Cheukting/mathqa huggingface dataset:
Question (general): when positive integer n is divided by 5 , the remainder is 1 . when n is divided by 7 , the remainder is 3 . what is the smallest positive integer k such that k + n is a multiple of 75 .
Options: a ) 3 , b ) 4 , c ) 12 , d ) 32 , e ) 35
Rationale: "first , let us say i have a number n which is divisible by 5 and by 7 . we all agree that it will be divisible by 35 , the lcm of 5 and 7 . now , if i have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 1 , we can say the number is of the form n = 5 a + 1 e . g . 5 + 1 , 10 + 1 , 15 + 1 , 20 + 1 , 25 + 1 , 30 + 1 , 35 + 1 etc and n = 7 b + 1 e . g . 7 + 1 , 14 + 1 , 21 + 1 , 28 + 1 , 35 + 1 etc so when it is divided by the lcm , 35 , it will give 1 as remainder ( as is apparent above ) next , if i have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 3 , we can say the number is of the form n = 5 a + 1 and n = 7 b + 3 now , the only thing you should try to understand here is that when n is divided by 5 and if i say the remainder is 1 , it is the same as saying the remainder is - 4 . e . g . when 6 is divided by 5 , remainder is 1 because it is 1 more than a multiple of 5 . i can also say it is 4 less than the next multiple of 5 , ca n ' t i ? 6 is one more than 5 , but 4 less than 10 . therefore , we can say n = 5 x - 4 and n = 7 y - 4 ( a remainder of 3 when divided by 7 is the same as getting a remainder of - 4 ) now this question is exactly like the question above . so when you divide n by 75 , remainder will be - 4 i . e . n will be 4 less than a multiple of 75 . so you must add 35 to n to make it a multiple of 75 e"
Answer: e
Question (physics): in what time will a train 130 m long cross an electric pole , it its speed be 144 km / hr ?
Options: a ) 2.5 sec , b ) 3.25 sec , c ) 5 sec , d ) 12.5 sec , e ) 6 sec
Rationale: "speed = 144 * 5 / 18 = 40 m / sec time taken = 130 / 40 = 3.25 sec . answer : b"
Answer: b
Question (physics): donald duck can can swim his pool downstream ( with the pool current helping time ) in exact 40 seconds and upstream ( against the pool current ) in a pool in exact 60 seconds . the length of pool is 2 kilometers . how long donald duck can cover distance of one side at a still pool ( with no current ) .
Options: a ) 40 minutes , b ) 45 minutes , c ) 38 minutes , d ) 48 minutes , e ) 30 minutes
Rationale: d 48 minutes . donald duck ' s speed = x km / seconds pool current speed = y km / seconds 2 / ( x + y ) = 40 2 / ( x - y ) = 60 solving the simultaneous equations gives x = 1 / 24 therefore , to cover 2 km will take 2 / x = 48 seconds
Answer: d
Question (other): a number is increased by 11 % and then reduced by 10 % . after these operations , the number :
Options: a ) does not change , b ) decreases by 1 % , c ) increases by 1 % , d ) increases by 0.1 % , e ) none of these
Rationale: "let the original number be 100 . then , the new number = 100 × 1.1 × 0.9 = 99 i . e . the number decreases by 1 % . answer b"
Answer: b
Question (physics): an plane covers a certain distance at a speed of 240 kmph in 5 hours . to cover the same distance in 5 / 3 hours , it must travel at a speed of ?
Options: a ) 100 , b ) 720 , c ) 1100 , d ) 940 , e ) 860
Rationale: we know distance = speed * time = 240 * 5 = 1200 km now to cover 1200 km in 5 / 3 hrs , speed = distance / time = 1200 / ( 5 / 3 ) = 720 kmph ans - b
Answer: b
Question (general): 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 : 4 . if the sum of their ages is 132 , what is the difference between the ages of patrick and monica ?
Options: a ) 27 , b ) 48 , c ) 45 , d ) 72 , e ) 33
Rationale: ages of p and mi = 3 x : 5 x ages of mi and mo = 3 x : 4 x rationalizing their ages . ratio of their ages will be 9 x : 15 x : 20 x sum = 44 x = 132 x = 3 difference if ages of pa and mo = 20 x - 9 x = 11 x = 11 * 3 = 33 answer e
Answer: e
Question (other): two vessels contains equal number of mixtures milk and water in the ratio 5 : 2 and 6 : 1 . both the mixtures are now mixed thoroughly . find the ratio of milk to water in the new mixture so obtained ?
Options: a ) 1 : 3 , b ) 9 : 13 , c ) 5 : 11 , d ) 11 : 3 , e ) 15 : 4
Rationale: "the ratio of milk and water in the new vessel is = ( 5 / 7 + 6 / 7 ) : ( 2 / 7 + 1 / 7 ) = 11 / 7 : 3 / 7 = 11 : 3 answer is d"
Answer: d
Question (general): ashok secured average of 80 marks in 6 subjects . if the average of marks in 5 subjects is 74 , how many marks did he secure in the 6 th subject ?
Options: a ) 38 , b ) 27 , c ) 99 , d ) 110 , e ) 80
Rationale: "explanation : number of subjects = 6 average of marks in 6 subjects = 80 therefore total marks in 6 subjects = 80 * 6 = 480 now , no . of subjects = 5 total marks in 5 subjects = 74 * 5 = 370 therefore marks in 6 th subject = 480 – 370 = 110 answer : d"
Answer: d
Question (other): out of 410 students of a school , 325 play football , 175 play cricket and 50 neither play football nor cricket . how many students play both football and cricket ?
Options: a ) 120 , b ) 150 , c ) 100 , d ) 140 , e ) 220
Rationale: n ( a ) = 325 , n ( b ) = 175 , n ( aub ) = 410 - 50 = 360 . required number = n ( anb ) = n ( a ) + n ( b ) - n ( aub ) = 325 + 175 - 360 = 140 . answer is d
Answer: d
Question (general): a number consists of 3 digit whose sum is 10 . the middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed . the number is :
Options: a ) 145 , b ) 253 , c ) 370 , d ) 352 , e ) 300
Rationale: explanation : let the middle digit be x . then , 2 x = 10 or x = 5 . so , the number is either 253 or 352 . since the number increases on reversing the digits , so the hundred ' s digit is smaller than the unit ' s digit . hence , required number = 253 . answer is b
Answer: b
Question (gain): what amount does an investor receive if the investor invests $ 5000 at 10 % p . a . compound interest for two years , compounding done annually ?
Options: a ) $ 5850 , b ) $ 5950 , c ) $ 6050 , d ) $ 6150 , e ) $ 6250
Rationale: "a = ( 1 + r / 100 ) ^ n * p ( 1.1 ) ^ 2 * 5000 = 1.21 * 5000 = 6050 the answer is c ."
Answer: c
Question (general): of the 3,600 employees of company x , 1 / 4 are clerical . if the clerical staff were to be reduced by 1 / 4 , what percent of the total number of the remaining employees would then be clerical ?
Options: a ) 25 % , b ) 22.2 % , c ) 20 % , d ) 12.5 % , e ) 11.1 %
Rationale: "let ' s see , the way i did it was 1 / 4 are clerical out of 3600 so 900 are clerical 900 reduced by 1 / 4 is 900 * 1 / 4 so it reduced 225 people , so there is 675 clerical people left but since 225 people left , it also reduced from the total of 3600 so there are 3375 people total since 675 clerical left / 3375 people total you get ( c ) 20 %"
Answer: c
Question (general): there are 12 teams in a certain league and each team plays each of the other teams exactly once . what is the total number of games played ?
Options: a ) 55 , b ) 66 , c ) 77 , d ) 88 , e ) 99
Rationale: "12 c 2 = 66 the answer is b ."
Answer: b
Question (general): tough and tricky questions : statistics . set x consists of prime numbers { 3 , 11 , 7 , a , 17 , 19 } . if integer y represents the product of all elements in set x and if 11 y is an even number , what is the range of set x ?
Options: a ) 14 , b ) 16 , c ) 17 , d ) 20 , e ) 26
Rationale: since 11 y = even therefore y has to beevensince 11 is a odd integer ( even * odd = even ) similarly , y is the product of all integers in set x but all integers in set x are odd except the unknown a and since x contains only prime numbers , a has to equal to 2 . . . ( 2 is the only even prime number and the product of all prime numbers in set x has to be even , even * odd = even ) since you know value of a you can calculate the range = largest integer in the set minus smallest integer in the set = 19 - 2 = 17 answer is c
Answer: c
Question (general): in a simultaneous throw of a pair of dice , find the probability of getting a total more than 4
Options: a ) 1 / 2 , b ) 7 / 12 , c ) 5 / 13 , d ) 5 / 12 , e ) 1 / 3
Rationale: "total number of cases = 3 * 3 = 9 favourable cases = [ ( 2,3 ) , ( 3,2 ) , ( 3,3 ) ] = 3 so probability = 3 / 9 = 1 / 3 answer is e"
Answer: e
Question (general): what is the total number of integers between 100 and 250 that are divisible by 5 ?
Options: a ) 27 , b ) 28 , c ) 29 , d ) 30 , e ) 25
Rationale: "105 , 110 , 115 , . . . , 240,245 this is an equally spaced list ; you can use the formula : n = ( largest - smallest ) / ( ' space ' ) + 1 = ( 245 - 105 ) / ( 5 ) + 1 = 140 / 5 + 1 = 28 + 1 = 29 answer is c"
Answer: c
Question (gain): what profit percent is made by selling an article at a certain price , if by selling at 4 / 5 rd of that price , there would be a loss of 20 % ?
Options: a ) 0 % , b ) 29 % , c ) 70 % , d ) 27 % , e ) 28 %
Rationale: "sp 2 = 4 / 5 sp 1 cp = 100 sp 2 = 80 4 / 5 sp 1 = 80 sp 1 = 100 100 - - - 100 = > 0 % answer : a"
Answer: a
Question (gain): on a sum of money , the simple interest for 2 years is rs . 320 , while the compound interest is rs . 340 , the rate of interest being the same in both the cases . the rate of interest is
Options: a ) 15 % , b ) 14.25 % , c ) 12.5 % , d ) 10.5 % , e ) 11.5 %
Rationale: explanation : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - solution 1 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - simple interest for 2 years is rs . 320 = > simple interest for first year = 320 / 2 = 160 = > similarly , simple interest for second year is also 160 compound interest for first year = 160 compound interest for second year = 340 - 160 = 180 we can see that compound interest for second year is more than simple interest for second year by 180 - 160 = 20 i . e . , rs . 20 is the simple interest on rs . 160 for 1 year r = 100 × si / pt = ( 100 × 20 ) / ( 160 × 1 ) = 12.5 % - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - solution 2 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - the difference between compound interest and simple interest on rs . p for 2 years at r % per annum = ( r × si ) / ( 2 × 100 ) difference between the compound interest and simple interest = 340 - 320 = 20 ( r × si ) / ( 2 × 100 ) = 20 ( r × 320 ) / ( 2 × 100 ) = 20 r = 20 × 100 × 2320 = 12.5 % answer : option 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 xyz is
Options: a ) 120 , b ) 50 , c ) 60 , d ) 70 , e ) 90
Rationale: "xy + xz = 62 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 1 ) yz + yx = 82 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 2 ) xz + zy = 100 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 3 ) re - writing equation 3 as follows : xz + zy = 82 + 18 xz + zy = yz + yx + 18 xz = yx + 18 . . . . . . . . . . . . . . . ( 4 ) adding ( 1 ) ( 4 ) 2 xz = 80 xz = 40 xyz has to be multiple of 40 , only 120 fits in answer = a"
Answer: a
Question (general): of the families in city x in 1992 , 30 percent owned a personal computer . the number of families in city x owning a computer in 1999 was 50 percent greater than it was in 1992 , and the total number of families in city x was 5 percent greater in 1999 than it was in 1994 . what percent of the families in city x owned a personal computer in 1999 ?
Options: a ) 43 % , b ) 42.85 % , c ) 45.25 % , d ) 46.23 % , e ) 41.66 %
Rationale: "say a 100 families existed in 1992 then the number of families owning a computer in 1992 - 30 number of families owning computer in 1999 = 30 * 150 / 100 = 45 number of families in 1999 = 105 the percentage = 45 / 105 * 100 = 42.85 % . answer : b"
Answer: b
Question (gain): of the votes cast on a certain proposal , 70 more were in favor of the proposal than were against it . if the number of votes against the proposal was 40 percent of the total vote , what was the total number of votes cast ? ( each vote cast was either in favor of the proposal or against it . )
Options: a ) 350 , b ) 375 , c ) 400 , d ) 425 , e ) 450
Rationale: "let x be the total number of votes cast . 0.6 x = 0.4 x + 70 0.2 x = 70 x = 350 the answer is a ."
Answer: a
Question (physics): a man can do a piece of work in 4 days , but with the help of his son he can do it in 3 days . in what time can the son do it alone ?
Options: a ) 12 days , b ) 6 days , c ) 5 days , d ) 4 days , e ) none of these
Rationale: "explanation : in this type of question , where we have one person work and together work done . then we can easily get the other person work just by subtracting them . as son ' s one day work = ( 1 / 3 − 1 / 4 ) = ( 4 − 3 ) / 12 = 1 / 12 so son will do whole work in 12 days answer : a"
Answer: a
Question (physics): beginning in town a , biker bob rides his bike 10 miles west , 5 miles north , 5 miles east , and then 15 miles north , to town b . how far apart are town a and town b ? ( ignore the curvature of the earth . )
Options: a ) 22 miles , b ) 20.62 miles , c ) 25 miles , d ) 26 miles , e ) 28 miles
Rationale: "using pythagoras we have one side i , e total distance traveled in north direction = 15 + 5 = 20 m other being the base ie distance traveled west - distance traveled eat = 10 - 5 = 5 m now this third side or the distance between town a and town b = 20 ^ 2 + 5 ^ 2 = sq root 425 = 20.62 mile answer : b"
Answer: b
Question (general): a , b and c have rs . 400 between them , a and c together have rs . 300 and b and c rs . 150 . how much does c have ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 100
Rationale: "a + b + c = 400 a + c = 300 b + c = 150 - - - - - - - - - - - - - - a + b + 2 c = 450 a + b + c = 400 - - - - - - - - - - - - - - - - c = 50 answer : b"
Answer: b
Question (general): 0.0002152 / 0.000205 x 12.05 = ?
Options: a ) 19.64 , b ) 14.64 , c ) 12.6 , d ) 15.64 , e ) 13.64
Rationale: "explanation : ? = 0.0002152 / 0.000205 x 12.05 = 12.6 answer : option c"
Answer: c
Question (general): city x has a population 8 times as great as the population of city y , which has a population twice as great as the population of city z . what is the ratio of the population of city x to the population of city z ?
Options: a ) 1 : 8 , b ) 1 : 4 , c ) 2 : 1 , d ) 4 : 1 , e ) 16 : 1
Rationale: "x = 8 y , y = 2 * z x : y , y : z 8 : 1 , 2 : 1 16 : 2 , 2 : 1 so , x : z = 16 : 1 ( e )"
Answer: e
Question (general): in digging a pond 20 m * 10 m * 8 m the volumes of the soil extracted will be ?
Options: a ) 3387 , b ) 1600 , c ) 2866 , d ) 2787 , e ) 1121
Rationale: "20 * 10 * 8 = 1600 answer : b"
Answer: b
Question (gain): a man took loan from a bank at the rate of 12 % p . a . s . i . after 10 years he had to pay rs . 1500 interest only for the period . the principal amount borrowed by him was ?
Options: a ) 1502 , b ) 1900 , c ) 1250 , d ) 1750 , e ) 2000
Rationale: "principal = ( 100 * 1500 ) / ( 12 * 10 ) = rs . 1250 answer : c"
Answer: c
Question (general): in a bus left side are 15 seats available , 3 few seats in right side because in rear exit door . each seat hold 3 people . in addition , there is a seat back can sit 8 people all together . how many people can sit in a bus ?
Options: a ) 52 , b ) 49 , c ) 95 , d ) 88 , e ) 89
Rationale: "right side = 15 seat left side = 15 - 3 ( 3 few seat in right side ) = 12 seat total = 15 + 12 = 27 people can seat in 27 seat = 27 * 3 = 81 people can seat in last seat = 8 total people can seat = 81 + 8 = 89 answer : e"
Answer: e
Question (gain): if a town of 45,000 people is growing at a rate of approx . 1 % per year , the population of the town in 5 years will be closest to ?
Options: a ) a . 46000 , b ) b . 47000 , c ) c . 48000 , d ) d . 49000 , e ) e . 50000
Rationale: 1 % is quite small and hence the answer is a )
Answer: a
Question (general): a computer wholesaler sells 10 different computers and each is priced differently . if the wholesaler chooses 3 computers for display at a trade show , what is the probability ( all things being equal ) that the two most expensive computers will be among the 3 chosen for display ?
Options: a ) 15 / 56 , b ) 3 / 28 , c ) 1 / 28 , d ) 1 / 15 , e ) 1 / 168
Rationale: since , two of the choices are prefixed , we are free to choose 1 from the rest of the 8 avilable . so 8 c 1 is the numerator . total no of ways we can choose 3 from 10 is 10 c 3 , which is the denominator . so , the probability : 8 c 1 / 10 c 3 = 1 / 15 ans is d .
Answer: d
Question (geometry): how many internal diagonals does a octagon ( eight sided polygon ) have ?
Options: a ) 90
b ) 85
c ) 70
d ) 35
e ) 20
Rationale: number of diagonals in any polygon can be found using this formula : n ( n - 3 ) / 2 here n = 8 no . of diagonals = 8 ( 8 - 3 ) / 2 = 20 ans e
Answer: e
Question (general): on thursday mabel handled 90 transactions . anthony handled 10 % more transactions than mabel , cal handled 2 / 3 rds of the transactions that anthony handled , and jade handled 17 more transactions than cal . how much transactions did jade handled ?
Options: a ) 80 , b ) 81 , c ) 82 , d ) 83 , e ) 84
Rationale: "solution : mabel handled 90 transactions anthony handled 10 % more transactions than mabel anthony = 90 + 90 × 10 % = 90 + 90 × 0.10 = 90 + 9 = 99 cal handled 2 / 3 rds of the transactions than anthony handled cal = 2 / 3 × 99 = 66 jade handled 16 more transactions than cal . jade = 66 + 17 = 83 jade handled = 83 transactions . answer : d"
Answer: d
Question (other): among 600 students , 56 % study sociology , 44 % study mathematics and 40 % study biology . if 30 % of students study both mathematics and sociology , what is the largest possible number of students who study biology but do not study either mathematics or sociology ?
Options: a ) 30 , b ) 90 , c ) 120 , d ) 172 , e ) 180
Rationale: "i would just like to add a bit of explanation after the step where you calculate that the number of students studying both m and s = 180 using your analysis : we see that the total number of students who study either maths or sociology = 264 + 336 - 180 = 420 so , in the image we know that the number of students in the zone with the black boundary = 420 let ' s assume the number of students who studyonlybiology to beb ( this is the number that we have to maximize ) and , let ' s assume the number of students who study none of the three subjects , that is the number of students in the white space = w since the total number of students = 600 , we can write : 420 + b + w = 600 or , b + w = 600 - 420 = 180 that is , b = 180 - w so , the maximum value ofbwill happen forw = 0 this is how we get , the maximum value ofb = 180 e"
Answer: e
Question (general): if a farmer sells 15 of his goats , his stock of feed will last for 4 more days than planned , but if he buys 20 more goats , he will run out of feed 3 days earlier than planned . if no goats are sold or bought , the farmer will be exactly on schedule . how many goats does the farmer have ?
Options: a ) 12 , b ) 24 , c ) 48 , d ) 60 , e ) 55
Rationale: "say farmer has n goat and he is good for d days . : - we have 3 equations given in question : - ( n - 15 ) * d + 4 = ( n + 20 ) * ( d - 3 ) = n * d solving these : ( you can solve 1 st and 3 rd and 2 nd and 3 rd together ) we get : 20 d - 3 n = 60 4 n - 15 d = 60 = > n = 60 ans d it is !"
Answer: d
Question (physics): 15 men take 21 days of 8 hrs . each to do a piece of work . how many days of 3 hrs . each would it take for 21 women if 3 women do as much work as 2 men ?
Options: a ) 60 , b ) 20 , c ) 19 , d ) 29 , e ) 39
Rationale: "let 1 man does 1 unit / hr of work 15 m in 21 days of 8 hrs will do ( 15 * 21 * 8 ) units 3 w = 2 m 1 w = ( 2 / 3 ) units / hr 21 w with 3 hrs a day will take ( 15 * 21 * 8 ) / ( 21 * 3 * ( 2 / 3 ) ) days = > 60 days answer : a"
Answer: a
Question (physics): if a tire rotates at 400 revolutions per minute when the car is traveling 72 km / h , what is the circumference of the tire ?
Options: a ) 7 meters , b ) 9 meters , c ) 8 meters , d ) 5 meters , e ) 3 meters
Rationale: "400 rev / minute = 400 * 60 rev / 60 minutes = 24,000 rev / hour 24,000 * c = 72,000 m : c is the circumference c = 3 meters correct answer e"
Answer: e
Question (general): a , b , c subscribe rs . 50000 for a business . a subscribes rs . 4000 more than b and b rs . 5000 more than c . out of a total profit of rs . 35000 , c receives :
Options: a ) s . 14,000 , b ) s . 14,200 , c ) s . 4,400 , d ) s . 8,400 , e ) s . 4,800
Rationale: let c = x . then , b = x + 5000 and a = x + 5000 + 4000 = x + 9000 . so , x + x + 5000 + x + 9000 = 50000 3 x = 36000 x = 12000 a : b : c = 21000 : 17000 : 12000 = 21 : 17 : 12 . c ' s share = rs . ( 35000 x 12 / 50 ) = rs . 8,400 . d
Answer: d
Question (general): the sum of number of boys and girls in a school is 900 . if the number of boys is x , then the number of girls becomes x % of the total number of students . the number of boys is ?
Options: a ) 50 , b ) 40 , c ) 60 , d ) 90 , e ) 70
Rationale: we have x + x % of 900 = 900 x + x / 100 * 900 = 900 10 * x = 900 x = 90 answer is d
Answer: d
Question (general): one half of a two digit number exceeds its one fourth by 3 . what is the sum of the digits of the number ?
Options: a ) 3 , b ) 9 , c ) 11 , d ) 12 , e ) 15
Rationale: explanation : x / 2 – x / 4 = 3 = > x = 12 1 + 2 = 3 a
Answer: a
Question (general): a student chose a number , multiplied it by 2 , then subtracted 200 from the result and got 110 . what was the number he chose ?
Options: a ) 168 , b ) 100 , c ) 155 , d ) 160 , e ) 200
Rationale: "solution : let x be the number he chose , then 2 * x * 200 = 110 2 x = 310 x = 155 correct answer c"
Answer: c
Question (physics): 20 beavers , working together in a constant pace , can build a dam in 3 hours . how many hours will it take 12 beavers that work at the same pace , to build the same dam ?
Options: a ) 2 . , b ) 4 . , c ) 5 . , d ) 6 , e ) 8 .
Rationale: "total work = 20 * 3 = 60 beaver hours 12 beaver * x = 60 beaver hours x = 60 / 12 = 5 answer : d"
Answer: d
Question (general): the average expenditure of a labourer for 6 months was 90 and he fell into debt . in the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30 . his monthly income i
Options: a ) 70 , b ) 72 , c ) 75 , d ) 78 , e ) 81
Rationale: income of 6 months = ( 6 × 90 ) – debt = 540 – debt income of the man for next 4 months = 4 × 60 + debt + 30 = 270 + debt ∴ income of 10 months = 810 average monthly income = 810 ÷ 10 = 81 answer e
Answer: e
Question (physics): an aeroplane covers a certain distance at a speed of 240 kmph in 5 hours . to cover the same distance in 1 hours , it must travel at a speed of :
Options: a ) 300 kmph , b ) 360 kmph , c ) 600 kmph , d ) 720 kmph , e ) 750 kmph
Rationale: "explanation : distance = ( 240 x 5 ) = 1200 km . speed = distance / time speed = 1200 / ( 5 / 3 ) km / hr . required speed = ( 1200 x 3 / 5 ) km / hr = 720 km / hr . answer is d"
Answer: d
Question (geometry): the length of rectangle is thrice its breadth and its perimeter is 48 m , find the area of the rectangle ?
Options: a ) 432 , b ) 108 , c ) 252 , d ) 992 , e ) 212
Rationale: "2 ( 3 x + x ) = 48 l = 18 b = 6 lb = 18 * 6 = 108 answer : b"
Answer: b
Question (general): find the value of ( √ 1.1 ) / ( √ 0.81 ) + ( √ 1.44 ) / ( √ 0.49 ) is
Options: a ) 195 / 63 , b ) 2.879 , c ) 155 / 63 , d ) 125 / 63 , e ) 185 / 63
Rationale: "( √ 1.1 ) / ( √ 0.81 ) + ( √ 1.44 ) / ( √ 0.49 ) = > 2.879 answer is b"
Answer: b
Question (gain): if rs . 7500 are borrowed at c . i at the rate of 4 % per annum , then after 6 years the amount to be paid is ?
Options: a ) 3377 , b ) 2688 , c ) 2688 , d ) 9490 , e ) 1268
Rationale: "a = 7500 ( 26 / 25 ) ^ 6 = 9490 answer : d"
Answer: d