Cheukting/mathqa huggingface dataset:
Question (gain): a , b and c enter into a partnership by investing $ 7000 , $ 11000 and $ 18000 respectively . at the end of 8 months , b receives $ 2200 as his share . find the share of a .
Options: a ) $ 1200 , b ) $ 1300 , c ) $ 1400 , d ) $ 1500 , e ) $ 1600
Rationale: "the ratio of capital of a , b and c = 7000 : 11000 : 18000 = 7 : 11 : 18 a ' s share = ( 7 / 11 ) * 2200 = $ 1400 the answer is c ."
Answer: c
Question (gain): if 40 % of a certain number is 160 , then what is 10 % of that number ?
Options: a ) 100 , b ) 40 , c ) 80 , d ) 120 , e ) 110
Rationale: explanation : 40 % = 40 * 4 = 160 10 % = 10 * 4 = 40 answer : option b
Answer: b
Question (gain): a man took loan from a bank at the rate of 12 % p . a . s . i . after 20 years he had to pay rs . 2100 interest only for the period . the principal amount borrowed by him was ?
Options: a ) 600 , b ) 715 , c ) 600 , d ) 875 , e ) 900
Rationale: "principal = ( 100 * 2100 ) / ( 12 * 20 ) = rs . 875 answer : d"
Answer: d
Question (general): the average ( arithmetic mean ) of 24 , 35 , and 58 is 6 more than the average of 19 , 51 , and x . what is x ?
Options: a ) 26 , b ) 27 , c ) 28 , d ) 29 , e ) 30
Rationale: "the average of 24 , 35 , and 58 is 39 . the average of 19 , 51 and x is 33 . then 19 + 51 + x = 99 . x = 29 . the answer is d ."
Answer: d
Question (general): instead of multiplying a number by 5 , the number is divided by 5 . what is the percentage of error obtained ?
Options: a ) 98 % , b ) 97 % , c ) 96 % , d ) 99 % , e ) 95 %
Rationale: "let the number be x the right number is 5 x the wrong number is x / 5 error is ( 5 x - x / 5 ) = 24 x / 5 percentage of error is ( ( 24 x / 5 ) / 5 x ) * 100 = 96 % answer : c"
Answer: c
Question (physics): a person crosses a 600 m long street in 5 minutes , what is his speed in km per hour ?
Options: a ) 4.3 , b ) 7.2 , c ) 2.3 , d ) 3.2 , e ) 1.1
Rationale: "explanation : speed = { \ color { blue } \ left ( \ frac { 600 } { 5 \ times 60 } \ right ) m / sec = 2 m / sec = \ left ( 2 \ times \ frac { 18 } { 5 } \ right ) km / hr = 7.2 km / hr } answer : b"
Answer: b
Question (physics): the length of a train and that of a platform are equal . if with a speed of 72 k / hr , the train crosses the platform in one minute , then the length of the train ( in meters ) is ?
Options: a ) 299 , b ) 266 , c ) 299 , d ) 750 , e ) 600
Rationale: "speed = [ 72 * 5 / 18 ] m / sec = 20 m / sec ; time = 1 min . = 60 sec . let the length of the train and that of the platform be x meters . then , 2 x / 60 = 20 = > x = 20 * 60 / 2 = 600 answer : e"
Answer: e
Question (geometry): square a has an area of 81 square centimeters . square b has a perimeter of 32 centimeters . if square b is placed within square a and a random point is chosen within square a , what is the probability the point is not within square b ?
Options: a ) 17 / 64
b ) 17 / 81
c ) 16 / 25
d ) 3 / 5
e ) 6 / 25
Rationale: i guess it ' s mean that square b is placed within square aentirely . since , the perimeter of b is 32 , then its side is 32 / 4 = 8 and the area is 4 ^ 2 = 64 ; empty space between the squares is 81 - 64 = 17 square centimeters , so if a random point is in this area then it wo n ' t be within square b : p = favorable / total = 17 / 81 . answer : b
Answer: b
Question (physics): one hour after yolanda started walking from x to y , a distance of 60 miles , bob started walking along the same road from y to x . if yolanda â s walking rate was 5 miles per hour and bob â s was 6 miles per hour , how many miles had bob walked when they met ?
Options: a ) 40 , b ) 25 , c ) 28 , d ) 30 , e ) 30.5
Rationale: "let t be the number of hours that bob had walked when he met yolanda . then , when they met , bob had walked 4 t miles and yolanda had walked 5 ( t + 1 ) miles . these distances must sum to 60 miles , so 6 t + 5 ( t + 1 ) = 60 , which may be solved for t as follows 6 t + 5 ( t + 1 ) = 60 6 t + 5 t + 5 = 60 11 t = 55 t = 5 ( hours ) therefore , bob had walked 6 t = 6 ( 5 ) = 30 miles when they met . the best answer is d ."
Answer: d
Question (other): in a class of 25 students , 15 play hockey and 16 play basketball . if there are 4 students who play neither sport , determine the number of students who play both hockey and basketball ?
Options: a ) 10 , b ) 11 , c ) 13 , d ) 14 , e ) 15
Rationale: let the number of who play both be x number of students who play sports 25 - 4 = 21 use venn diagram ( 15 - x ) + x + ( 16 - x ) = 21 which gives x = 10 answer is a 10 play both sport
Answer: a
Question (gain): what is the difference between 80 % of 170 and 35 % of 300 .
Options: a ) 30 , b ) 29 , c ) 37 , d ) 36 , e ) 31
Rationale: "( 80 / 100 ) * 170 â € “ ( 35 / 100 ) * 300 136 - 105 = 31 answer : e"
Answer: e
Question (general): a car travels first 160 km at 90 km / hr and the next 160 km at 80 km / hr . what is the average speed for the first 320 km of the tour ?
Options: a ) 71.11 , b ) 84.7 , c ) 71.1 , d ) 71.17 , e ) 71.13
Rationale: "car travels first 160 km at 90 km / hr time taken to travel first 160 km = distancespeed = 160 / 90 car travels next 160 km at 80 km / hr time taken to travel next 160 km = distancespeed = 160 / 80 total distance traveled = 160 + 160 = 2 × 160 total time taken = 160 / 90 + 160 / 80 average speed = total distance traveled / total time taken = 320 / ( 160 / 90 + 160 / 80 ) = 84.7 km / hr answer : b"
Answer: b
Question (physics): two trains are moving in the same direction at 72 kmph and 36 kmph . the faster train crosses a man in the slower train in 37 seconds . find the length of the faster train ?
Options: a ) 270 , b ) 370 , c ) 266 , d ) 299 , e ) 126
Rationale: "relative speed = ( 72 - 36 ) * 5 / 18 = 2 * 5 = 10 mps . distance covered in 37 sec = 37 * 10 = 370 m . the length of the faster train = 370 m . answer : b"
Answer: b
Question (physics): a water tank which could be filled in 5 hours takes one more hour to be filled as a result of a leak in its bottom . if the tank is full calculate the time it will take for the leak empty it ?
Options: a ) 32 hours , b ) 30 hours , c ) 34 hours , d ) 31 hours , e ) 33 hours
Rationale: part filled without leak in 1 hour = 1 / 5 part filled with leak in 1 hour = 1 / 6 work done by leak in 1 hour = 1 / 5 â ˆ ’ 1 / 6 = 30 hours answer : b
Answer: b
Question (general): country x taxes each of its citizens an amount equal to 10 percent of the first $ 40,000 of income , plus 20 percent of all income in excess of $ 40,000 . if a citizen of country x is taxed a total of $ 8,000 , what is her income ?
Options: a ) $ 40,000 , b ) $ 56,000 , c ) $ 60,000 , d ) $ 66,667 , e ) $ 80,000
Rationale: "equation is correct , so math must be a problem . 0.10 * 40,000 + 0.2 * ( x - 40,000 ) = 8,000 - - > 4,000 + 0.2 x - 8,000 = 8,000 - - > 0.2 x = 12,000 - - > x = 60,000 . answer : c ."
Answer: c
Question (physics): two trains of length 100 m and 200 m are 70 m apart . they start moving towards each other on parallel tracks , at speeds 54 kmph and 72 kmph . after how much time will the trains meet ?
Options: a ) 2 sec , b ) 32 / 3 sec , c ) 20 / 7 sec , d ) 32 / 3 sec , e ) 53 / 2 sec
Rationale: "they are moving in opposite directions , relative speed is equal to the sum of their speeds . relative speed = ( 54 + 72 ) * 5 / 18 = 7 * 5 = 35 mps . the time required = d / s = 70 / 35 = 2 sec . answer : a"
Answer: a
Question (geometry): the area of a rectangular plot is 24 times its breadth . if the difference between the length and the breadth is 10 metres , what is its breadth ?
Options: a ) 14 metres
b ) 5 metres
c ) 7.5 metres
d ) data inadequate
e ) none of these
Rationale: l × b = 24 × b ∴ l = 24 m and l – b = 10 ∴ b = 24 – 10 = 14 m answer a
Answer: a
Question (general): peter ' s average ( arithmetic mean ) test score on 4 tests is 78 . what must be the student ' s score on a 5 th test for the peter ' s average score on the 5 tests to be 80 ?
Options: a ) 80 , b ) 82 , c ) 84 , d ) 86 , e ) 88
Rationale: e . 88 peter must score at least an 80 for sure . if he scores an 8 , then he will need to score 2 pots for each of the 4 other tests tomake upthe difference . they each were at 78 ( at least the average is , but this is a small point and does n ' t matter to the answer ) . so 4 tests that were each 2 points short of the 80 average that is desired means the next test must be 8 points higher than the desired average , so 80 + 8 = 88 .
Answer: e
Question (physics): a 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 14 sec . what is the length of the platform ?
Options: a ) 287 m , b ) 350 m , c ) 267 m , d ) 535.71 m , e ) 656 m
Rationale: "speed = 300 / 14 = 150 / 7 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 39 = 150 / 7 = > x = 535.71 m . answer : d"
Answer: d
Question (general): a type of extra - large suv averages 12.2 miles per gallon ( mpg ) on the highway , but only 7.6 mpg in the city . what is the maximum distance , in miles , that this suv could be driven on 21 gallons of gasoline ?
Options: a ) 190 , b ) 284.6 , c ) 300 , d ) 256 , e ) 312
Rationale: "so 12.2 * 21 = 256 . . imo option d is correct answer . ."
Answer: d
Question (general): find the 15 th term of an arithmetic progression whose first term is 2 and the common difference is 3 .
Options: a ) 45 , b ) 38 , c ) 44 , d ) 40 , e ) 46
Rationale: "n th term of a . p = a + ( n - 1 ) * d = 2 + ( 15 - 1 ) * 3 , = 2 + 42 = 44 . answer : c"
Answer: c
Question (physics): a fill pipe can fill 1 / 2 of cistern in 15 minutes . in how many minutes , it can fill 1 / 2 of the cistern ?
Options: a ) 1 min , b ) 5 min , c ) 10 min , d ) 15 min , e ) 20 min
Rationale: "required time = 15 * 2 * 1 / 2 = 15 minutes answer is d"
Answer: d
Question (physics): a train passes a platform in 30 seconds . the same train passes a man standing on the platform in 20 seconds . if the speed of the train is 54 km / hr , the length of the platform is
Options: a ) 150 meter , b ) 240 meter , c ) 200 meter , d ) 260 meter , e ) none of these
Rationale: "explanation : speed of the train = 54 km / hr = ( 54 × 10 ) / 30 m / s = 15 m / s length of the train = speed × time taken to cross the man = 15 × 20 = 300 m let the length of the platform = l time taken to cross the platform = ( 300 + l ) / 15 = > ( 300 + l ) / 15 = 30 = > 300 + l = 15 × 30 = 450 = > l = 450 - 300 = 150 meter answer : option a"
Answer: a
Question (general): kiran has 85 currency notes in all , some of which were of rs . 100 denomination and the remaining of rs . 50 denomination . the total amount of all these currency notes was rs . 5000 . how much amount did she have in the denomination of rs . 50 ?
Options: a ) 1900 , b ) 3500 , c ) 4000 , d ) 4200 , e ) 4450
Rationale: "let the number of 50 – rupee notes be x . then , the number of 100 - rupee notes = ( 85 – x ) 50 x + 100 ( 85 – x ) = 5000 = x + 2 ( 85 – x ) = 100 = x = 70 so , required amount = rs . ( 50 x 70 ) = rs . 3500 answer : option b"
Answer: b
Question (physics): a 250 meter long train crosses a platform in 40 seconds while it crosses a signal pole in 20 seconds . what is the length of the platform ?
Options: a ) 500 , b ) 1000 , c ) 350 , d ) 250 , e ) 20
Rationale: "speed = [ 250 / 20 ] m / sec = 25 / 2 m / sec . let the length of the platform be x meters . then , x + 250 / 40 = 25 / 2 2 ( x + 250 ) = 1000 è x = 250 m . answer : d"
Answer: d
Question (general): in a 4 person race , medals are awarded to the fastest 3 runners . the first - place runner receives a gold medal , the second - place runner receives a silver medal , and the third - place runner receives a bronze medal . in the event of a tie , the tied runners receive the same color medal . ( for example , if there is a two - way tie for first - place , the top two runners receive gold medals , the next - fastest runner receives a silver medal , and no bronze medal is awarded ) . assuming that exactly 3 medals are awarded , and that the 3 medal winners stand together with their medals to form a victory circle , how many different victory circles are possible ?
Options: a ) 24 , b ) 52 , c ) 96 , d ) 144 , e ) 648
Rationale: gold can be awarded in 4 ways , then silver can be awarded in 3 ways and bronze in 2 ways . therefore the total number of ways are : 4 * 3 * 2 = 24 ways of awarding the medals and the same number of ways of forming the circle . this is when there is no tie . and if there is tie , for example all three receive the gold or the silver or the bronze , then there are 4 more cases . which implies 24 * 4 = 96 . ans : c
Answer: c
Question (physics): a goods train runs at the speed of 72 kmph and crosses a 350 m long platform in 26 seconds . what is the length of the goods train ?
Options: a ) 230 m , b ) 140 m , c ) 160 m , d ) 170 m , e ) none of these
Rationale: explanation : speed = [ 72 x ( 5 / 18 ) ] m / sec = 20 m / sec . time = 26 sec . let the length of the train be x metres . then , [ ( x + 350 ) / 26 ] = 20 = > x + 350 = 520 = > x = 170 . answer : d
Answer: d
Question (general): the population of a town increased from 1 , 62,500 to 2 , 62,500 in a decade . the average percent increase of population per year is :
Options: a ) 4.37 % , b ) 5 % , c ) 6.154 % , d ) 8.75 % , e ) none of these
Rationale: "solution increase in 10 year = ( 262500 - 162500 ) = 100000 . increase % = ( 100000 / 162500 x 100 ) % = 61.54 % â ˆ ´ required average = ( 61.54 / 10 ) % = 6.154 % answer c"
Answer: c
Question (probability): find the probability that a number selected from numbers 1 , 2 , 3 , . . . , 45 is a prime number , when each of the given numbers is equally likely to be selected ?
Options: a ) 10 / 45 , b ) 14 / 45 , c ) 8 / 45 , d ) 3 / 45 , e ) 7 / 45
Rationale: "let x be the event of selecting a prime number . x = { 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41,43 } n ( x ) = 14 , n ( s ) = 45 hence , the required probability is 14 / 45 . answer : b"
Answer: b
Question (gain): on increasing the price of t . v . sets by 80 % , their sale decreases by 20 % . what is the effect on the revenue receipts of the shop ?
Options: a ) 44 , b ) 5 , c ) 56 , d ) 2 , e ) 7
Rationale: "explanation : let the price be = rs . 100 , and number of units sold = 100 then , sale value = rs . ( 100 × 100 ) = rs . 10000 new sale value = rs . ( 180 × 80 ) = rs . 14400 increase % = 4400 / 10000 × 100 = 44 % answer : a"
Answer: a
Question (general): in a hostel , the number of students decreased by 15 % 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 ) 1.96 %
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 15 % , and the price of food increases by 20 % , c = f ( new ) * ( 0.85 n ) * ( 1.2 p ) = > f ( new ) = f / ( 0.85 * 1.2 ) = > f ( new ) = 0.9804 f therefore the new cost of food must be 98.04 % of the old cost , or the cost of food must decrease by 1.96 % ( option e )"
Answer: e
Question (general): a family pays $ 800 per year for an insurance plan that pays 70 percent of the first $ 1,000 in expenses and 100 percent of all medical expenses thereafter . in any given year , the total amount paid by the family will equal the amount paid by the plan when the family ' s medical expenses total .
Options: a ) $ 1,000 , b ) $ 1,200 , c ) $ 1,400 , d ) $ 1,800 , e ) $ 2,200
Rationale: "upfront payment for insurance plan = 800 $ family needs to pay 30 % of first 1000 $ in expense = 300 $ total amount paid by family when medical expenses are equal to or greater than 1000 $ = 800 + 300 = 1100 $ total amount paid by insurance plan for first 1000 $ = 800 $ total amount paid by family will equal amount paid by plan when medical expense = 1400 $ ( since insurance plan will pay 100 % of amount that exceeds 1100 $ ) answer c"
Answer: c
Question (other): a bag contains 5 red , 6 blue and 4 green balls . if 2 ballsare picked at random , what is the probability that both are red ?
Options: a ) 2 / 15 , b ) 2 / 21 , c ) 5 / 26 , d ) 3 / 29 , e ) 4 / 27
Rationale: p ( both are red ) , = 5 c 215 c 2 = 5 c 215 c 2 = 10 / 105 = 2 / 21 b
Answer: b
Question (gain): seed mixture x is 40 percent ryegrass and 60 percent bluegrass by weight ; seed mixture y is 25 percent ryegrass and 75 percent fescue . if a mixture of x and y contains 27 percent ryegrass , what percent of the weight of this mixture is x ?
Options: a ) 10 % , b ) 13.33 % , c ) 40 % , d ) 50 % , e ) 66.66 %
Rationale: "- - - - - - - - - - - - - - - - > ryegrass x - - - - - - - - - - - - - - > 40 % y - - - - - - - - - - - - - - > 25 % m ( mixture ) - - - - > 27 % 0.4 x + ( m - x ) 0.25 = 0.27 m 0.15 x = 0.02 m x = 0.1333 m x = 13.33 % of m b"
Answer: b
Question (general): a , b , c , d , e , f are the only 6 families in indira nagar . a , b , c , d , e and f has 7 , 8 , 10 , 13 , 6 , and 10 member in their families respectively . if 1 member from all the 6 families left their respective families to accommodate themselves in the hostel of iim lucknow , then the average number of member now in each family of indira nagar is
Options: a ) 8 , b ) 9 , c ) 10 , d ) 13 , e ) 15
Rationale: answer required average = ( ( 7 - 1 ) + ( 8 - 1 ) + ( 10 - 1 ) + ( 13 - 1 ) + ( 6 - 1 ) + ( 10 - 1 ) ) / 6 = ( 7 + 8 + 10 + 13 + 6 + 10 ) / 6 - ( 6 x 1 ) / 6 = 9 - 1 = 8 correct option : a
Answer: a
Question (geometry): a rectangular grass field is 75 m * 40 m , it has a path of 2.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 2 per sq m ?
Options: a ) s . 1350
b ) s . 1327
c ) s . 1200
d ) s . 1397
e ) s . 1927
Rationale: area = ( l + b + 2 d ) 2 d = ( 75 + 40 + 2.5 * 2 ) 2 * 2.5 = > 600 600 * 2 = rs . 1200 answer : c
Answer: c
Question (general): if - 2 x + 3 y = 8 and 4 x - 3 y = 20 , what is the sum of x and y ?
Options: a ) 24 , b ) 28 , c ) 18 , d ) 26 , e ) 32
Rationale: "given - 2 x + 3 y = 8 - - - eq 1 4 x - 3 y = 20 - - eq 2 sum both eqns we get 2 x = 28 = > x = 14 sub 2 x in eq 1 = > - 28 + 3 y = 8 . = > y = 12 now x + y = 12 + 14 = 26 option d is correct answer ."
Answer: d
Question (general): in a river flowing at 2 km / hr , a boat travels 72 km upstream and then returns downstream to the starting point . if its speed in still water be 6 km / hr , find the total journey time .
Options: a ) 10 hours , b ) 12 hours , c ) 14 hours , d ) 27 hours , e ) none of these
Rationale: explanation : speed of the boat = 6 km / hr speed downstream = ( 6 + 2 ) = 8 km / hr speed upstream = ( 6 - 2 ) = 4 km / hr distance travelled downstream = distance travelled upstream = 72 km total time taken = time taken downstream + time taken upstream = ( 72 / 8 ) + ( 72 / 4 ) = 27 hr . answer : option d
Answer: d
Question (physics): the area of a square field 3136 sq m , if the length of cost of drawing barbed wire 3 m around the field at the rate of rs . 3.50 per meter . two gates of 1 m width each are to be left for entrance . what is the total cost ?
Options: a ) s . 1014 , b ) s . 1140 , c ) s . 999 , d ) s . 1085 , e ) s . 2331
Rationale: "a 2 = 3136 = > a = 56 56 * 4 * 3 = 672 – 6 = 666 * 3.5 = 2331 answer : e"
Answer: e
Question (general): if a - b = 5 and a 2 + b 2 = 29 , find the value of ab .
Options: a ) 6 , b ) 8 , c ) 10 , d ) 11 , e ) 2
Rationale: 2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 29 - 25 = 4 ab = 2 . answer : e
Answer: e
Question (physics): how many miles is 320 km ?
Options: a ) 150 miles , b ) 175 miles , c ) 200 miles , d ) 225 miles , e ) 250 miles
Rationale: "200 miles 320 / 1.6 = 200 answer : c"
Answer: c
Question (physics): 60 women can complete a work in 7 days and 10 children take 14 days to complete the work . how many days will 5 women and 10 children take to complete the work ?
Options: a ) 8 days , b ) 6 days , c ) 7 days , d ) 9 days , e ) 12 days
Rationale: "1 women ' s 1 day work = 1 / 420 1 child ' s 1 day work = 1 / 140 ( 5 women + 10 children ) ' s 1 day work = ( 5 / 420 + 10 / 140 ) = 1 / 12 5 women and 10 children will complete the work in 12 days . answer : e"
Answer: e
Question (physics): how many seconds will it take for a car that is traveling at a constant rate of 14 miles per hour to travel a distance of 96 yards ? ( 1 mile = 1,160 yards )
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 17
Rationale: "speed = 14 miles / hr = 6.84 yard / s distance = 96 yards time = distance / speed = 96 / 6.84 = 14 sec ans - d"
Answer: d
Question (gain): in how many years rs 200 will produce the same interest at 10 % as rs . 400 produce in 5 years at 12 %
Options: a ) 16 , b ) 13 , c ) 12 , d ) 14 , e ) 15
Rationale: "explanation : clue : firstly we need to calculate the si with prinical 400 , time 5 years and rate 12 % , it will be rs . 240 then we can get the time as time = ( 100 * 240 ) / ( 200 * 10 ) = 12 option c"
Answer: c
Question (gain): a watch was sold at a loss of 10 % . if it was sold for rs . 196 more , there would have been a gain of 4 % . what is the cost price ?
Options: a ) s : 1000 , b ) s : 1067 , c ) s : 1278 , d ) s : 1028 , e ) s : 1400
Rationale: "90 % 104 % - - - - - - - - 14 % - - - - 196 100 % - - - - ? = > rs : 1400 answer : e"
Answer: e
Question (gain): seed mixture x is 40 % ryegrass and 60 % bluegrass by weight ; seed mixture y is 25 % ryegrass and 75 % fescue . if a mixture of x and y contains 37 % ryegrass , what percent of the weight of the mixture is from mixture x ?
Options: a ) 20 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 80 %
Rationale: "37 % is 12 % - points above 25 % and 3 % - points below 40 % . thus the ratio of mixture y to mixture x is 1 : 4 . the percent of mixture x is 4 / 5 = 80 % . the answer is e ."
Answer: e
Question (physics): how many cubes of 10 cm edge can be put in a cubical box of 1 m edge .
Options: a ) 10000 cubes , b ) 1000 cubes , c ) 100 cubes , d ) 50 cubes , e ) none of these
Rationale: "explanation : number of cubes = 100 ∗ 100 ∗ 100 / 10 ∗ 10 ∗ 10 = 1000 note : 1 m = 100 cm option b"
Answer: b
Question (physics): the speed of a car increases by 2 kms after every one hour . if the distance travelling in the first one hour was 35 kms . what was the total distance travelled in 12 hours ?
Options: a ) 456 kms , b ) 482 kms , c ) 552 kms , d ) 556 kms , e ) none of these
Rationale: "explanation : total distance travelled in 12 hours = ( 35 + 37 + 39 + . . . . . upto 12 terms ) this is an a . p with first term , a = 35 , number of terms , n = 12 , d = 2 . required distance = 12 / 2 [ 2 × 35 + { 12 - 1 ) × 2 ] = 6 ( 70 + 23 ) = 552 kms . answer : c"
Answer: c
Question (physics): a and b together can do a piece of work in 10 days . b alone can finish it in 20 days . in how many days can a alone finish the work ?
Options: a ) 20 , b ) 10 , c ) 15 , d ) 5 , e ) 7
Rationale: time taken by a to finish the work = xy / ( y - x ) = 10 x 20 / ( 20 - 10 ) = 200 / 10 = 20 days answer : a
Answer: a
Question (other): the ratio of pens to pencils is 5 to 6 . there are 7 more pencils than pens . how many pencils are there ?
Options: a ) 36 , b ) 42 , c ) 48 , d ) 55 , e ) 64
Rationale: "let the number of pens be 5 x and the number of pencils be 6 x . 6 x - 5 x = 7 x = 7 the number of pencils is 42 . the answer is b ."
Answer: b
Question (general): the average score of a cricketer for 10 matches is 38.9 runs . if the average for the first 6 matches is 42 , then find the average for the last 4 matches .
Options: a ) 33.5 , b ) 33.5 , c ) 34.25 , d ) 35 , e ) none of these
Rationale: solution required average = ( 38.9 x 10 ) - ( 42 x 6 ) / 4 = 137 / 4 = 34.25 answer c
Answer: c
Question (geometry): the area of a square is equal to seven times the area of a rectangle of dimensions 25 cm * 343 cm . what is the perimeter of the square ?
Options: a ) 810 cm , b ) 800 cm , c ) 980 cm , d ) 718 cm , e ) 860 cm
Rationale: "area of the square = s * s = 7 ( 343 * 25 ) = > s = 5 * 7 * 7 = 245 cm perimeter of the square = 4 * 245 = 980 cm . answer : c"
Answer: c