Cheukting/mathqa huggingface dataset:
Question (general): at the end of year x , automobile installment credit accounted for 43 % of all outstanding consumer installment credit . at that time automobile finance companies extended $ 50 billion of credit , or 1 / 4 of the automobile installment credit . how many billion dollars of consumer installment credit was outstanding at that time ?
Options: a ) 450 , b ) 465.12 , c ) 475 , d ) 500.15 , e ) 200
Rationale: system of equations a = ( 43 / 100 ) c ( 1 / 4 ) a = 50 - - > a = 200 substitution 200 = ( 43 / 100 ) c c = ( 100 / 43 ) 200 calculate 200 / 43 * 100 - the the correct answer is 465.12 . the correct answer is b .
Answer: b
Question (general): what is the lowest positive integer that is divisible by 1 through 3 , inclusive ?
Options: a ) 12 , b ) 6 , c ) 8 , d ) 18 , e ) 33
Rationale: "the integer should be divisible by : 1 , 2 , and 3 . the least common multiple of these integers is lcm = 1 * 2 * 3 = 6 answer : b"
Answer: b
Question (general): a courier charges for packages to a certain destination are 65 cents for the first 250 grams and 10 cents for each additional 100 grams or part thereof . what could be the weight in grams of a package for which the charge is $ 1.85 ?
Options: a ) 1680 , b ) 1420 , c ) 1120 , d ) 970 , e ) 740
Rationale: "the charge is 65 cents for the first 250 grams . this leaves a charge of $ 1.85 - $ 0.65 = $ 1.20 the charge for the next 1100 grams is $ 1.10 which leaves a charge of $ 0.10 the weight is somewhere between 1350 and 1450 . the answer is b ."
Answer: b
Question (general): during a certain two - week period , 60 percent of the movies rented from a video store were comedies , and of the remaining movies rented , there were 4 times as many dramas as action movies . if no other movies were rented during that two - week period and there were a action movies rented , then how many comedies , in terms of a , were rented during that two - week period ?
Options: a ) 14 , b ) 12 , c ) 10 , d ) 8 , e ) 7.5
Rationale: "total movies = 100 . comedies = 60 . action + drama = 40 . since there were 5 times as many dramas as action movies , then action + 4 * action = 40 - - > action = a = 8 . comedies = 60 = 7.5 a . answer : e"
Answer: e
Question (gain): a fruit seller sells mangoes at the rate of rs . 9 per kg and thereby loses 20 % . at what price per kg , he should have sold them to make a profit of 5 %
Options: a ) rs 8.81 , b ) rs 9.81 , c ) rs 10.81 , d ) rs 11.81 , e ) none of these
Rationale: "explanation : 85 : 9 = 105 : x x = ( 9 × 105 / 85 ) = rs 11.81 option d"
Answer: d
Question (general): if 21 / 22 = 0 . 95.45 , what is the 57 th digit to the right of the decimal point of the fraction ?
Options: a ) 1 , b ) 4 , c ) 5 , d ) 7 , e ) 9
Rationale: we are not concerned what 21 / 22 means . . we have to look at the decimal . . 0.9544 means 0.95454545 . . . . so leaving first digit to the right of decimal , all odd numbered digits are 4 and all even numbered are 5 . . here 57 is odd , so ans is 4 answer is b
Answer: b
Question (general): an army ’ s recruitment process included n rounds of selection tasks . for the first a rounds , the rejection percentage was 60 percent per round . for the next b rounds , the rejection percentage was 50 percent per round and for the remaining rounds , the selection percentage was 70 percent per round . if there were 20000 people who applied for the army and 196 were finally selected , what was the value of n ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 10
Rationale: "step ( 1 ) 8000 accepted . step ( 2 ) another 40 % of 8000 = 3200 accepted . here it is quiet observable that if we further deduct candidate by 60 % it would change our probablity of easy going 2000 candidate . so i would get to second stage of recruitment where 50 % is accepted step ( 3 ) 50 % of 3200 = 1600 step ( 4 ) 50 % of 1600 = 800 step ( 5 ) 50 % of 800 = 400 step ( 6 ) 50 % of 400 = 200 70 % of 400 = 280 and last step of accepting 70 % of 280 = 196 ( our target ) total 8 steps required . ans d"
Answer: d
Question (general): how many multiples of 5 are there between 50 and 500 ?
Options: a ) 128 , b ) 91 , c ) 89 , d ) 61 , e ) 60
Rationale: "it should be mentioned whether 50 and 500 are inclusive . if 50 and 500 are inclusive , then the answer is ( 500 - 50 ) / 5 + 1 = 91 . if 50 and 500 are not inclusive , then the answer is ( 495 - 55 ) / 5 + 1 = 89 . since oa is c , then we have not inclusive case ."
Answer: c
Question (physics): two stations a and b are 110 km apart on a straight line . one train starts from a at 4 a . m . and travels towards b at 20 kmph . another train starts from b at 8 a . m . and travels towards a at a speed of 25 kmph . at what time will they meet ?
Options: a ) 15 a . m , b ) 10 a . m , c ) 7 a . m , d ) 02 a . m , e ) 05 a . m
Rationale: "suppose they meet x hours after 4 a . m . distance covered by a in x hours = 20 x km . distance covered by b in ( x - 1 ) hours = 25 ( x - 1 ) km . therefore 20 x + 25 ( x - 1 ) = 110 45 x = 135 x = 3 . so , they meet at 7 a . m . answer : c"
Answer: c
Question (physics): the height of the wall is 6 times its width and lenght of the wall is 7 times its height . if the volume of the wall be 16128 cu . m . its width is
Options: a ) 4 m
b ) 5 m
c ) 6 m
d ) 7 m
e ) 8 m
Rationale: explanation : let width = x then , height = 6 x and length = 42 x 42 x × 6 x × x = 16128 x = 4 answer : a
Answer: a
Question (general): find the sum of all odd numbers upto 100 .
Options: a ) 200 , b ) 1000 , c ) 2500 , d ) 3140 , e ) 3200
Rationale: "sol . the given numbers are 1 , 3 , 5 , 7 , . . . , 99 . this is an a . p . with a = 1 and d = 2 . let it contain n terms . then , 1 + ( n - 1 ) x 2 = 99 or n = 50 .  required sum = ( n / 2 ) ( first term + last term ) = 50 ( 1 + 99 ) / 2 = 2500 . answer c 2500"
Answer: c
Question (physics): two stations p and q are 110 km apart on a straight track . one train starts from p at 7 a . m . and travels towards q at 20 kmph . another train starts from q at 8 a . m . and travels towards p at a speed of 25 kmph . at what time will they meet ?
Options: a ) 10.30 , b ) 10 , c ) 8.45 , d ) 9.3 , e ) 11
Rationale: "explanation : assume both trains meet after x hours after 7 am distance covered by train starting from p in x hours = 20 x km distance covered by train starting from q in ( x - 1 ) hours = 25 ( x - 1 ) total distance = 110 = > 20 x + 25 ( x - 1 ) = 110 = > 45 x = 135 = > x = 3 means , they meet after 3 hours after 7 am , ie , they meet at 10 am . answer : b"
Answer: b
Question (gain): a milk man has 10 liters of milk . if he mixes 5 liters of water , which is freely available , in 20 liters of pure milk . if the cost of pure milk is rs . 18 per liter , then the profit of the milkman , when he sells all the mixture at cost price is :
Options: a ) 20 % , b ) 15 % , c ) 33.33 % , d ) 18 % , e ) none of these
Rationale: "explanation : when the water is freely available and all the water is sold at the price of the milk , then the water gives the profit on the cost of 10 liters of milk . therefore , profit percentage = 15 % . answer : b"
Answer: b
Question (general): if * stands for / , / stands for - , + stands for * and - stands for + , then 9 / 8 * 7 + 5 - 10 = ?
Options: a ) 13.3 , b ) 10.8 , c ) 10.7 , d ) 11.4 , e ) 12.5
Rationale: 9 / 8 * 7 + 5 - 10 this expression becomes 9 - 8 / 7 * 5 + 10 after exchanging the symbols then the values for it would be 9 - 1.142 * 5 + 10 = 13.290 ( app ) = 13.3 answer : a
Answer: a
Question (physics): hcf and lcm two numbers are 12 and 396 respectively . if one of the numbers is 36 , then the other number is ?
Options: a ) 36 , b ) 66 , c ) 132 , d ) 264 , e ) 152
Rationale: "12 * 396 = 36 * x x = 132 answer : c"
Answer: c
Question (general): what is the tens digit of 36 ^ 30 ?
Options: a ) 1 , b ) 7 , c ) 5 , d ) 3 , e ) 9
Rationale: "36 ^ 10 = 6 ^ 20 ( 6 ^ 2 ) = 6 * 6 = 36 ( 6 ^ 3 ) = 36 * 6 = . 16 ( 6 ^ 4 ) = . 16 * 6 = . . 96 ( 6 ^ 5 ) = . . 96 * 6 = . . 76 ( 6 ^ 6 ) = . . 76 * 6 = . . . 56 ( 6 ^ 7 ) = . . . . 56 * 6 = . . . . 36 if you see there is a pattern here in tens digits 3 , 1,9 , 7,5 , 3,1 and so on . . . continue the pattern up to 6 ^ 30 ( dont actually calculate full values ) and answer is b : 7"
Answer: b
Question (general): a 4 digit number is such that the product of all of its digits is 126 . the sum of all the digits is equal to the 2 digit number formed by using thousands digit and tens digit ( 1000 digit in tens place & 10 digit in units place ) which in turn is equal to 19 . then difference of units and 1000 place of the number is , given that this difference is positive .
Options: a ) 1692 , b ) 1792 , c ) 1795 , d ) 1892 , e ) 1992
Rationale: the number is 1792 . let the number be represented as 1000 x + 100 y + 10 z + t acc to ques , xyzt = 126 x + y + z + t = 10 x + z = 19 so , number in thousands and tens place are 1 and 9 respectively . the remaining factor is 14 which is 7 * 2 so the number is 1792 . answer : b
Answer: b
Question (gain): p and q started a business investing rs . 54,000 and rs . 18,000 respectively . in what ratio the profit earned after 2 years be divided between p and q respectively ?
Options: a ) 3 : 1 , b ) 4 : 3 , c ) 5 : 4 , d ) 6 : 5 , e ) 17 : 4
Rationale: "p : q = 54000 : 18000 = 3 : 1 . answer : a"
Answer: a
Question (general): a man loses 1 / 3 rd of his money , then wins rs . 10 loses 1 / 3 rd of what he has and wins rs . 20 and finds that he has exactly what be had at the beginning . what was the amount he originally bad ?
Options: a ) 25 , b ) 36 , c ) 10 , d ) 48 , e ) 45
Rationale: let x be that amount so accordind to question , eqn will be like : ( ( ( x - x / 3 ) + 10 ) - ( ( ( x - x / 3 ) + 10 ) / 3 ) ) + 20 = x = > ( ( 2 x / 3 + 10 ) - ( ( 2 x / 3 + 10 ) / 3 ) ) + 20 = x = > 3 x - 4 x / 3 = 80 = > x = 48 answer : d
Answer: d
Question (probability): what is the probability of getting sum of 10 on rolling three dices ?
Options: a ) 28 / 216 , b ) 27 / 216 , c ) 29 / 216 , d ) 26 / 216 , e ) 25 / 216
Rationale: "the no of ways to roll three dies is 6 ^ 3 = 216 the possibles of getting sum as 10 is 631 = 3 ! = 6 622 = 3 ! / 2 ! = 3 541 = 3 ! = 6 523 = 3 ! = 6 442 = 3 ! / 2 ! = 3 433 = 3 ! / 2 ! = 3 total possibles for getting sum as 10 is 27 the probabilty is 27 / 216 answer : b"
Answer: b
Question (general): for any integer n greater than 1 , # n denotes the product of all the integers from 1 to n , inclusive . how many prime numbers are there between # 6 + 2 and # 6 + 6 , inclusive ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: "given that n * denotes the product of all the integers from 1 to n , inclusive so , 6 * + 2 = 6 ! + 2 and 6 * + 6 = 6 ! + 6 . now , notice that we can factor out 2 our of 6 ! + 2 so it can not be a prime number , we can factor out 3 our of 6 ! + 3 so it can not be a prime number , we can factor out 4 our of 6 ! + 4 so it can not be a prime number , . . . the same way for all numbers between 6 * + 2 = 6 ! + 2 and 6 * + 6 = 6 ! + 6 , inclusive . which means that there are no primes in this range . answer : a ."
Answer: a
Question (physics): a carpenter worked alone for 1 day on a job that would take him 6 more days to finish . he and another carpenter completed the job in 7 more days . how many days would it have taken the second carpenter to do the complete job working alone ?
Options: a ) 4.5 , b ) 7.5 , c ) 9.5 , d ) 14.5 , e ) 24.5
Rationale: "a carpenter worked only 1 day on something that takes him 6 more days . means ; carpenter finishes his work in 7 days . let his buddy finish the same task in x days . respective rates per day : 1 / 7 and 1 / x to complete 1 work : first guy worked for 5 days @ rate = 1 / 7 per day . second one worked for 7 days @ rate = 1 / x per day expression : days * rate = work 5 * 1 / 7 + 7 * 1 / x = 1 5 x + 49 = 7 x 2 x = 49 x = 24.5 days . ans : e"
Answer: e
Question (physics): if 4 is the remainder when m is divided by 10 , what is the remainder when 4 m is divided by 10 ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 0
Rationale: "we can put m = 10 * k + 4 . so 4 * m = 40 * k + 16 - - - > 40 * k + 16 = 10 * ( 4 * m + 1 ) + 6 - - - > the remainder is 6 . the answer is , therefore , ( c ) ."
Answer: c
Question (general): for an agricultural experiment , 300 seeds were planted in one plot and 200 were planted in a second plot . if exactly 25 percent of the seeds in the first plot germinated and exactly 35 percent of the seeds in the second plot germinated , what percent of the total number of seeds germinated ?
Options: a ) 12 % , b ) 26 % , c ) 29 % , d ) 30 % , e ) 60 %
Rationale: in the first plot 25 % of 300 seeds germinated , so 0.25 x 300 = 75 seeds germinated . in the second plot , 35 % of 200 seeds germinated , so 0.35 x 200 = 70 seeds germinated . since 75 + 70 = 145 seeds germinated out of a total of 300 + 200 = 500 seeds , the percent of seeds that germinated is ( 145 / 500 ) x 100 % , or 29 % . answer : c .
Answer: c
Question (physics): on the first day of her vacation , louisa traveled 240 miles . on the second day , traveling at the same average speed , she traveled 420 miles . if the 240 - mile trip took 3 hours less than the 420 - mile trip , what was the average speed , in miles per hour ?
Options: a ) 65 , b ) 50 , c ) 55 , d ) 60 , e ) 58
Rationale: "( time ) * ( rate ) = ( distance ) - - > ( rate ) = ( distance ) / ( time ) - - > given : ( rate ) = 240 / t = 420 / ( t + 3 ) - - > 4 / t = 7 / ( t + 3 ) - - > 4 t + 12 = 7 t - - - - > 3 t = 12 . t = 4 - - - - > ( rate ) = 240 / 4 = 60 answer : d"
Answer: d
Question (general): the number of positive integers n in the range 12 ≤ n ≤ 40 such that the product ( n − 1 ) ( n − 2 ) . . . 3 . 2.1 is not divisible by n is
Options: a ) 5 , b ) 7 , c ) 13 , d ) 14 , e ) 16
Rationale: explanation : ( n - 1 ) ! is always divisible by n unless and untill n is a prime number e . g . ( 5 - 1 ) ! = 4 ! which is not divisible by 5 bcuz 5 is a prime number therefore , find all prime numbers in the range of 12 to 40 i . e 13 , 17 , 19 , 23 , 29 , 31 and 37 hence , the number of positive integers n is 7 . answer : b
Answer: b
Question (general): 79 laboratories raise the bacterium , the laboratory have 48 culture dishes on average , which has about 25,073 bacteria each . how many bacteria are there approximately ?
Options: a ) 10 ^ 7 , b ) 10 ^ 9 , c ) 10 ^ 8 , d ) 10 ^ 10 , e ) 10 ^ 11
Rationale: 79 laboratories raise the bacterium , the laboratory have 48 culture dishes on average , which has about 25,073 bacteria each . how many bacteria are there approximately ? a . 10 ^ 7 b . 10 ^ 8 c . 10 ^ 9 d . 10 ^ 10 e . 10 ^ 11 - > due to approximately , 79 = 80 , 48 = 50 , 25,073 = 25,000 are derived , which makes ( 79 ) ( 48 ) ( 25,075 ) = ( 80 ) ( 50 ) ( 25,000 ) = 10 ^ 8 . the answer is c .
Answer: c
Question (general): a set consists of 15 numbers , all are even or multiple of 5 . if 8 numbers are even and 10 numbers are multiple of 5 , how many numbers is multiple of 10 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5
Rationale: "{ total } = { even } + { multiple of 5 } - { both } + { nether } . since { neither } = 0 ( allare even or multiple of 5 ) then : 15 = 8 + 10 - { both } + 0 ; { both } = 3 ( so 1 number is both even and multiple of 5 , so it must be a multiple of 10 ) . answer : d ."
Answer: d
Question (general): the greatest number that divides 2928 and 3240 leaving remainders 5 and 1 respectively is :
Options: a ) 74 , b ) 78 , c ) 79 , d ) 81 , e ) 85
Rationale: "explanation : 2928 - 5 = 2923 , 3240 - 1 = 3239 highest number that can divide 2923 and 3239 is hcf of numbers . hcf of 2923 and 3239 = 79 answer : c"
Answer: c
Question (general): find large number from below question the difference of 2 no ' s is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder
Options: a ) 1236 , b ) 1356 , c ) 1470 , d ) 1556 , e ) 1635
Rationale: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 15 5 x = 1350 x = 270 large number = 270 + 1365 = 1635 e"
Answer: e
Question (gain): a sum was put at simple interest at certain rate for 3 years . had it been put at 1 % higher rate it would have fetched rs . 72 more . the sum is : a . rs . 2,400 b . rs . 2,100 c . rs . 2,200 d . rs . 2,480
Options: a ) 2000 , b ) 2100 , c ) 2200 , d ) 2300 , e ) 2400
Rationale: 1 percent for 3 years = 72 1 percent for 1 year = 24 = > 100 percent = 2400 answer : e
Answer: e
Question (physics): a and b together can do a work in 3 days . if a alone can do it in 6 days . in how many days can b alone do it ?
Options: a ) 10 , b ) 99 , c ) 77 , d ) 55 , e ) 6
Rationale: "1 / 3 – 1 / 6 = 1 / 6 = > 6 answer : e"
Answer: e
Question (general): a man is 26 years older than his studen . in two years , his age will be twice the age of his student . the present age of his student is :
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: let the student ' s present age be x years . then , man ' s present age = ( x + 26 ) years . ( x + 26 ) + 2 = 2 ( x + 2 ) x + 28 = 2 x + 4 x = 24 . answer : e
Answer: e
Question (general): a = { 2 , 3 , 4 , 5 } b = { 4 , 5 , 6 , 7 , 8 } two integers will be randomly selected from the sets above , one integer from set a and one integer from set b . what is the probability t that the sum of the two integers will equal 9 ?
Options: a ) 0.15 , b ) 0.20 , c ) 0.25 , d ) 0.30 , e ) 0.33
Rationale: rearrange the first set : a = { 54 , 32 } b = { 45 , 67 , 8 } as you can see numbers in each column ( the numbers of the same color ) give the sum of 9 . so there are 4 such pares possible , total # of pairs is 4 * 5 = 20 . t = favorable / total = 4 / 20 = 0.2 . answer : b . or : we can select any number from set a ( 4 / 4 = 1 ) but in this case we must select its matching pair from set b ( the number of the same color ) and since there are only one matching pair of this particular number in b then the probability of this is 1 / 5 . so , overall : t = 1 * 1 / 5 . answer : b .
Answer: b
Question (general): the population of a bacteria culture doubles every 4 minutes . approximately how many minutes will it take for the population to grow from 1,000 to 500,000 bacteria
Options: a ) 10 , b ) 12 , c ) 14 , d ) 36 , e ) 18
Rationale: "this one ' s easy . 1000 * 2 ^ t = 500,000 2 ^ t = 500 now gauging , since 2 ^ 8 = 256 , then 2 ^ 9 = 512 so t = 9 but be careful , ' t ' is in time intervals of 4 minutes so answer is 9 * 4 = 36 minutes answer ( d )"
Answer: d
Question (geometry): how many pieces can a square pizza be cut into by making 4 linear cuts ?
Options: a ) 10
b ) 11
c ) 12
d ) 13
e ) 14
Rationale: 1 cut makes two pieces a second cut can make 4 pieces by cutting through 2 of the pieces a third cut can make 7 pieces by cutting through 3 of the pieces a fourth cut can make 11 pieces by cutting through 4 of the pieces b
Answer: b
Question (physics): two trains of length 220 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively . in what time will they be clear of each other from the moment they meet ?
Options: a ) 28 , b ) 266 , c ) 990 , d ) 25 , e ) 11
Rationale: "relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 220 + 280 = 500 m . the time required = d / s = 500 / 20 = 25 sec . answer : d"
Answer: d
Question (general): we bought orange juice and apple juice at the store . a bottle of orange juice costs 70 cents and a bottle of apple juice costs 60 cents . we bought a total of 70 bottles for $ 46.20 . how many bottles of orange juice did we buy ?
Options: a ) 32 , b ) 36 , c ) 38 , d ) 42 , e ) 48
Rationale: let oj be the bottles of orange juice and let aj be the bottles of apple juice . ( oj ) + aj = 70 . aj = 70 - ( oj ) . 70 ( oj ) + 60 aj = 4620 . 70 ( oj ) + 60 ( 70 - oj ) = 4620 . 10 ( oj ) + 4200 = 4620 . oj = 42 . the answer is d .
Answer: d
Question (general): if x is to be chosen at random from the integers between 1 to 7 , inclusive , and y is to be chosen at random from the integers between 7 and 11 , inclusive , what is the probability that x + y will be even ?
Options: a ) 3 / 5 , b ) 4 / 7 , c ) 5 / 7 , d ) 18 / 35 , e ) 23 / 35
Rationale: "x + y will be even if x and y are both even or both odd . p ( x and y are both even ) = 3 / 7 * 2 / 5 = 6 / 35 p ( x and y are both odd ) = 4 / 7 * 3 / 5 = 12 / 35 p ( x + y is even ) = 6 / 35 + 12 / 35 = 18 / 35 the answer is d ."
Answer: d
Question (general): a glucose molecule contains 6 carbon , 12 hydrogen and 6 oxygen atoms . during photosynthesis , green plants create glucose daily . if , over a period of 12 days , an eucalyptus plant ( a green plant ) creates 12000 molecules of glucose then approximately how many more atoms of hydrogen than carbon are created on average per day ?
Options: a ) 60,000 , b ) 6,000 , c ) 2,500 , d ) 250 , e ) 0
Rationale: solution : we know that 12,000 glucose molecules are created over a period of 12 days . therefore 12,000 / 12 = 1,000 glucose molecules are created on average per day . each glucose molecule contains 6 carbon atoms and 12 hydrogen atoms . so 1,000 glucose molecules contain 6 × 1,000 = 6,000 carbon atoms and 12 × 1,000 = 12,000 hydrogen atoms . the difference is 12,000 – 6,000 = 6,000 . the correct answer is b .
Answer: b
Question (general): a basketball player practices 2 hours a day monday through friday . how many hours must he practice saturday and sunday combined if he wants to practice an average ( arithmetic mean ) of 3 hours a day for the 7 day week ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: total number of hours practiced mon through fri : 5 * 2 = 10 total number of hours that will be practiced in a 7 day week considering 3 hours a day average : 7 * 3 = 21 thus 21 - 10 = 11 hours still need to be practiced ( on sat and sun combined ) d
Answer: d
Question (general): when the positive integer k is divided by the positive integer n , the remainder is 11 . if k / n = 83.2 , what is the value of n ?
Options: a ) 9 , b ) 20 , c ) 55 , d ) 70 , e ) 81
Rationale: here ' s an approach that ' s based on number properties and a bit ofbrute forcemath : we ' re told that k and n are both integers . since k / n = 81.2 , we can say that k = 81.2 ( n ) n has tomultiply outthe . 2 so that k becomes an integer . with the answers that we have to work with , n has to be a multiple of 5 . eliminate a and e . with the remaining answers , we can test the answers and find the one that fits the rest of the info ( k / n = 81.2 and k / n has a remainder of 11 ) answer b : if n = 20 , then k = 1624 ; 1624 / 20 has a remainder of 4 not a match answer c : if n = 55 , then k = 4466 ; 4466 / 55 has a remainder of 11 match . final answer : e
Answer: e
Question (gain): what sum of money will produce rs . 90 as simple interest in 4 years at 4 1 / 2 percent ?
Options: a ) rs . 550 , b ) rs . 650 , c ) rs . 600 , d ) rs . 500 , e ) rs . 700
Rationale: "explanation : 90 = ( p * 4 * 9 / 2 ) / 100 90 = 36 p / 100 p = 500 answer : option d"
Answer: d
Question (physics): two trains are moving in the same direction at 72 kmph and 36 kmph . the faster train crosses a man in the slower train in 7 seconds . find the length of the faster train ?
Options: a ) 70 , b ) 20 , c ) 30 , d ) 75 , e ) 15
Rationale: "relative speed = ( 72 - 36 ) * 5 / 18 = 2 * 5 = 10 mps . distance covered in 27 sec = 7 * 10 = 70 m . the length of the faster train = 70 m . answer : a"
Answer: a
Question (general): if the average ( arithmetic mean ) of a and b is 80 , and the average of b and c is 180 , what is the value of a − c ?
Options: a ) − 220 , b ) − 200 , c ) 100 , d ) 135 , e ) it can not be determined from the information given
Rationale: "a + b = 160 b + c = 360 a - c = - 200 . imo option b ."
Answer: b