Cheukting/mathqa huggingface dataset:
Question (gain): a person buys an article at rs . 500 . at what price should he sell the article so as to make a profit of 30 % ?
Options: a ) 650 , b ) 882 , c ) 772 , d ) 652 , e ) 271
Rationale: "cost price = rs . 500 profit = 30 % of 500 = rs . 150 selling price = cost price + profit = 500 + 150 = 650 answer : a"
Answer: a
Question (general): if the sum and difference of two numbers are 20 and 8 respectively , then the difference of their square is :
Options: a ) 12 , b ) 28 , c ) 160 , d ) 180 , e ) 18
Rationale: "let the numbers be x and y . then , x + y = 20 and x - y = 8 x 2 - y 2 = ( x + y ) ( x - y ) = 20 * 8 = 160 . answer : c"
Answer: c
Question (physics): raja complete a journey in 10 hours . he travels first half of the journey at the rate of 21 km / hr and second half at the rate of 24 km / hr . find the total journey in km .
Options: a ) 200 km , b ) 250 km , c ) 224 km , d ) 255 km , e ) 260 km
Rationale: consider x - - > ( 1 / 2 ) x / 21 + ( 1 / 2 ) x / 24 = 10 = = > x / 21 + x / 24 = 20 15 x = 168 * 20 = = > 224 km answer c
Answer: c
Question (geometry): the percentage increase in the area of a rectangle , if each of its sides is increased by 20 % is :
Options: a ) 44 % , b ) 46 % , c ) 48 % , d ) 50 % , e ) 51 %
Rationale: "let original length = x metres and original breadth = y metres . original area = ( xy ) m 2 . new length = 120 x m = 6 x m . 100 5 new breadth = 120 y m = 6 y m . 100 5 new area = 6 x x 6 y m 2 = 36 xy m 2 . 5 5 25 the difference between the original area = xy and new - area 36 / 25 xy is = ( 36 / 25 ) xy - xy = xy ( 36 / 25 - 1 ) = xy ( 11 / 25 ) or ( 11 / 25 ) xy increase % = 11 xy x 1 x 100 % = 44 % . 25 xy a"
Answer: a
Question (physics): a person travels equal distances with speeds of 2 km / hr , 4 km / hr , 6 km / hr . and takes a total time of 11 minutes . find the total distance ?
Options: a ) 1 km , b ) 500 mts , c ) 600 mts , d ) 2 km , e ) 250 mts
Rationale: "let the each distance be x km total distance = 3 x then total time , ( x / 2 ) + ( x / 4 ) + ( x / 6 ) = 11 / 60 x = 0.2 total distance = 3 * 0.2 = 0.6 km = 600 meters correct option is c"
Answer: c
Question (geometry): the ratio of the radius of two circles is 1 : 9 , and then the ratio of their areas is ?
Options: a ) 1 : 8 , b ) 1 : 6 , c ) 1 : 9 , d ) 1 : 3 , e ) 1 : 81
Rationale: "r 1 : r 2 = 1 : 9 π r 12 : π r 22 r 12 : r 22 = 1 : 81 answer : e"
Answer: e
Question (general): the average salary of all the workers in a workshop is rs . 9000 . the average salary of 6 technicians is rs . 12000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is ?
Options: a ) a ) 23 , b ) b ) 21 , c ) c ) 52 , d ) d ) 56 , e ) e ) 12
Rationale: "let the total number of workers be x . then , 9000 x = ( 12000 * 6 ) + 6000 ( x - 6 ) = > 3000 x = 36000 = x = 12 . answer : e"
Answer: e
Question (gain): the first flight out of phoenix airport had a late departure . if the next 3 flights departed on - time , how many subsequent flights need to depart from phoenix on - time , for the airport ' s on - time departure rate to be higher than 60 % ? i will see what is the quickest way to solve it then i will provide the explanation
Options: a ) 6 , b ) 7 , c ) 9 , d ) 4 , e ) 11
Rationale: the following approach might be the easiest one and less error prone . we need on - time departure rate to be higher than 6 / 10 , so it should be at least 7 / 11 , which means that 7 out of 11 flights must depart on time . since for now 3 out of 4 flights departed on time then 7 - 3 = 4 subsequent flights need to depart on - time . answer : d
Answer: d
Question (other): 6 ) a marketing firm determined that , of 300 households surveyed , 80 used neither brand a nor brand b soap . 60 used only brand a soap and for every household that used both brands of soap , 3 used only brand b soap . how many of the 200 household surveyed used both brands of soap ?
Options: a ) a ) 15 , b ) b ) 20 , c ) c ) 30 , d ) d ) 40 , e ) e ) 45
Rationale: "220 = at least one of soap a or b both brands = x brand b = 3 x = > 60 + x + 3 x = 220 = > 4 x = 160 = > x = 40 answer - d"
Answer: d
Question (physics): tom , working alone , can paint a room in 6 hours . peter and john , working independently , can paint the same room in 3 hours and 8 hours , respectively . tom starts painting the room and works on his own for one hour . he is then joined by peter and they work together for an hour . finally , john joins them and the three of them work together to finish the room , each one working at his respective rate . what fraction of the whole job was done by peter ?
Options: a ) 7 / 15 , b ) 11 / 25 , c ) 17 / 35 , d ) 23 / 45 , e ) 27 / 55
Rationale: "tom paints 1 / 6 of the room in the first hour . tom and peter paint 1 / 6 + 1 / 3 = 1 / 2 of the room in the next hour for a total of 4 / 6 . the three people then paint the remaining 2 / 6 in a time of ( 2 / 6 ) / ( 15 / 24 ) = 8 / 15 hours peter worked for 23 / 15 hours so he painted 23 / 15 * 1 / 3 = 23 / 45 of the room . the answer is d ."
Answer: d
Question (geometry): a perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer . how many positive integers n are there such that n is less than 50,000 and at the same time n is a perfect square and a perfect cube ?
Options: a ) 3
b ) 4
c ) 5
d ) 6
e ) 7
Rationale: if n is a perfect square and a perfect cube , then n = a ^ 6 for some integer a . the numbers are 1 ^ 6 = 1 , 2 ^ 6 = 64 , 3 ^ 6 = 729 , 4 ^ 6 = 4096 , 5 ^ 6 = 15,625 , 6 ^ = 46,656 . the answer is d .
Answer: d
Question (gain): at joel ’ s bookstore , the current inventory is 40 % historical fiction . of the historical fiction books , 40 % are new releases , while 40 % of the other books are new releases . what fraction of all new releases are the historical fiction new releases ?
Options: a ) 4 / 25 , b ) 8 / 23 , c ) 2 / 5 , d ) 8 / 15 , e ) 2 / 5
Rationale: "let there be 100 books in all historic fiction books = 40 % of total = 40 other books = 60 new historic fiction = 40 % of 40 = 16 other new books = 40 % of 60 = 24 total new books = 24 + 16 = 40 fraction = 16 / 40 = 2 / 5 ans : e"
Answer: e
Question (general): the price of lunch for 15 people was $ 209.00 , including a 15 percent gratuity for service . what was the average price per person , excluding the gratuity ?
Options: a ) $ 11.73 , b ) $ 12.66 , c ) $ 13.80 , d ) $ 14.00 , e ) $ 15.87
Rationale: "take the initial price before the gratuity is 100 the gratuity is calculated on the final price , so as we assumed the final bill before adding gratuity is 100 so gratuity is 15 % of 100 is 15 so the total price of meals is 115 so the given amount i . e 209 is for 115 then we have to calculate for 100 for 115 209 for 100 x so by cross multiplication we get 115 x = 100 * 209 = > x = 100 * 209 / 110 by simplifying we get x as 190 which is the price of lunch before gratuity so the gratuity is 19 so as the question ask the average price person excluding gratuity is 190 / 15 = 12.66 so our answer is b )"
Answer: b
Question (general): the average of 50 numbers id 44 . if two numbers , namely 45 and 55 are discarded , the average of the remaining numbers is :
Options: a ) 22.35 , b ) 33.25 , c ) 22.25 , d ) 11.35 , e ) 43.75
Rationale: "explanation : total of 50 numbers = ( 50 × 44 ) = 2200 total of 48 numbers = ( 2200 - ( 45 + 55 ) ] = 2100 required average = 2100 / 48 = 43.75 answer : e"
Answer: e
Question (general): mike earns $ 14 per hour and phil earns $ 12 per hour . approximately how much less , as a percentage , does phil earn than mike per hour ?
Options: a ) 25 % , b ) 32.5 % , c ) 14 % , d ) 37.5 % , e ) 40 %
Rationale: "what % less of 14 is 12 let it be x % less , then = 14 ( 1 - x / 100 ) = 12 1 - x / 100 = 12 / 14 x = 100 / 7 x = 14 % ans c"
Answer: c
Question (general): what is the remainder when 45 * 49 is divided by 8 ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 5 , e ) 7
Rationale: "we can make use of the rule : remainder of { ( a * b ) / n } } = remainder of ( a / n ) * remainder of ( b / n ) here remainder of { 45 * 49 ) / 8 } } = remainder of ( 45 / 8 ) * remainder of ( 49 / 8 ) = 5 * 1 = 7 answer : d"
Answer: d
Question (general): 6 persons in an organization including a and b were to be divided in two groups of 3 members each . the total number of groups containing both a and b is what fraction of the total number of groups which can be formed ?
Options: a ) 3 / 10 , b ) 1 / 70 , c ) 3 / 14 , d ) 1 / 10 , e ) 11 / 14
Rationale: the fraction is nothing but the probability . . number to choose 3 out of 6 = 6 c 3 number to choose a and b and 2 from remaining 4 = 4 c 2 . . prob of a and b choosen = 4 c 2 / 6 c 3 = 3 / 10 answer : a
Answer: a
Question (gain): solution x is 80 % chemical a and 20 % chemical b by volume . solution y is 50 % chemical a and 50 % chemical b by volume . if a mixture of x and y is 68 % chemical a , what percent of the mixture is solution x ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 40 %
Rationale: "the volume of the mixture be x + y . 0.8 x + 0.5 y = 0.68 ( x + y ) 0.12 x = 0.18 y x = 3 y / 2 x / ( x + y ) = ( 3 y / 2 ) / ( 5 y / 2 ) = 3 / 5 = 40 % . the answer is e ."
Answer: e
Question (other): what number has a 5 : 1 ratio to the number 11 ?
Options: a ) 22 , b ) 50 , c ) 55 , d ) 52 , e ) 12
Rationale: "5 : 1 = x : 10 x = 55 answer : c"
Answer: c
Question (gain): in a class , if 50 % of the boys were girls , then there would be 50 % more girls than boys . what percentage of the overall class is girls ?
Options: a ) 25 % , b ) 33.33 % , c ) 40 % , d ) 20 % , e ) 10 %
Rationale: detailed solution for questions of this type , it is best to go from the final step . in the final state , the number of girls should be 1.5 * the number of boys . when 50 % of the boys are taken as girls , let the number of boys = x number of girls = 1.5 x total number of students = 2.5 x original number of boys = 2 x ( 50 % of boys = x ) original number of girls = 0.5 x girls form 20 % of the overall class . correct answer d .
Answer: d
Question (gain): a man can row downstream at the rate of 30 kmph and upstream at 10 kmph . find the man ’ s rate in still water and rate of current ?
Options: a ) 10 , b ) 8.0 , c ) 9.5 , d ) 9.0 , e ) 8.25
Rationale: "rate of still water = 1 / 2 ( down stream + upstream ) = 1 / 2 ( 30 + 10 ) = 20 kmph rate of current = 1 / 2 ( down stream - upstream ) = 1 / 2 ( 30 - 10 ) = 1 / 2 ( 20 ) = 10 kmph answer is a ."
Answer: a
Question (general): the cost of a one - family home was $ 120,000 in 1980 . in 1988 , the price had increased to $ 192,000 . what was the percent increase in the cost of the home ?
Options: a ) 60 % , b ) 50 % , c ) 55 % , d ) 40 % , e ) 33.3 %
Rationale: increase = 192000 - 120000 = 72000 % increase = 72000 * 100 / 120000 = 60 % answer : option a
Answer: a
Question (gain): a dishonest dealer professes to sell goods at the cost price but uses a weight of 900 grams per kg , what is his percent ?
Options: a ) 11.11 % , b ) 25 % , c ) 22 % , d ) 29 % , e ) 45 %
Rationale: "900 - - - 100 100 - - - ? = > 11.11 % answer : a"
Answer: a
Question (other): in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the sport formulation , the ratio of flavoring to corn syrup is three times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of the sport formulation contains 5 ounces of corn syrup , how many ounces of water does it contain ?
Options: a ) 45 , b ) 50 , c ) 55 , d ) 60 , e ) 75
Rationale: "f : c : w 1 : 12 : 30 sport version : f : c 3 : 12 f : w 1 : 60 or 3 : 180 so c : f : w = 12 : 3 : 180 c / w = 12 / 180 = 3 ounces / x ounces x = 5 * 180 / 12 = 75 ounces of water e"
Answer: e
Question (general): what is the value of x ^ 2 yz − xyz ^ 2 , if x = - 1 , y = 1 , and z = 3 ?
Options: a ) 20 , b ) 24 , c ) 30 , d ) 12 , e ) 48
Rationale: "1 * 1 * 3 - ( - 1 * 1 * 9 ) = 3 + 9 = 12 ans : d"
Answer: d
Question (general): a batsman in his 19 th inning makes a score of 100 and their by increasing his average by 2 . what is his average after the 19 th inning ?
Options: a ) 58 , b ) 60 , c ) 62 , d ) 64 , e ) 66
Rationale: "18 x + 100 = 19 ( x + 2 ) x = 62 + 2 = 64 answer : d"
Answer: d
Question (physics): b takes 12 more days than a to finish a task . b and a start this task and a leaves the task 12 days before the task is finished . b completes 60 % of the overall task . how long would b have taken to finish the task if he had worked independently ?
Options: a ) 48 days , b ) 36 days , c ) 28 days , d ) 32 days , e ) 22 days
Rationale: detailed solution let us say a and b split their share of the task and started doing their respective shares simultaneously . let ’ s say a takes a days to finish the task . therefore , b takes a + 12 days to finish the entire task . a has to finish 40 % of the task , since b is doing the rest . so a will only take 2 a / 5 number of days . b only has to finish 60 % of the task , so b will take ( 3 ( a + 12 ) / 5 ) number of days . but as we know , b starts working along with a and finishes 12 days after a stops working . so , ( 3 ( a + 12 ) / 5 ) = ( ( 2 a ) / 5 + 12 ) 3 a + 36 = 2 a + 60 a = 24 ; b = 36 days . answer choice b
Answer: b
Question (physics): a train 100 m long is running with a speed of 68 kmph . in what time will it pass a man who is running at 8 kmph in the same direction in which the train is going ?
Options: a ) 6 sec . , b ) 7 sec . , c ) 9 sec . , d ) 11 sec . , e ) none
Rationale: "solution speed of the train relative to man = ( 68 - 8 ) = 60 kmph = 60 x 5 / 18 = 50 / 3 m / sec . time taken by it to cover 100 m at ( 50 / 3 ) m / sec = ( 100 x 3 / 50 ) sec = 6 sec . answer a"
Answer: a
Question (physics): with a uniform speed a car covers the distance in 8 hours . had the speed been increased by 4 km / hr , the same distance could have been covered in 7 1 / 2 hours . what is the distance covered ?
Options: a ) 347 , b ) 480 , c ) 288 , d ) 278 , e ) 131
Rationale: "let the distance be x km . then , x / ( 7 1 / 2 ) - x / 8 = 4 2 x / 15 - x / 8 = 4 = > x = 480 km . answer : b"
Answer: b
Question (gain): an error 19 % in excess is made while measuring the side of a square . now what is the percentage of error in the calculated area of the square ?
Options: a ) 6.64 % , b ) 41.61 % , c ) 45.64 % , d ) 46.64 % , e ) 10.64 %
Rationale: "percentage error in calculated area = ( 19 + 19 + ( 19 ã — 19 ) / 100 ) % = 41.61 % answer : b"
Answer: b
Question (gain): in the first 20 overs of a cricket game , the run rate was only 4.2 . what should be the run rate in the remaining 30 overs to reach the target of 324 runs ?
Options: a ) 7.25 , b ) 8.5 , c ) 8 , d ) 9.15 , e ) 10
Rationale: "explanation : required run rate = ( 324 - 4.2 20 ) = 240 / 30 = 8 . answer : c"
Answer: c
Question (general): x and y are integers . a + b < 11 , and a > 6 . what is the smallest possible value of a - b ?
Options: a ) 1 , b ) 2 , c ) 4 , d ) - 2 , e ) - 4
Rationale: focus on the transition points and plug in the values . a > 6 so a could be 7 , 8 , 9 , 10 , 11 etc look at a = 7 7 + b < 11 b < 4 b could be 3 , 2 , 1 , 0 , - 1 etc when b is 3 , we get a - b = 4 this must be the smallest value because as a increases , b reduces so a - b increases . take another example . a = 11 so b < 0 . a - b will give a value greater than 11 . answer ( c ) .
Answer: c
Question (physics): a mobile battery in 1 hour charges to 20 percent . how much time ( in minute ) will it require more to charge to 65 percent .
Options: a ) 145 , b ) 150 , c ) 195 , d ) 160 , e ) 130
Rationale: 1 hr = 20 percent . thus 15 min = 5 percent . now to charge 65 percent 195 min . answer : c
Answer: c
Question (general): if x is the product of the positive integers from 1 to 8 , inclusive , and if i , k , m , and p are positive integers such that x = 2 ^ i * 3 ^ k * 5 ^ m * 7 ^ p , then i + k + m + p =
Options: a ) 4 , b ) 7 , c ) 8 , d ) 11 , e ) 12
Rationale: given that x = 8 ! = 2 ^ 7 ∗ 3 ^ 2 ∗ 5 ∗ 7 x . hence , x = 2 ^ 7 ∗ 3 ^ 2 ∗ 5 ^ 1 ∗ 7 ^ 1 = 2 ^ i ∗ 3 ^ k ∗ 5 ^ m ∗ 7 p , since i , k , m , and p are positive integers , then we can equate the exponents , so we have that i = 7 , k = 2 , m = 1 , and p = 1 therefore , i + k + m + p = 7 + 2 + 1 + 1 = 11 answer : d .
Answer: d
Question (geometry): find the base k of the number system , if ( 524 ) 8 = ( 664 ) k ?
Options: a ) 4
b ) 5
c ) 6
d ) 7
e ) 8
Rationale: 5 * 8 ^ 2 + 2 * 8 ^ 1 + 4 * 8 ^ 0 = 6 * k ^ 2 + 6 * k ^ 1 + 4 * k ^ 0 320 + 16 + 4 = 6 ( k ^ 2 ) + 6 k + 4 340 = 6 ( k ^ 2 ) + 6 k + 4 6 ( k ^ 2 ) + 6 k + 4 - 340 = 0 6 ( k ^ 2 ) + 6 k - 336 = 0 dividing by 6 ; ( k ^ 2 ) + k - 56 = 0 solving this quadratic equation we get , k = 7 and k = - 8 thus k = 7 answer : d
Answer: d
Question (general): if n is the greatest number that will divide 1305 , 4665 and 6905 , leaving the same remainder in each case . what is the sum of the digits of n ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 4
Rationale: n = h . c . f . of ( 4665 - 1305 ) , ( 6905 - 4665 ) and ( 6905 - 1305 ) = h . c . f . of 3360 , 2240 and 5600 = 1120 . sum of digits in n = ( 1 + 1 + 2 + 0 ) = 4 answer : e
Answer: e
Question (geometry): an area of a circularplace is 17 hectares . find the cost of fencing it at the rate of rs . 3 permeter approximately .
Options: a ) rs . 4000
b ) rs . 4450
c ) rs . 4457
d ) rs . 4560
e ) rs . 5457
Rationale: area = ( 17.56 x 10000 ) m 2 = 175600 m 2 . π r 2 = 175600 ⇔ ( r ) 2 = ( 175600 x ( 7 / 22 ) ) ⇔ r = 236.37 m . circumference = 2 π r = ( 2 x ( 22 / 7 ) x 236.37 ) m = 1485.78 m . cost of fencing = rs . ( 1485.78 x 3 ) = rs . 4457 . c
Answer: c
Question (general): having received his weekly allowance , john spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 0.90 at the candy store . what is john ’ s weekly allowance ?
Options: a ) $ 2.40 , b ) $ 3.00 , c ) $ 3.40 , d ) $ 3.60 , e ) $ 4.80
Rationale: "total allowance = x amount spent at the arcade = 3 / 5 x amount remaining = 2 / 5 x amount spent at the toy store = 2 / 5 * 1 / 3 x = 2 / 15 x amount remaining = 2 / 5 x - 2 / 15 x = 4 / 15 x now , 4 / 15 x = $ 0.9 therefore , x = $ 3.40 . answer c"
Answer: c
Question (physics): if a tire rotates at 400 revolutions per minute when the car is traveling 96 km / h , what is the circumference of the tire ?
Options: a ) 7 meters , b ) 9 meters , c ) 4 meters , d ) 5 meters , e ) 3 meters
Rationale: "400 rev / minute = 400 * 60 rev / 60 minutes = 24,000 rev / hour 24,000 * c = 96,000 m : c is the circumference c = 4 meters correct answer c"
Answer: c
Question (general): a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 68 % of the distribution lies one standard deviation f of the mean , what percent of the distribution is less than m + f ?
Options: a ) 16 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 %
Rationale: "16 % ________________________________________________ m + f 34 % ________________________________________________ m 34 % ________________________________________________ m - f 16 % since 68 % lies one standard deviation from mean m , = > 50 % of 68 % lies on either side as it is symmetric about m . thus 16 % lie below m - f and 16 % lie above m + f now below m + f = 16 + 34 + 34 = 84 % hence d"
Answer: d
Question (general): the result when a number subtracted from 100 is the same as the number added to 40 . what is the number ?
Options: a ) 70 , b ) 65 , c ) 80 , d ) 140 , e ) 60
Rationale: "answer let the number be x . then , x - 40 = 100 - x â ‡ ’ 2 x = 100 + 40 = 140 â ‡ ’ 2 x = 140 â ˆ ´ x = 70 correct option : a"
Answer: a
Question (general): if a / b = 6 / 5 , then ( 5 a + 4 b ) / ( 5 a - 4 b ) = ?
Options: a ) 4 , b ) 7 , c ) 5 , d ) 3 , e ) 6
Rationale: "answer dividing numerator as well as denominator by b , we get given exp . = ( 5 a + 4 b ) / ( 5 a - 4 b ) = ( 5 a / b + 4 ) / ( 5 a / b - 4 ) since a / b = 6 / 5 this implies that = [ ( 5 * 6 ) / 5 + 4 ] / [ ( 5 * 6 ) / 5 - 4 ) ] = ( 6 + 4 ) / ( 6 - 4 ) = 5 option : c"
Answer: c
Question (general): running at their respective constant rate , machine x takes 2 days longer to produce w widgets than machines y . at these rates , if the two machines together produce 5 w / 4 widgets in 3 days , how many days would it take machine x alone to produce 1 w widgets .
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: "i am getting 12 . e . hope havent done any calculation errors . . approach . . let y = no . of days taken by y to do w widgets . then x will take y + 2 days . 1 / ( y + 2 ) + 1 / y = 5 / 12 ( 5 / 12 is because ( 5 / 4 ) w widgets are done in 3 days . so , x widgets will be done in 12 / 5 days or 5 / 12 th of a widget in a day ) solving , we have y = 4 = > x takes 6 days to doing x widgets . answer : b"
Answer: b
Question (general): if the number 761 * 829 is completely divisible by 9 , then the smallest whole number in place of * will b
Options: a ) 4 , b ) 5 , c ) 3 , d ) 8 , e ) 9
Rationale: sum of digits = ( 7 + 6 + 1 + x + 8 + 2 + 9 ) = ( 33 + x ) , which must be divisible by 9 . x = 3 . c )
Answer: c
Question (other): teas worth rs . 126 per kg and rs . 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs 157 per kg , the price of the third variety per kg will be ?
Options: a ) rs . 147.50 , b ) rs . 785.50 , c ) rs . 179.50 , d ) rs . 258.50 , e ) none of these
Rationale: explanation : since first and second varieties are mixed in equal proportions . so , their average price = rs . ( 126 + 135 ) / 2 . = > rs . 130.50 . so , the mixture is formed by mixing two varieties , one at rs . 130.50 per kg and the other at say , rs . x per kg in the ratio 2 : 2 , i . e . , 1 : 1 . we have to find x . by the rule of alligation , we have : cost of 1 kg cost of 1 kg of 1 st kind of 2 nd kind ( rs . 130.50 ) ( rs . x ) \ / mean price ( rs . 157 ) / \ x â ˆ ’ 157 22.50 = > x â ˆ ’ ( 157 / 22.50 ) = 1 . = > x â ˆ ’ 157 = 22.50 . = > x = 179.50 rs . answer : c
Answer: c
Question (other): the sub - duplicate ratio of 9 : 25 is
Options: a ) 4 : 3 , b ) 1 : 2 , c ) 3 : 5 , d ) 1 : 4 , e ) 2 : 3
Rationale: root ( 9 ) : root ( 25 ) = 3 : 5 answer : c
Answer: c
Question (general): sushil got thrice as many marks in english as in science . his total marks in english , science and maths are 162 . if the ratio of his marks in english and maths is 3 : 5 , find his marks in science ?
Options: a ) 18 , b ) 68 , c ) 67 , d ) 55 , e ) 56
Rationale: "s : e = 1 : 3 e : m = 3 : 5 - - - - - - - - - - - - s : e : m = 3 : 9 : 15 3 / 27 * 162 = 18 answer : a"
Answer: a
Question (physics): a train moves past a post and a platform 264 m long in 8 seconds and 20 seconds respectively . what is the speed of the train ?
Options: a ) 79.2 km / hr , b ) 69 km / hr , c ) 74 km / hr , d ) 61 km / hr , e ) none of these
Rationale: let x is the length of the train and v is the speed time taken to move the post = 8 s = > x / v = 8 = > x = 8 v - - - ( 1 ) time taken to cross the platform 264 m long = 20 s ( x + 264 ) / v = 20 = > x + 264 = 20 v - - - ( 2 ) substituting equation 1 in equation 2 , we get 8 v + 264 = 20 v = > v = 264 / 12 = 22 m / s = 22 × 36 / 10 km / hr = 79.2 km / hr answer : b
Answer: b
Question (general): of 120 applicants for a job , 56 had at least 4 years ' experience , 72 had degrees , and 12 had less than 4 years ' experience and did not have a degree . how many of the applicants had at least 4 years ' experience and a degree ?
Options: a ) 10 , b ) 15 , c ) 22 , d ) 20 , e ) 24
Rationale: "120 - 12 = 108 108 - 56 - 72 = - 20 then 20 are in the intersection between 4 years experience and degree . answer : d"
Answer: d
Question (gain): a started a business with an investment of rs . 70000 and after 6 months b joined him investing rs . 120000 . if the profit at the end of a year is rs . 39000 , then the share of b is ?
Options: a ) a ) 34500 , b ) b ) 24000 , c ) c ) 24098 , d ) d ) 19007 , e ) e ) 18000
Rationale: "ratio of investments of a and b is ( 70000 * 12 ) : ( 120000 * 6 ) = 7 : 6 total profit = rs . 39000 share of b = 6 / 13 ( 39000 ) = rs . 18000 answer : e"
Answer: e