Cheukting/mathqa huggingface dataset:
Question (probability): three 6 faced dice are thrown together . the probability that all the three show the same number on them is -
Options: a ) 1 / 39 , b ) 1 / 36 , c ) 1 / 32 , d ) 1 / 31 , e ) 1 / 30
Rationale: "explanation : it all 3 numbers have to be same basically we want triplets . 111 , 222 , 333 , 444 , 555 and 666 . those are six in number . further the three dice can fall in 6 * 6 * 6 = 216 ways . hence the probability is 6 / 216 = 1 / 36 answer : b"
Answer: b
Question (physics): how many bricks , each measuring 5 cm x 11 cm x 6 cm , will be needed to build a wall of 8 m x 6 m x 2 cm ?
Options: a ) 5600 , b ) 6000 , c ) 2909 , d ) 7200 , e ) 8600
Rationale: "number of bricks = volume of the wall / volume of 1 brick = ( 800 x 600 x 2 ) / ( 5 x 11 x 6 ) = 2909 . answer : option c"
Answer: c
Question (physics): a can do a piece of work in 7 days and b can do it in 6 days how long will they both work together to complete the work ?
Options: a ) 6 / 11 , b ) 8 / 13 , c ) 3 / 13 , d ) 9 / 11 , e ) 10 / 13
Rationale: "explanation : a ’ s one day work = 1 / 5 b ’ s one day work = 1 / 6 ( a + b ) ’ s one day work = 1 / 7 + 1 / 6 = 13 / 42 = > time = 42 / 13 = 3 3 / 13 days answer : option c"
Answer: c
Question (general): 60 % of the population of a village is 23040 . the total population of the village is ?
Options: a ) 38400 , b ) 24000 , c ) 24936 , d ) 25640 , e ) none
Rationale: answer ∵ 60 % of p = 23040 ∴ p = ( 23040 x 100 ) / 60 = 38400 correct option : a
Answer: a
Question (general): when positive integer x is divided by positive integer y , the remainder is 9 . if x / y = 96.25 , what is the value of y ?
Options: a ) 96 , b ) 75 , c ) 36 , d ) 25 , e ) 12
Rationale: "guys , one more simple funda . 5 / 2 = 2.5 now . 5 x 2 = 1 is the remainder 25 / 4 = 6.25 now . 25 x 4 = 1 is the remainder 32 / 5 = 6.4 now . 4 x 5 = 2 is the remainder given x / y = 96.25 and remainder is 9 so . 25 x y = 9 hence y = 36 ans c"
Answer: c
Question (general): what least number should be subtracted from 13605 such that the remainder is divisible by 87 ?
Options: a ) 27 , b ) 29 , c ) 28 , d ) 30 , e ) 33
Rationale: 13605 ÷ 87 = 156 , remainder = 33 hence 33 is the least number which can be subtracted from 13605 such that the remainder is divisible by 87 answer is e
Answer: e
Question (general): 378 × ? = 252
Options: a ) 2 / 3 , b ) 3 / 4 , c ) 1 / 2 , d ) 2 / 8 , e ) none of these
Rationale: "explanation : 378 × ? = 252 ? = 252 / 378 = 126 / 189 = 14 / 21 = 2 / 3 answer is a"
Answer: a
Question (general): the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 20 kg . what is the weight of the new person ?
Options: a ) 75 , b ) 65 , c ) 85 , d ) 40 , e ) 80
Rationale: total increase in weight = 8 × 2.5 = 20 if x is the weight of the new person , total increase in weight = x − 20 = > 20 = x - 20 = > x = 20 + 20 = 40 answer is d .
Answer: d
Question (physics): liam is pulled over for speeding just as he is arriving at work . he explains to the police officer that he could not afford to be late today , and has arrived at work only four minutes before he is to start . the officer explains that if liam had driven 5 mph slower for his whole commute , he would have arrived at work exactly on time . if liam ' s commute is 20 miles long , how fast was he actually driving ? ( assume that liam drove at a constant speed for the duration of his commute . )
Options: a ) 50 mph , b ) 45 mph , c ) 48 mph , d ) 52 mph , e ) 40 mph
Rationale: "let t be the number of hours he would need to reach office on time . when he is driving with over speed , he reached office 4 min earlier ! so the equation for this is s ( t - 4 / 60 ) = 20 where s is the speed and 20 is the distance . if he decreases his speed by 5 mph then he would have reached his office on time : ( s - 5 ) t = 20 if you solve above equations , you will arrive at t = 2 / 3 hr and s = 40 mph therefore answer is e"
Answer: e
Question (general): rs . 1690 is divided so that 4 times the first share , thrice the 2 nd share and twice the third share amount to the same . what is the value of the third share ?
Options: a ) s . 528 , b ) s . 542 , c ) s . 780 , d ) s . 540 , e ) s . 549
Rationale: "a + b + c = 1690 4 a = 3 b = 2 c = x a : b : c = 1 / 4 : 1 / 3 : 1 / 2 = 3 : 4 : 6 6 / 13 * 1690 = rs . 780 answer : c"
Answer: c
Question (general): if 41 / 88 = 0.46590 , what is the 77 th digit to the right of the decimal point of the fraction ?
Options: a ) 6 , b ) 2 , c ) 5 , d ) 0 , e ) 9
Rationale: "we are not concerned what 41 / 88 means . . we have to look at the decimal . . 0.6590 means 0.465909090 . . . . so leaving girst , second and third digit to the right of decimal , all odd numbered are 0 and all even numbered are 9 . . here 77 is odd , so ans is 0 answer is d"
Answer: d
Question (physics): a train running at the speed of 100 km / hr crosses a pole in 18 seconds . what is the length of the train ?
Options: a ) 300 , b ) 400 , c ) 500 , d ) 600 , e ) 700
Rationale: speed = ( 100 * 5 / 18 ) m / sec = ( 250 / 9 ) m / sec length of the train = ( speed x time ) = ( 250 / 9 * 18 ) m = 500 m . answer : c
Answer: c
Question (general): there has been successive increases of 15 % and then 10 % in the price of gas from the previous month . by what percentage should a driver reduce gas consumption so that the expenditure does not change ?
Options: a ) 12 % , b ) 15 % , c ) 18 % , d ) 21 % , e ) 24 %
Rationale: "let p be the original price per unit of gas . let x be the original gas consumption . let y be the reduced gas consumption . y * 1.1 * 1.15 * p = x * p y = x / ( 1.1 * 1.15 ) which is about 0.79 x which is a decrease of about 21 % . the answer is d ."
Answer: d
Question (gain): two numbers are less than a third number by 30 % and 37 % . how much percent is the second number is less than the first ?
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 30 %
Rationale: let the third number be x first number = 70 % of x = 7 x / 10 ; second number = 63 % of x = 63 x / 100 ; difference = 7 x / 10 - 63 x / 100 = 7 x / 100 ; required percentage = 7 x / 100 * 10 / 7 x * 100 = 10 % answer is a
Answer: a
Question (gain): there are 300 seniors at morse high school , and 40 % of them have cars . of the remaining grades ( freshmen , sophomores , and juniors ) , only 10 % of them have cars . if 15 % of all the students at morse have cars , how many students are in those other 3 lower grades ?
Options: a ) 600 , b ) 900 , c ) 1200 , d ) 1350 , e ) 1500
Rationale: let the total no of students be n . the no of seniors having cars is 40 % of 300 i . e . 120 . the rest of the students with other three grades who have cars is 10 % of ( n - 300 ) . the total no of students with cars is 15 % of n . thus , 0.15 n = 120 + 0.1 ( n - 300 ) on solving this , we get n = 1800 . hence , the no of students with other three grades is 1800 - 300 , i . e . 1500 ( e ) .
Answer: e
Question (physics): in an examination , a student scores 6 marks for every correct answer and loses 1 mark for every wrong answer . if he attempts all 60 questions and secures 280 marks , the no of questions he attempts correctly is :
Options: a ) a ) 20 , b ) b ) 38 , c ) c ) 90 , d ) d ) 88 , e ) e ) 37
Rationale: "let the number of correct answers be x . number of incorrect answers = ( 60 – x ) . 6 x – ( 60 – x ) = 280 = > 7 x = 340 = > x = 20 answer : a"
Answer: a
Question (geometry): a box measuring 90 inches long by 45 inches wide by 9 inches deep is to be filled entirely with identical cubes . no space is to be left unfilled . what is the smallest number of cubes that can accomplish this objective ?
Options: a ) 17 , b ) 18 , c ) 50 , d ) 108 , e ) 864
Rationale: "least number of cubes will be required when the cubes that could fit in are biggest . 9 is the biggest number that could divide all three , 90 , 45 and 9 . thus side of cube must be 9 , and total number of cubes = 90 / 9 * 45 / 9 * 9 / 9 = 50 ans c it is ."
Answer: c
Question (general): you collect baseball cards . suppose you start out with 11 . maria takes half of one more than the number of baseball cards you have . since you ' re nice , you give peter 1 baseball card . since his father makes baseball cards , paul decides to triple your baseball cards . how many baseball cards do you have at the end ?
Options: a ) 12 , b ) 18 , c ) 19 , d ) 20 , e ) 21
Rationale: "solution start with 11 baseball cards . maria takes half of one more than the number of baseball cards you have . so maria takes half of 11 + 1 which is 6 , so you ' re left with 11 - 6 = 5 . peter takes 1 baseball card from you : 5 - 1 = 4 baseball cards . paul triples the number of baseball cards you have : 4 ã — 3 = 12 baseball cards . so you have 12 at the end . correct answer : a"
Answer: a
Question (physics): a bullet train 130 m long is running with a speed of 50 kmph . in what time will it pass a man who is running at 10 kmph in the direction opposite to that in which the bullet train is going ?
Options: a ) 23 sec , b ) 13 sec , c ) 12 sec , d ) 11 sec , e ) 16 sec
Rationale: "b 13 sec speed of the bullet train relative to man = ( 50 + 10 ) kmph = 60 * 5 / 18 m / sec = 30 / 3 m / sec . time taken by the bullet train to cross the man = time taken by it to cover 130 m at ( 30 / 3 ) m / sec = ( 130 * 3 / 30 ) sec = 13 sec"
Answer: b
Question (general): find the smallest number of five digits exactly divisible by 22 , 33,66 and 44 .
Options: a ) 10101 , b ) 11000 , c ) 10110 , d ) 10111 , e ) 10100
Rationale: "smallest number of five digits is 10000 . required number must be divisible by l . c . m . of 22,33 , 66,44 i . e 132 , on dividing 10000 by 132 , we get 32 as remainder . therefore , required number = 10000 + ( 132 â € “ 32 ) = 10100 . answer is e ."
Answer: e
Question (physics): a man walking at a constant rate of 5 miles per hour is passed by a woman traveling in the same direction along the same path at a constant rate of 25 miles per hour . the woman stops to wait for the man 5 minutes after passing him , while the man continues to walk at his constant rate . how many minutes must the woman wait until the man catches up ?
Options: a ) 16 , b ) 20 , c ) 24 , d ) 25 , e ) 28
Rationale: "when the woman passes the man , they are aligned ( m and w ) . they are moving in the same direction . after 5 minutes , the woman ( w ) will be ahead the man ( m ) : m - - - - - - m - - - - - - - - - - - - - - - w w in the 5 minutes , after passing the man , the woman walks the distance mw = ww , which is 5 * 25 / 60 = 25 / 12 miles and the man walks the distance mm , which is 5 * 5 / 60 = 5 / 12 mile . the difference of 25 / 12 - 5 / 12 = 1 / 3 miles ( mw ) will be covered by the man in ( 4 / 3 ) / 4 = 1 / 3 of an hour , which is 20 minutes . answer b ."
Answer: b
Question (general): the ages of two persons differ by 20 years . if 5 years ago , the elder one be 5 times as old as the younger one , their present ages ( in years ) are respectively
Options: a ) 20,20 , b ) 20,10 , c ) 25,15 , d ) 30,10 , e ) none of these
Rationale: explanation : let their ages be x and ( x + 20 ) years . 5 ( x - 5 ) = ( x + 20 - 5 ) or 4 x = 40 or x = 10 . their present ages are 30 years and 10 years option d
Answer: d
Question (general): p and q are the only two applicants qualified for a short - term research project that pays 300 dollars in total . candidate p has more experience and , if hired , would be paid 50 percent more per hour than candidate q would be paid . candidate q , if hired , would require 10 hours more than candidate p to do the job . candidate p ’ s hourly wage is how many dollars greater than candidate q ’ s hourly wage ?
Options: a ) $ 5 , b ) $ 10 , c ) $ 15 , d ) $ 20 , e ) $ 25
Rationale: "let q ' s hourly wage be x , then p ' s hourly wage is 1.5 x let t be the number of hours that q needs , then p needs t - 10 hours to do the job . since they both are paid an equal total amount of $ 300 : x * t = 1.5 x * ( t - 10 ) t = 30 hours and q ' s hourly wage is 300 / 30 = $ 10 p ' s hourly wage is 300 / ( t - 10 ) = $ 15 which is $ 5 per hour more . the answer is a ."
Answer: a
Question (geometry): the average length of the sides of triangle abc is 12 . what is the perimeter of triangle abc ?
Options: a ) 4
b ) 6
c ) 12
d ) 24
e ) 36
Rationale: ( average ) = ( perimeter ) / 3 ; 12 = ( perimeter ) / 3 ; ( perimeter ) = 36 . answer : e .
Answer: e
Question (gain): a retailer buys 140 pens at the market price of 36 pens from a wholesaler , if he sells these pens giving a discount of 1 % , what is the profit % ?
Options: a ) 105 , b ) 155 , c ) 125 , d ) 185 , e ) 285
Rationale: "let the market price of each pen be $ 1 then , cost price of 140 pens = $ 36 selling price of 140 pens = 99 % of $ 140 = $ 138.60 profit % = ( ( 102.60 * 100 ) / 36 ) % = 285 % answer e"
Answer: e
Question (general): if 3 log ( 4 * 5 ^ 2 ) = x , find x
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "3 ( log 2 ^ 2 * 5 ^ 2 ) = x 3 log ( 5 * 2 ) ^ 2 = x 3 * 2 log ( 5 * 2 ) = x 6 log 10 = x log 10 base 10 = 1 so 6 * 1 = x x = 6 answer : b"
Answer: b
Question (physics): two trains of equal lengths take 10 sec and 18 sec respectively to cross a telegraph post . if the length of each train be 120 m , in what time will they cross other travelling in opposite direction ?
Options: a ) 11 , b ) 9 , c ) 13 , d ) 14 , e ) 12.8
Rationale: "speed of the first train = 120 / 10 = 12 m / sec . speed of the second train = 120 / 18 = 6.7 m / sec . relative speed = 12 + 6.7 = 18.7 m / sec . required time = ( 120 + 120 ) / 18.7 = 12.8 sec . answer : option e"
Answer: e
Question (general): if one - third of one fourth of a number is 15 , then 3 - tenth of that number is :
Options: a ) 35 , b ) 25 , c ) 45 , d ) 54 , e ) 52
Rationale: let the number be x . then , 1 / 3 of 1 / 4 of x = 15 x = 15 * 12 = 180 so , required number = ( 3 / 10 * 180 ) = 54 . answer : d
Answer: d
Question (physics): r is the set of positive even integers less than 201 , and s is the set of the squares of the integers in r . how many elements does the intersection of r and s contain ?
Options: a ) none , b ) two , c ) four , d ) five , e ) seven
Rationale: "r is the set of positive even integers less than 201 , and s is the set of the squares of the integers in r . how many elements does the intersection of r and s contain ? r = 2,4 , 6,8 , 10,12 . . . s = 4,16 , 36,64 . . . numbers : 4 , 16 , 36 , 64 , 100 , 144 , and 196 are even integers ( less than 201 ) that are in both sets . solution : seven answer : e"
Answer: e
Question (general): on dividing a number by 7 , we get 3 as quotient and 0 as remainder . on dividing the same number by 3 , what will be the remainder ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 0 , e ) 4
Rationale: "number = 7 * 3 + 0 = 21 3 ) 21 ( 7 21 - - - - - - - - 0 required number = 0 . answer : d"
Answer: d
Question (general): the unit digit in the product ( 722 * 774 * 889 * 223 ) is :
Options: a ) 2 , b ) 7 , c ) 6 , d ) 8 , e ) 1
Rationale: "explanation : unit digit in the given product = unit digit in ( 2 * 4 * 9 * 3 ) = 6 answer : c"
Answer: c
Question (gain): a and b invests rs . 3000 and rs . 7000 respectively in a business . if a doubles his capital after 6 months . in what ratio should a and b divide that year ' s profit ?
Options: a ) 9 : 6 , b ) 9 : 8 , c ) 9 : 14 , d ) 9 : 9 , e ) 9 : 5
Rationale: "( 3 * 6 + 6 * 6 ) : ( 7 * 12 ) 54 : 84 = > 9 : 14 . answer : c"
Answer: c
Question (geometry): cubes with each side one inch long are glued together to form a larger cube . the larger cube ' s face is painted with red color and the entire assembly is taken apart . 23 small cubes are found with no paints on them . how many of unit cubes have at least one face that is painted red ?
Options: a ) 64
b ) 72
c ) 86
d ) 98
e ) 102
Rationale: use the options . the options which after getting added to 23 shows a cube of a number could be right . here 64 + 23 = 87 72 + 23 = 95 86 + 23 = 109 98 + 23 = 121 102 + 23 = 125 - - - ( 5 * 5 * 5 ) so we have 102 as the answer ! e
Answer: e
Question (geometry): what is the % change in the area of a rectangle when its length increases by 25 % and its width decreases by 25 % ?
Options: a ) 0 % , b ) 20 % increase , c ) 20 % decrease , d ) 6 % decrease , e ) insufficient data
Rationale: "( 125 / 10 ) * ( 75 / 10 ) = 9375 / 100 ~ 94 of original area 0.94 is a 6 % decrease from 100 / 100 - > d"
Answer: d
Question (other): bag a contains red , white and blue marbles such that the red to white marble ratio is 1 : 3 and the white to blue marble ratio is 2 : 3 . bag b contains red and white marbles in the ratio of 1 : 4 . together , the two bags contain 70 white marbles . how many red marbles could be in bag a ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 6 , e ) 14
Rationale: "6 is the answer . bag a - r : w : b = 2 : 6 : 9 let w in bag a be 6 k bab b - r : w = 1 : 4 let w in bag b be 4 k w = 70 = 6 k + 4 k = > k = 7 total red ' s in bag a will be 2 k = 14 e"
Answer: e
Question (general): sandy gets 3 marks for each correct sum and loses 2 marks for each incorrect sum . sandy attempts 30 sums and obtains 60 marks . how many sums did sandy get correct ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 24 , e ) 26
Rationale: "let x be the correct sums and ( 30 - x ) be the incorrect sums . 3 x - 2 ( 30 - x ) = 60 5 x = 120 x = 24 the answer is d ."
Answer: d
Question (gain): a car dealership has 40 cars on the lot , 20 % of which are silver . if the dealership receives a new shipment of 80 cars , 35 % of which are not silver , what percentage of total number of cars are silver ?
Options: a ) 30 % , b ) 35 % , c ) 40 % , d ) 45 % , e ) 50 %
Rationale: "the number of silver cars is 0.2 * 40 + 0.35 * 80 = 36 the percentage of cars which are silver is 36 / 120 = 30 % the answer is a ."
Answer: a
Question (general): at a certain company , each employee has a salary grade s that is at least 1 and at most 5 . each employee receives an hourly wage p , in dollars , determined by the formula p = 9.50 + 0.25 ( s – 1 ) . an employee with a salary grade of 5 receives how many more dollars per hour than an employee with a salary grade of 2 ?
Options: a ) $ 0.50 , b ) $ 0.75 , c ) $ 1.25 , d ) $ 1.50 , e ) $ 1.75
Rationale: "salary grade of 5 is p ( 5 ) = 9.50 + 0.25 ( 5 – 1 ) = 9.50 + 0.25 * 4 ; salary grade of 2 is p ( 2 ) = 9.50 + 0.25 ( 2 – 1 ) = 9.50 + 0.25 ; p ( 5 ) - p ( 2 ) = 9.50 + 0.25 * 4 - 9.50 - 0.25 = 0.75 . answer : b ."
Answer: b
Question (general): what is the product of all the possible values of x if x ^ 2 - 2 x - 8 ?
Options: a ) – 29 , b ) – 12 , c ) - 8 , d ) 29 , e ) 168
Rationale: "explanation : = > y = x ^ 2 - 2 x - 8 = > y = ( x + 2 ) ( x - 4 ) = > x = - 2 , y = 4 product x = ( - 2 ) ( 4 ) = - 8 answer option - 8 answer : c"
Answer: c
Question (general): in a class of 30 students , 5 students did not borrow any books from the library , 10 students each borrowed 1 book , 8 students each borrowed 2 books , and the rest of the students each borrowed at least 4 books . if the average ( arithmetic mean ) number of books borrowed per student was 2 , what is the maximum number of books that any single student could have borrowed ?
Options: a ) 5 , b ) 8 , c ) 16 , d ) 18 , e ) 20
Rationale: "the average number of books per student was 2 means that total of 2 * 30 = 60 books were borrowed ; 5 + 12 + 8 = 25 students borrowed total of 5 * 0 + 12 * 1 + 8 * 2 = 28 books ; so 60 - 28 = 32 books are left to distribute among 30 - 25 = 5 students , these 5 arethe rest who borrowed at least 4 books ; tomaximizethe number of books one student from above 5 could have borrowed we shouldminimizethe number of books other 4 students from 5 could have borrowed . minimum these 4 students could have borrowed is 4 books per student , so total number of books they could have borrowed is 4 * 4 = 16 books . so the 5 th student could have borrowed is 32 - 16 = 16 books . answer : c ."
Answer: c
Question (general): in a office work is distribute between p persons . if 1 / 4 members are absent then work increased for each person is ?
Options: a ) 33.33 % , b ) 24.33 % , c ) 15.33 % , d ) 16.33 % , e ) 17.33 %
Rationale: "let total % of work is 100 % total person = p 1 / 4 person are absent of total person . so absent person is 1 / 4 p ie p / 4 . left person is , p - p / 4 = 3 p / 4 . p person do the work 100 % 1 person do the work 100 * p % 3 p / 4 person do the work ( 100 * p * 4 ) / 3 p % = 133.33 % work increased for each person is = ( 133.33 - 100 ) % = 33.33 % answer : a"
Answer: a
Question (general): john has $ 1,200 at the beginning of his trip , after spending money , he still has exactly $ 800 less than he spent on the trip . how much money does john still have ?
Options: a ) $ 200 , b ) $ 400 , c ) $ 600 , d ) $ 800 , e ) $ 1,200
Rationale: "suppose total money spent = x not spend ( money he still has ) = x - 800 x + x - 800 = 1200 x = 1000 money not spend = 1000 - 800 = 200 answer : a"
Answer: a
Question (physics): if a , b and c together can finish a piece of work in 2 days . a alone in 12 days and b in 18 days , then c alone can do it in ?
Options: a ) 5 days , b ) 4 days , c ) 3 days , d ) 2 days , e ) 7 days
Rationale: "c = 1 / 2 - 1 / 12 – 1 / 18 = 1 / 3 = > 3 days answer : c"
Answer: c
Question (physics): a tank with a volume of 30 cubic feet has one inlet pipe and 2 outlet pipes . the inlet pipe fills water into the tank at the rate of 3 cubic inches / min and the 2 outlet pipes empty it out at the rates of 9 cubic inches / min and 6 cubic inches / min respectively . if all 3 pipes are opened when the tank is full , how many minutes does it take to empty the tank ? ( 1 foot = 12 inches )
Options: a ) 2110 , b ) 3210 , c ) 4320 , d ) 5430 , e ) 6540
Rationale: "the tank is emptied at this rate : 9 + 6 - 3 = 12 cubic inches / min the tank has a volume of 30 * 12 * 12 * 12 = 51840 cubic inches . the time it takes to empty the tank is 51840 / 12 = 4320 minutes . the answer is c ."
Answer: c
Question (physics): a cistern is normally filled in 12 hours but takes two hours longer to fill because of a leak in its bottom . if the cistern is full , the leak will empty it in ?
Options: a ) 33 , b ) 84 , c ) 40 , d ) 99 , e ) 11
Rationale: "1 / 12 - 1 / x = 1 / 14 x = 84 answer : b"
Answer: b
Question (general): when positive integer n is divided by positive integer j , the remainder is 28 . if n / j = 154.04 , what is value of j ?
Options: a ) 400 , b ) 350 , c ) 700 , d ) 750 , e ) 800
Rationale: "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 154.04 here 154 is the quotient . given that remainder = 28 so , 154.04 = 154 + 28 / j so , j = 700 answer : c"
Answer: c
Question (general): what least number should be subtracted from 13602 such that the remainder is divisible by 87 ?
Options: a ) 27 , b ) 29 , c ) 28 , d ) 30 , e ) 31
Rationale: "13602 ÷ 87 = 156 , remainder = 30 hence 30 is the least number which can be subtracted from 13602 such that the remainder is divisible by 87 answer is d"
Answer: d
Question (physics): 45 litres of diesel is required to travel 600 km using a 800 cc engine . if the volume of diesel required to cover a distance varies directly as the capacity of the engine , then how many litres of diesel is required to travel 800 km using 1200 cc engine ?
Options: a ) 80 litres , b ) 90 litres , c ) 120 litres , d ) 170 litres , e ) none of these
Rationale: "explanatory answer to cover a distance of 800 kms using a 800 cc engine , the amount of diesel required = 800 / 600 * 45 = 60 litres . however , the vehicle uses a 1200 cc engine and the question states that the amount of diesel required varies directly as the engine capacity . i . e . , for instance , if the capacity of engine doubles , the diesel requirement will double too . therefore , with a 1200 cc engine , quantity of diesel required = 1200 / 800 * 60 = 90 litres . answer b"
Answer: b
Question (general): christine and siri have 21 rs between them . christine has 20 rs more than siri . how much does christine have .
Options: a ) 16.5 , b ) 17.5 , c ) 18.5 , d ) 19.5 , e ) 20.5
Rationale: let siri has x rs , then christine has 20 + x rs given x + ( 20 + x ) = 21 = > 2 x = 1 or x = 0.5 so christine and siri has 20.5 and 0.5 rs respectively . answer : e
Answer: e