 25 km and then takes the direction back to reach the main road . in the mean time , due to minor break down the other car has run only 35 km along the main road . what would be the distance between two cars at this point ?
Options: a ) 65 , b ) 38 , c ) 60 , d ) 28 , e ) 21
Rationale: answer : c ) 60 km
Answer: c
Question (gain): if the given two numbers are respectively 6 % and 30 % of a third number , then what percentage is the first of the second ?
Options: a ) 20 % , b ) 25 % , c ) 18 % , d ) 30 % , e ) none of these
Rationale: here , l = 6 and m = 30 therefore , first number = l / m x 100 % of second number = 6 / 30 x 100 % of second number = 20 % of second number answer : a
Answer: a