regisss/math_qa huggingface dataset:
Problem: if a man earns rs 20 on first day and spends rs 15 on second day , and earns rs 20 on third day and spends rs 15 on fourth day and goes on on which day he will be having rs 60 .
Options: a ) 40 rs , b ) 45 rs , c ) 50 rs , d ) 55 rs , e ) 60 rs
Rationale: earns rs 20 on first day and spends rs 15 on second day means , end of day 2 , he have 5 rs . therefore , in 16 days he have 40 rs 2 * 8 = 16 days 5 rs * 8 = 40 rs and on the 17 th day again he earn rs . 20 , 40 + 20 = 60 rs . answer : e
Answer: e
Problem: 4 mat - weaves can weaves 4 mats in 4 days . at the same rate , how many mats would be woven by 8 mat - weaves in 8 days ?
Options: a ) 4 , b ) 8 , c ) 12 , d ) 16 , e ) 17
Rationale: solution let the required number of mats be x . more weaves , more mats ( direct proportion ) more days , more mats ( direct proportion ) ∴ 4 × 4 × x = 8 × 8 × 4 ⇔ x = ( 8 x 8 x 4 ) / ( 4 x 4 ) = 16 . answer d
Answer: d
Problem: the average age of 36 students in a group is 14 years . when teacher ’ s age is included to it , the average increases by one . what is the teacher ’ s age in years ?
Options: a ) 31 , b ) 36 , c ) 41 , d ) 51 , e ) none
Rationale: "sol . age of the teacher = ( 37 × 15 – 36 × 14 ) years = 51 years . answer d"
Answer: d
Problem: two trains of equal length are running on parallel lines in the same direction at 46 km / hr and 36 km / hr . the faster train catches and completely passes the slower train in 18 seconds . what is the length of each train ( in meters ) ?
Options: a ) 20 , b ) 25 , c ) 35 , d ) 50 , e ) 65
Rationale: "the relative speed = 46 - 36 = 10 km / hr = 10 * 5 / 18 = 25 / 9 m / s in 18 seconds , the relative difference in distance traveled is 18 * 25 / 9 = 50 meters this distance is twice the length of each train . the length of each train is 50 / 2 = 25 meters the answer is b ."
Answer: b
Problem: the numbers 272738 and 232342 , when divided by n , a 2 digit number leave a remainder 13 and 17 respectively . find the sum of digits of n ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "we have to find the h . c . f of both 1.272738 - 13 2.232325 - 17 h . c . f is 25 ans is 7 answer : d"
Answer: d
Problem: a train is 360 meter long is running at a speed of 90 km / hour . in what time will it pass a bridge of 140 meter length ?
Options: a ) 27 seconds , b ) 29 seconds , c ) 40 seconds , d ) 11 seconds , e ) 20 seconds
Rationale: "speed = 90 km / hr = 90 * ( 5 / 18 ) m / sec = 25 m / sec total distance = 360 + 140 = 500 meter time = distance / speed = 500 * ( 1 / 25 ) = 20 seconds answer : e"
Answer: e
Problem: for each month of a given year except december , a worker earned the same monthly salary and donated one - tenth of that salary to charity . in december , the worker earned n times his usual monthly salary and donated one - fourth of his earnings to charity . if the worker ' s charitable contributions totaled one - eighth of his earnings for the entire year , what is the value of n ?
Options: a ) 8 / 5 , b ) 5 / 2 , c ) 3 , d ) 22 / 10 , e ) 4
Rationale: "let monthly salary for each of the 11 months except december was x , then 11 x * 1 / 10 + nx * 1 / 4 = 1 / 8 ( 11 x + nx ) ; 11 / 10 + n / 4 = 1 / 8 ( 11 + n ) = > 44 + 10 n / 40 = 11 + n / 8 352 + 80 n = 440 + 40 n = > 40 n = 88 n = 88 / 40 = 22 / 10 answer : d ."
Answer: d
Problem: if sharon ' s weekly salary increased by 16 percent , she would earn $ 348 per week . if instead , her weekly salary were to increase by 20 percent , how much would she earn per week ?
Options: a ) $ 374 , b ) $ 382 , c ) $ 385 , d ) $ 360 , e ) $ 399
Rationale: "( 348 / 116 ) 120 = 360 in this case long division does not take much time . ( 348 / 116 ) = 3 3 * 120 = 360 ( 300 + 60 ) answer d"
Answer: d
Problem: if the ratio of a to b is 11 to 3 and the ratio of b to c is 1 to 5 , what is the ratio of a to c ?
Options: a ) 4 / 15 , b ) 11 / 15 , c ) 2 / 5 , d ) 4 / 5 , e ) 7 / 6
Rationale: "a : b = 11 : 3 - - 1 b : c = 1 : 5 = > b : c = 3 : 15 - - 2 from 1 and 2 , we get a : c = 11 : 15 answer b"
Answer: b
Problem: what should be the least number to be added to the 2496 number to make it divisible by 5 ?
Options: a ) 12 , b ) 17 , c ) 18 , d ) 4 , e ) 26
Rationale: "answer : 4 option : d"
Answer: d
Problem: 1 ⁄ 5 of a number is equal to 5 ⁄ 8 of the second number . if 35 is added to the first number then it becomes 4 times of second number . what is the value of the second number ?
Options: a ) 125 , b ) 70 , c ) 40 , d ) 25 , e ) none of these
Rationale: let x be the first number and y be the second number . 1 ⁄ 5 x = 5 ⁄ 8 y \ x ⁄ y = 25 ⁄ 8 . . . . . . ( i ) x + 35 = 4 y or , 25 ⁄ 8 y + 35 = 4 y \ y = 40 answee c
Answer: c
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: if x ^ 2 + y ^ 2 = 15 and xy = 3 , then ( x − y ) ^ 2 =
Options: a ) 8 , b ) 9 , c ) 14 , d ) 17 , e ) 20
Rationale: but you can not take xy + 3 to mean xy = - 3 . . only if xy + 3 = 0 , it will mean xy = - 3 . . rest your solution is perfect and you will get your correct answer as 15 - 2 * 3 = 9 . . answer b
Answer: b
Problem: the perimeter of a triangle is 48 cm and the in radius of the triangle is 2.5 cm . what is the area of the triangle ?
Options: a ) 76 , b ) 88 , c ) 60 , d ) 55 , e ) 35
Rationale: "area of a triangle = r * s where r is the in radius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 48 / 2 = 60 cm 2 answer : c"
Answer: c
Problem: if h = { 1 , 7 , 18 , 20 , 29 , 33 } , how much less is the mean of the numbers in h than the median of the numbers in h ?
Options: a ) 1.0 , b ) 1.5 , c ) 2.0 , d ) 2.5 , e ) 3.0
Rationale: this is a good question to understand the difference between mean and median . mean : average of all the numbers . ( sum of all the elements divided by the number of elements ) median : arrange the elements of the set in increasing order . if the number of terms is odd , the middle term is the median . if the number of terms is even , the average of middle two terms is the median coming to this question , mean = ( 1 + 7 + 18 + 20 + 29 + 33 ) / 6 = 18 median = ( 18 + 20 ) / 2 = 19 difference = 1 option a
Answer: a
Problem: what will be the cost of house to paint which area equal to 484 sq ft , if the price per foot of building is rs . 20
Options: a ) 1800 , b ) 1760 , c ) 1400 , d ) 2600 , e ) 3600
Rationale: let the side of the square plot be a ft . a 2 = 484 = > a = 22 length of the fence = perimeter of the plot = 4 a = 88 ft . cost of building the fence = 88 * 20 = rs . 1760 . answer : b
Answer: b
Problem: x varies inversely as square of y . given that y = 2 for x = 1 . the value of x for y = 6 will be equal to ?
Options: a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 0 , d ) 1 / 9 , e ) 1 / 5
Rationale: "given x = k / y 2 , where k is a constant . now , y = 2 and x = 1 gives k = 4 . x = 4 / y 2 = > x = 4 / 62 , when y = 6 = > x = 4 / 36 = 1 / 9 . answer : d"
Answer: d
Problem: two mba admissions committees are to be formed randomly from 6 second year mbas with 3 members each . what is the probability r that jane will be on the same committee as albert ?
Options: a ) 12 % , b ) 20 % , c ) 33 % , d ) 40 % , e ) 50 %
Rationale: "total number of ways to choose 3 member committee - 6 c 3 = ( 6 ! / 3 ! 3 ! ) = 20 no . of ways albert n jane are in same committee : - ( 4 c 1 * 2 ) = 8 probability r = ( 8 / 20 ) * 100 = 40 % . + 1 for me . . : d"
Answer: d
Problem: there are , in a certain league , 50 teams , and each team face another team for a total of 4 times . how many games are played in the season ?
Options: a ) 6660 , b ) 3600 , c ) 2400 , d ) 4900 , e ) 5400
Rationale: by using the formula , t [ n ( n - 1 ) / 2 ] , where t = no . of games between two teams and n = total no . of teams , we get : 4900 option d .
Answer: d
Problem: a cycle is bought for rs . 1000 and sold for rs . 2000 , find the gain percent ?
Options: a ) 11 , b ) 20 , c ) 100 , d ) 77 , e ) 12
Rationale: "1000 - - - - 1000 100 - - - - ? = > 100 % answer : c"
Answer: c
Problem: a 360 m long train is running at a speed of 55 km / hr . it crossed a platform of length 520 m in ?
Options: a ) 57.6 sec , b ) 20.2 sec , c ) 31.8 sec , d ) 50.4 sec , e ) none of the above
Rationale: "speed = 55 km / hr ( to convert km / hr in to m / s ) = 55 x 5 / 18 m / s distance = 360 m + 520 m ( if questions is about train crossing a post you need to consider only the length of train , ) = 880 m time = distance / speed = 880 x 18 / ( 5 x 55 ) = 57.6 sec ans is : a"
Answer: a
Problem: 5 x 1.6 - 2 x 1.4 / 1.3 = ?
Options: a ) 3 , b ) 0 , c ) 5 , d ) 4 , e ) 2
Rationale: "given expression = ( 8 - 2.8 ) / 1.3 = 5.2 / 1.3 = 52 / 1.3 = 4 . answer is d ."
Answer: d
Problem: the speed of a car is 98 km in the first hour and 70 km in the second hour . what is the average speed of the car ?
Options: a ) 76 kmph , b ) 75 kmph , c ) 87 kmph , d ) 56 kmph , e ) 84 kmph
Rationale: "s = ( 98 + 70 ) / 2 = 84 kmph answer : e"
Answer: e
Problem: 12 men work 8 hours per day to complete the work in 10 days . to complete the same work in 10 days , working 12 hours a day , the number of men required ?
Options: a ) 10 days , b ) 9 days , c ) 6 days , d ) 8 days , e ) 7 days
Rationale: "that is , 1 work done = 12 × 8 × 10 then , 12 8 × 10 = ? × 12 × 10 ? ( i . e . no . of men required ) = 12 × 8 × 10 / 12 × 10 = 8 days d )"
Answer: d
Problem: divide rs . 1301 between a and b , so that the amount of a after 7 years is equal to the amount of b after 9 years , the interest being compounded at 4 % per annum .
Options: a ) 625 , b ) 367 , c ) 288 , d ) 209 , e ) 198
Rationale: explanation : let the two parts be rs . x and rs . ( 1301 - x ) . 625 x = 676 ( 1301 - x ) 1301 x = 676 x 1301 x = 676 . so , the parts are rs . 676 and rs . ( 1301 - 676 ) i . e rs . 676 and rs . 625 answer : a ) rs . 625
Answer: a
Problem: heinz produces tomato puree by boiling tomato juice . the tomato puree has only 20 % water while the tomato juice has 90 % water . how many liters of tomato puree will be obtained from 40 litres of tomato juice ?
Options: a ) 2.8 liters . , b ) 2.5 liters . , c ) 5 liters . , d ) 2.6 liters . , e ) 2.1 liters .
Rationale: "answer : explanation : in each of the solutions , there is a pure tomato component and some water . so while boiling , water evaporates but tomato not . so we equate tomato part in the both equations . â ‡ ’ â ‡ ’ 10 % ( 40 ) = 80 % ( x ) â ‡ ’ â ‡ ’ x = 5 liters . answer : c"
Answer: c
Problem: david works at a resort from the beginning of march to the end of september . during the month of august this past year , he made 4 times the average ( arithmetic mean ) of his monthly totals in tips for the other months . his total tips for august were what fraction of his total tips for all of the months he worked ?
Options: a ) 3 / 5 , b ) 2 / 5 , c ) 4 / 5 , d ) 1 / 5 , e ) 6 / 5
Rationale: first notice the number of months for which he worked - march to sept i . e . 7 months avg of monthly totals in tips for months other than august = x tips in august = 4 x total tips for all months = 6 * x + 4 x = 10 x tips for august / total tips for all months = 4 x / 10 x = 2 / 5 answer : b
Answer: b
Problem: a train 330 metres long is moving at a speed of 25 kmph . it will cross a man coming from the opposite direction at a speed of 2 km per hour in :
Options: a ) 30 sec , b ) 32 sec , c ) 36 sec , d ) 38 sec , e ) 44 sec
Rationale: "relative speed = ( 25 + 2 ) km / hr = 27 km / hr = ( 27 × 5 / 18 ) m / sec = 15 / 2 m / sec . time taken by the train to pass the man = ( 330 × 2 / 15 ) sec = 44 sec answer : e"
Answer: e
Problem: walking at 4 / 5 of her normal speed , a worker is 15 minutes later than usual in reaching her office . the usual time ( in minutes ) taken by her to cover the distance between her home and her office is
Options: a ) 45 , b ) 50 , c ) 55 , d ) 60 , e ) 65
Rationale: "let v be her normal speed and let t be her normal time . d = ( 4 / 5 ) v * ( t + 15 ) since the distance is the same we can equate this to a regular day which is d = v * t v * t = ( 4 / 5 ) v * ( t + 15 ) t / 5 = 12 t = 60 the answer is d ."
Answer: d
Problem: a cylinder of height h is 8 / 9 of water . when all of the water is poured into an empty cylinder whose radius is 25 percent larger than that of the original cylinder , the new cylinder is 3 / 5 full . the height of the new cylinder is what percent of h ?
Options: a ) 25 % , b ) 50 % , c ) 68 % , d ) 80 % , e ) 100 %
Rationale: basically we can disregard the radius is 25 % information , as we are only asked about the height of the original and the new cylinder . this is becausethe new cylinder is 3 / 5 fullmeans the same as that it ' s height is 3 / 5 . original cylinder 8 / 9 new cylinder 3 / 5 so 3 / 5 / 8 / 9 = 3 / 5 * 9 / 8 = 12 / 15 = 4 / 5 = 0.680 or 68 % . answer c
Answer: c
Problem: mary passed a certain gas station on a highway while traveling west at a constant speed of 40 miles per hour . then , 15 minutes later , paul passed the same gas station while traveling west at a constant speed of 60 miles per hour . if both drivers maintained their speeds and both remained on the highway for at least 2 hours , how long after he passed the gas station did paul catch up with mary ?
Options: a ) 1 / 2 , b ) 2 , c ) 1 , d ) 4 , e ) 5
Rationale: "d = rt m : r = 40 mph , t = t + 1 / 4 hr d = 40 ( t + 1 / 4 ) p : r = 60 , t = t d = 60 t since they went the same distance : 40 t + 40 / 4 = 60 t 20 t = 40 / 4 t = 1 / 2 or 1 / 2 hr a"
Answer: a
Problem: a can do a job in 15 days and b in 30 days . if they work on it together for 4 days , then the fraction of the work that is left is ?
Options: a ) 2 / 15 , b ) 3 / 5 , c ) 3 / 11 , d ) 1 / 12 , e ) 6 / 13
Rationale: "a ' s 1 day work = 1 / 15 b ' s 1 day work = 1 / 30 a + b 1 day work = 1 / 15 + 1 / 30 = 3 / 30 = 1 / 10 a + b 4 days work = 1 / 10 * 4 = 2 / 5 remaining work = 1 - 2 / 5 = 3 / 5 answer is b"
Answer: b
Problem: the population of a city increases by 9 % per year but due to migration it decrease by 1 % per years . what will be the percentage increase in population in 3 years ?
Options: a ) 9 % , b ) 9.27 % , c ) 25.97 % , d ) 12 % , e ) none of these
Rationale: "actual increase in population = 8 % let , earlier population = 100 then the population after 3 years = 100 ( 1 + 8 / 100 ) ^ 3 = 125.97 ∴ required percentage = 25.97 % answer : c"
Answer: c
Problem: a cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.5 m and its walls are 5 cm thick . the thickness of the bottom is :
Options: a ) 90 cm , b ) 5 dm , c ) 1 m , d ) 1.1 cm , e ) none of these
Rationale: "explanation : let the thickness of the bottom be x cm . then , [ ( 330 - 10 ) × ( 260 - 10 ) × ( 150 - x ) ] = 8000 × 1000 = > 320 × 250 × ( 150 - x ) = 8000 × 1000 = > ( 150 - x ) = 8000 × 1000 / 320 = 100 = > x = 50 cm = 5 dm . answer : b"
Answer: b
Problem: if k is the greatest positive integer such that 3 ^ k is a divisor of 18 ! then k =
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: "18 / 3 = 6 18 / 9 = 2 6 + 2 = 8 k = 8 answer : e"
Answer: e
Problem: if 18888 – n is divisible by 11 , and 0 < n < 11 , what is n ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: 18,888 / 11 = 1717 with a remainder of 1 . we need to subtract the remainder to get a multiple of 11 . the answer is a .
Answer: a
Problem: after decreasing 56 % in the price of an article costs rs . 4400 . find the actual cost of an article ?
Options: a ) 12000 , b ) 15000 , c ) 1200 , d ) 1000 , e ) 10000
Rationale: "cp * ( 44 / 100 ) = 4400 cp = 100 * 100 = > cp = 10000 answer : e"
Answer: e
Problem: for each of her sales , a saleswoman receives a commission equal to 20 percent of the first $ 500 of the total amount of the sale , plus 45 percent of the total amount in excess of $ 500 . if the total amount of one of her sales was $ 800 , the saleswoman ’ s commission was approximately what percent of the total amount of the sale ?
Options: a ) 22 % , b ) 24 % , c ) 25 % , d ) 29 % , e ) 28 %
Rationale: total sales = 800 comission = ( 20 / 100 ) * 500 + ( 45 / 100 ) * 300 = 100 + 135 = 235 % comission = ( 235 / 800 ) * 100 = 29.4 ~ 29 % answer is d
Answer: d
Problem: a shop owner sells 50 mtr of cloth and gains sp of 10 mtrs . find the gain % ?
Options: a ) 25 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 70 %
Rationale: here , selling price of 10 m cloth is obtained as profit . profit of 10 m cloth = ( s . p . of 50 m cloth ) – ( c . p . of 50 m cloth ) selling price of 40 m cloth = selling price of 50 m of cloth let cost of each metre be rs . 100 . therefore , cost price of 40 m cloth = rs . 4000 and s . p . of 40 m cloth = rs . rs . 5000 profit % = 10 / 40 × 100 = 25 % profit of 25 % was made by the merchant . a
Answer: a
Problem: find compound interest on rs . 7500 at 4 % per annum for 2 years , compounded annually .
Options: a ) rs . 512 , b ) rs . 552 , c ) rs . 612 , d ) rs . 622 , e ) none
Rationale: "solution amount = rs [ 7500 x ( 1 + 4 / 100 ) ² ] = rs . ( 7500 x 26 / 25 x 26 / 25 ) = rs . 8112 . c . i = rs ( 8112 - 7500 ) = rs . 612 . answer c"
Answer: c
Problem: a number is 4 less than 6 times the other number . if the sum of both the number is 38 , what are the numbers ?
Options: a ) 632 , b ) 731 , c ) 533 , d ) 434 , e ) none of the above
Rationale: that numbers are x , 6 x - 4 so sum = x + 6 x - 4 = 38 7 x = 42 = = > x = 6 another no is 32 answer is 6 , 32 answer : a
Answer: a
Problem: two trains of length 250 m and 120 m are 50 m apart . they start moving towards each other on parallel tracks , at speeds 64 kmph and 42 kmph . after how much time will the trains meet ?
Options: a ) 15 / 10 , b ) 17 / 10 , c ) 16 / 10 , d ) 18 / 10 , e ) 16 / 10
Rationale: "they are moving in opposite directions , relative speed is equal to the sum of their speeds . relative speed = ( 64 + 42 ) * 5 / 18 = 7 * 5 = 29.4 mps . the time required = d / s = 50 / 29.4 = 17 / 10 sec . answer : b"
Answer: b
Problem: the area of sector of a circle whose radius is 12 metro and whose angle at the center is 38 ° is ?
Options: a ) 30 m 2 , b ) 40 m 2 , c ) 47.7 m 2 , d ) 50 m 2 , e ) 55 m 2
Rationale: "38 / 360 * 22 / 7 * 12 * 12 = 47.7 m 2 answer : c"
Answer: c
Problem: if the l . c . m of two numbers is 750 and their product is 18750 , find the h . c . f of the numbers .
Options: a ) 50 , b ) 30 , c ) 125 , d ) 25 , e ) none of these
Rationale: "h . c . f = ( product of the numbers ) / ( their l . c . m ) = 18750 / 750 = 25 . answer : d"
Answer: d
Problem: the population of a bacteria culture doubles every 2 minutes . approximately how many minutes will it take for the population to grow from 1,000 to 200,000 bacteria
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "the question basically asks how many minutes it takes for a population to increase by factor 200 ( 200,000 / 1,000 = 200 ) . now you know that every two minutes the population doubles , i . e . is multiplied by 2 . so the equation becomes : 2 ^ x > = 200 , where x represents the number of times the population doubles . a lot of people remember that 2 ^ 10 = 1,024 . hence , 2 ^ 8 = 256 , i . e . the population has to double 8 times . since it takes the population 2 minutes to double once it takes 8 * 2 minutes = 16 minutes to double 8 times . thus , solution d = 16 is correct ."
Answer: d
Problem: the marks obtained by polly and sandy are in the ratio 3 : 5 and those obtained by sandy and willy are in the ratio of 3 : 2 . the marks obtained by polly and willy are in the ratio of . . . ?
Options: a ) 3 : 4 , b ) 5 : 6 , c ) 7 : 8 , d ) 9 : 10 , e ) 11 : 12
Rationale: "polly : sandy = 3 : 5 = 9 : 15 sandy : willy = 3 : 2 = 15 : 10 polly : sandy : willy = 9 : 15 : 10 polly : willy = 9 : 10 the answer is d ."
Answer: d
Problem: if the largest 3 digit number is subtracted from the smallest 5 digit number , then the remainder is
Options: a ) 1 , b ) 9000 , c ) 9001 , d ) 90001 , e ) none
Rationale: solution required remainder = ( 10000 - 999 ) = 9001 answer c
Answer: c
Problem: x and y started a business investing rs . 50000 and rs 40000 respectively . in what ratio the profit earned after 2 years be divided between x and y respectively ?
Options: a ) 3 : 2 , b ) 9 : 2 , c ) 5 : 4 , d ) 1 : 4 , e ) 18 : 4
Rationale: x : y = 50000 : 40000 = 5 : 4 answer : c
Answer: c
Problem: a man can row downstream at 26 kmph and upstream at 10 kmph . find the speed of the man in still water and the speed of stream respectively ?
Options: a ) 2 , 9 , b ) 4 , 9 , c ) 8 , 9 , d ) 18 , 8 , e ) 7 , 9
Rationale: "let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 26 - - - ( 1 ) and x - y = 10 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 36 = > x = 18 , y = 8 . answer : d"
Answer: d
Problem: if log 1087.5 = 3.9421 , then the number of digits in ( 875 ) 10 is ?
Options: a ) 30 , b ) 28 , c ) 27 , d ) 50 , e ) 25
Rationale: "x = ( 875 ) 10 = ( 87.5 x 10 ) 10 therefore , log 10 x = 10 ( log 1087.5 + 1 ) = 10 ( 3.9421 + 1 ) = 10 ( 4.9421 ) = 49.421 x = antilog ( 49.421 ) therefore , number of digits in x = 50 . answer : d"
Answer: d
Problem: if $ 5,000 is invested in an account that earns 12 % interest compounded semi - annually , then the interest earned after one year would be how much greater than if the $ 5,000 had been invested at 8 % simple yearly interest ?
Options: a ) $ 4 , b ) $ 8 , c ) $ 12 , d ) $ 16 , e ) $ 432
Rationale: "solution amount ( ci ) = p + ( 1 + r / n ) ^ nt = 5000 + ( 1 + 0.12 / 2 ) ^ 2 = 5412 amount ( si ) = p + ptr / 100 = 5000 + ( 5000 * 1 * 12 / 100 ) = 5400 difference = 5412 - 5400 = 12 $ c"
Answer: c
Problem: the sides of a triangle are in the ratio 5 : 12 : 13 and its perimeter is 180 m , its area is ?
Options: a ) 90 , b ) 882 , c ) 277 , d ) 261 , e ) 281
Rationale: "5 x + 12 x + 13 x = 180 = > x = 6 a = 30 , b = 72 , c = 78 s = ( 30 + 72 + 78 ) / 2 = 90 answer : a"
Answer: a
Problem: if 2 ^ 4 , 2 ^ 3 , and 11 ^ 3 are factors of the product of 1,452 and w , where w is a positive integer , what is the smallest possible value of w ?
Options: a ) 176 , b ) 288 , c ) 363 , d ) 396 , e ) 484
Rationale: i will go with a ( pending elements to match is 2 ^ 2 * 2 ^ 2 * 11 ^ 1 = 176
Answer: a
Problem: what is the sum of 80 consecutive integers from - 39 inclusive , in a increasing order ?
Options: a ) - 29 , b ) 39 , c ) - 30 , d ) 40 , e ) 60
Rationale: "from - 39 to - 1 - - > 39 nos . zero - - > 1 number from + 1 to + 39 - - > 39 nos . when we add up nos . from - 39 to + 39 sum will be zero . total 79 nos will be added . 80 th number will be 40 . sum of these 80 nos . = 40 . d is the answer ."
Answer: d
Problem: the profit earned by selling an article for rs . 832 is equal to the loss incurred when the same article is sold for rs . 448 . what should be the sale price for making 70 % profit ?
Options: a ) 277 , b ) 1088 , c ) 277 , d ) 266 , e ) 121
Rationale: "let c . p . = rs . x . then , 832 - x = x - 448 2 x = 1280 = > x = 640 required s . p . = 170 % of rs . 640 = 170 / 100 * 640 = rs . 1088 . answer : b"
Answer: b
Problem: a man has some hens and cows . if the number of heads be 46 and the number of feet equals 136 , then the number of hens will be
Options: a ) 22 , b ) 24 , c ) 26 , d ) 20 , e ) 28
Rationale: "explanation : let number of hens = h and number of cows = c number of heads = 46 = > h + c = 46 - - - ( equation 1 ) number of feet = 136 = > 2 h + 4 c = 136 = > h + 2 c = 68 - - - ( equation 2 ) ( equation 2 ) - ( equation 1 ) gives 2 c - c = 68 - 46 = > c = 22 substituting the value of c in equation 1 , we get h + 22 = 46 = > h = 46 - 22 = 24 i . e . , number of hens = 24 answer : b"
Answer: b
Problem: find the smallest number which when divided by 13 and 17 leaves respective remainders of 3 and 7 .
Options: a ) 187 , b ) 211 , c ) 207 , d ) 219 , e ) 227
Rationale: "let ' n ' is the smallest number which divided by 13 and 17 leaves respective remainders of 3 and 7 . required number = ( lcm of 13 and 17 ) - ( common difference of divisors and remainders ) = ( 221 ) - ( 10 ) = 211 . answer : b"
Answer: b
Problem: a ' s speed is 20 / 13 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that b beats a by 25 % of the length of the race ?
Options: a ) 44 % , b ) 48 % , c ) 52 % , d ) 42 % , e ) 61 %
Rationale: "first calculate the distance , b has covered with his speed in the time , in which a reached 60 % of the race . then add the remaining distance as head start for b to win the race . its best to apply ratios concept here . since a ' s speed is 20 / 13 of b , therefore , b ' s speed is 13 / 20 of a distance covered by b = speed x time = ( 13 / 20 ) x ( 0.6 ) = 0.39 % ( which means b would have covered 0.39 of the race length during the time in which a has covered 0.6 of the race length . therefore to win , b needs a headstart of ( 1 - 0.39 = ) 0.61 of the race length . so the answer is e"
Answer: e