Cheukting/mathqa huggingface dataset:
Question (physics): a can finish a work in 48 days , b in 9 days and c in 2 days , b and c start the work but are forced to leave after 3 days . the remaining work was done by a in ?
Options: a ) 10 days , b ) 12 days , c ) 6 days , d ) 20 days , e ) 8 days
Rationale: "b + c 1 day work = 1 / 9 + 1 / 12 = 7 / 36 work done by b and c in 3 days = 7 / 36 * 3 = 7 / 12 remaining work = 1 - 7 / 12 = 5 / 12 1 / 48 work is done by a in 1 day 5 / 12 work is done by a in 48 * 5 / 12 = 20 days answer is d"
Answer: d
Question (physics): the length of the bridge , which a train 140 metres long and travelling at 45 km / hr can cross in 30 seconds , is :
Options: a ) 200 m , b ) 235 m , c ) 245 m , d ) 250 m , e ) 270 m
Rationale: "let the length of the bridge : l the equation now is l + 140 / 12.5 m / s ( 45 km / hr or 12.5 m / s ) = 30 solving , l = 235 m answer : b"
Answer: b
Question (other): in a certain animal shelter , the ratio of the number of catsto the number of dogs is 15 to 7 . if 16 additional dogs were to be taken in by the shelter , the ratio of the number of cats to the number of dogs would be 15 to 11 . how many cats are in the shelter ?
Options: a ) 15 , b ) 25 , c ) 30 , d ) 45 , e ) 60
Rationale: "this ratio question can be solved in a couple of different ways . here ' s an algebraic approach . . . we ' re told that the ratio of the number of cats to the number of dogs is 15 : 7 . we ' re then told that 16 more dogs are added to this group and the ratio becomes 15 : 11 . we ' re asked for the number of cats . algebraically , since the number of cats is a multiple of 15 and the number of dogs is a multiple of 7 , we can write this initial relationship as . . . 15 x / 7 x when we add the 16 cats and factor in the ' ending ratio ' , we have an equation . . . . 15 x / ( 7 x + 16 ) = 15 / 11 here we have 1 variable and 1 equation , so we can solve for x . . . . ( 15 x ) ( 11 ) = ( 7 x + 16 ) ( 15 ) ( x ) ( 11 ) = ( 7 x + 16 ) ( 1 ) 11 x = 7 x + 16 4 x = 16 x = 4 with this x , we can figure out the initial number of dogs and cats . . . initial dogs = 15 x = 15 ( 4 ) = 60 final answer : d"
Answer: d
Question (general): for the positive integers x , x + 2 , x + 4 , x + 7 , and x + 32 , the mean is how much greater than the median ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 4 , e ) 5
Rationale: "mean = ( x + x + 2 + x + 4 + x + 7 + x + 32 ) / 5 = ( 5 x + 45 ) / 5 = x + 9 median = x + 4 thus mean - median = x + 9 - ( x + 4 ) = 5 answer = e"
Answer: e
Question (geometry): the ratio of the volumes of two cubes is 27 : 64 . what is the ratio of their total surface areas ?
Options: a ) 18 : 21
b ) 81 : 13
c ) 8 : 15
d ) 16 : 21
e ) 1 : 13
Rationale: ratio of the sides = ³ √ 27 : ³ √ 64 = 3 : 4 ratio of surface areas = 32 : 42 = 16 : 21 answer : d
Answer: d
Question (general): a driver would have reduced the time it took to drive from home to the store by 1 / 3 if the average speed had been increased by 18 miles per hour . what was the actual average speed , in miles per hour , when the driver drove from home to the store ?
Options: a ) 36 , b ) 40 , c ) 44 , d ) 48 , e ) 52
Rationale: "let r be the original speed and let t be the original time . since the distance remains the same ( we ' re just changing the rate and time ) , any increase in rate or time is met with a decrease in the other term . decreasing the time by 1 / 3 would give us : d = ( r ) ( t ) = ( 2 t / 3 ) ( x * r ) x = 3 / 2 since ( 2 t / 3 ) ( 3 r / 2 ) = ( r ) ( t ) = d 3 r / 2 = r + 18 r / 2 = 18 r = 36 the answer is a ."
Answer: a
Question (probability): what is the probability q of randomly selecting an arrangement of the letters of the wordmediterraneanin which the first letter is e and the last letter is r ?
Options: a ) 1 / 13 , b ) 1 / 20 , c ) 1 / 26 , d ) 1 / 50 , e ) 1 / 100
Rationale: why do you calculate the total combinations and everything , it is much easier to calculate as follows : 3 / 13 * 1 * 1 * 1 * 1 . . . . . * 2 / 12 = 6 / 156 = 1 / 26 this is because 3 / 13 = probability that first letter will be e and 2 / 12 = probability that thefirstletter will be r . between everything else cuts down to 1 * 1 * 1 . . . e . g . probability q of the second letter is 11 / 11 = 1 , > we do not care what ' s in between . c
Answer: c
Question (physics): the speed of a train is 90 kmph . what is the distance covered by it in 20 minutes ?
Options: a ) 15 , b ) 66 , c ) 77 , d ) 30 , e ) 42
Rationale: "90 * 20 / 60 = 30 kmph answer : d"
Answer: d
Question (gain): a man can row downstream at the rate of 45 kmph and upstream at 23 kmph . find the man ’ s rate in still water and rate of current ?
Options: a ) 8.5 , b ) 10.0 , c ) 12.5 , d ) 11.0 , e ) 8.25
Rationale: rate of still water = 1 / 2 ( down stream + upstream ) = 1 / 2 ( 45 + 23 ) = 34 kmph rate of current = 1 / 2 ( down stream - upstream ) = 1 / 2 ( 45 - 23 ) = 1 / 2 ( 22 ) = 11 kmph answer is d .
Answer: d
Question (general): how many numbers from 9 to 79 are exactly divisible by 11 ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 11 , e ) 12
Rationale: "9 / 11 = 0 and 79 / 11 = 7 = = > 7 - 0 = 7 numbers answer : b"
Answer: b
Question (physics): the speed of a car is 20 km in the first hour and 60 km in the second hour . what is the average speed of the car ?
Options: a ) 79 kmph , b ) 40 kmph , c ) 34 kmph , d ) 23 kmph , e ) 14 kmph
Rationale: "s = ( 20 + 60 ) / 2 = 40 kmph answer : b"
Answer: b
Question (general): what least number should be added to 1053 , so that the sum is completely divisible by 23
Options: a ) a ) 4 , b ) b ) 1 , c ) c ) 2 , d ) d ) 3 , e ) e ) 5
Rationale: "explanation : ( 1053 / 23 ) gives remainder 18 18 + 5 = 23 , so we need to add 5 answer : option e"
Answer: e
Question (gain): an error 5 % in excess is made while measuring the side of a square . the percentage of error in the calculated area of the square is
Options: a ) 10.4 % , b ) 10.25 % , c ) 10.23 % , d ) 10.26 % , e ) 10.5 %
Rationale: "100 cm is read as 102 cm . a 1 = ( 100 x 100 ) cm 2 and a 2 ( 105 x 105 ) cm 2 . ( a 2 - a 1 ) = [ ( 105 ) 2 - ( 100 ) 2 ] = ( 105 + 100 ) x ( 105 - 100 ) = 1025 cm 2 . percentage error = 10.25 b"
Answer: b
Question (general): the average weight of 6 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?
Options: a ) 76 kg , b ) 80 kg , c ) 85 kg , d ) data inadequate , e ) none of these
Rationale: "explanation : total weight increased = ( 6 x 2.5 ) kg = 15 kg . weight of new person = ( 65 + 15 ) kg = 80 kg . answer : b"
Answer: b
Question (physics): which greatest possible length can be used to measure exactly 10 meter 40 cm , 14 meter 10 cm and 7 meter 90 cm
Options: a ) 45 cm , b ) 25 cm , c ) 24 cm , d ) 15 cm , e ) 10 cm
Rationale: "explanation : convert first all terms into cm . i . e . 1040 cm , 1410 cm , 790 cm . now whenever we need to calculate this type of question , we need to find the hcf . hcf of above terms is 10 . option e"
Answer: e
Question (gain): a shopkeeper sells 200 metres of cloth for rs . 12000 at a loss of rs . 6 per metre . find his cost price for one metre of cloth ?
Options: a ) s . 59 , b ) s . 58 , c ) s . 09 , d ) s . 50 , e ) s . 66
Rationale: "sp per metre = 12000 / 200 = rs . 60 loss per metre = rs . 6 cp per metre = 60 + 6 = rs . 66 answer : e"
Answer: e
Question (general): in what ratio must rice at $ 9.30 / kg be mixed with rice at $ 10.80 / kg so that the mixture is worth $ 10 / kg ?
Options: a ) 1 : 3 , b ) 9 : 4 , c ) 8 : 7 , d ) 11 : 9 , e ) 11 : 7
Rationale: 9.30 x + 10.80 y = 10 ( x + y ) . 80 y = . 70 x x / y = 8 / 7 c is the answer
Answer: c
Question (other): a can contains a mixture of liquids a and b is the ratio 7 : 5 . when 9 litres of mixture are drawn off and the can is filled with b , the ratio of a and b becomes 7 : 9 . how many liter q of liquid a was contained by the can initially ?
Options: a ) 10 , b ) 20 , c ) 21 , d ) 25 , e ) 27
Rationale: "as a : b : : 7 : 5 - - - > only option c is a multiple of 7 and hence it is a good place to start . also a : b : : 7 : 5 means that , a = ( 712 ) * total and b = ( 5 / 12 ) * total if a = 21 , b = 15 - - - > remove 9 litres - - - > you remove ( 7 / 12 ) * 9 of a - - - > a remaining = 21 - ( 7 / 12 ) * 9 = 63 / 4 similarly , for b , you remove ( 5 / 12 ) * 9 - - - > b remaining = 15 - ( 5 / 12 ) * 9 = 45 / 4 and then add 9 more litres of b - - - > 9 + 45 / 4 = 81 / 4 thus a / b ( final ratio ) = ( 45 / 4 ) / ( 81 / 4 ) = 7 : 9 , the same as the final ratio mentioned in the question . hence c is the correct answer . a / b = 7 / 9 = ( 7 x - ( 7 / 12 ) * 9 ) / ( 5 x - ( 5 / 12 ) * 9 + 9 ) , where 7 x and 5 x are initial quantities of a and b respectively . thus , 7 / 9 = ( 7 x - ( 7 / 12 ) * 9 ) / ( 5 x - ( 5 / 12 ) * 9 + 9 ) - - - > giving you x = 3 . thus a ( original ) q = 7 * 3 = 21 . c"
Answer: c
Question (gain): a sum of money at simple interest amounts to rs . 855 in 3 years and to rs . 854 in 4 years . the sum is :
Options: a ) s . 650 , b ) s . 690 , c ) s . 738 , d ) s . 700 , e ) s . 718
Rationale: "s . i . for 1 year = rs . ( 854 - 815 ) = rs . 39 . s . i . for 3 years = rs . ( 39 x 3 ) = rs . 117 . principal = rs . ( 855 - 117 ) = rs . 738 . answer : option c"
Answer: c
Question (gain): a salesperson received a commission of 3 percent of the sale price for each of the first 100 machines that she sold and 4 percent of the sale price for each machine that she sold after the first 100 . if the sale price of each machine was $ 10,000 and the salesperson received a $ 42,000 commission , how many machines did she sell ?
Options: a ) 90 , b ) 103 , c ) 130 , d ) 115 , e ) 120
Rationale: first 100 machines = 3 % commission = 0.03 * 100 * 10000 = 30000 commission from sale of next machines = 42000 - 30000 = 12000 so 30 more machines . . total = 130 machines imo c . . .
Answer: c
Question (general): in a class of students , 1 / 2 of the number of girls is equal to 1 / 6 of the total number of students . what is the ratio of boys to girls in the class ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 2 / 1 , d ) 3 / 2 , e ) 4 / 3
Rationale: "( 1 / 2 ) g = ( 1 / 6 ) ( b + g ) 6 g = 2 b + 2 g 4 g = 2 b b / g = 2 / 1 . the answer is c ."
Answer: c
Question (general): if x is less than y by 45 % then y exceed x by :
Options: a ) 33.33 % , b ) 25 % , c ) 81.81 % , d ) 66.66 % , e ) none of these
Rationale: "using formula ( x / ( 100 - x ) * 100 ) where x is percentage decrease ( here it is 25 % ) = > 45 / ( 100 - 45 ) * 100 = 81.81 % answer : c"
Answer: c
Question (general): if the least common multiple of two prime numbers x and y is 77 , where x > y , then the value of 2 x + y is
Options: a ) 11 , b ) 17 , c ) 21 , d ) 29 , e ) 33
Rationale: "lcm ( x , y ) = 77 and both x an y are prime . the only values of x and y can be 11 and 7 ( x = 11 and y = 7 ) 2 x + y = 2 * 11 + 7 = 29 correct option : d"
Answer: d
Question (physics): convert 0.35 in to a vulgar fraction ?
Options: a ) 18 / 50 , b ) 16 / 50 , c ) 7 / 20 , d ) 19 / 50 , e ) none
Rationale: "answer 0.35 = 35 / 100 = 7 / 20 correct option : c"
Answer: c
Question (general): how many multiples of 10 are there between 10 and 1000 , exclusive ?
Options: a ) 98 , b ) 99 , c ) 100 , d ) 101 , e ) 97
Rationale: "98 multiples of 5 between 1 and 36 exclusive . from 10 * 2 upto 10 * 99 , ( 2 , 3,4 , . . . , 99 ) . hence , 98 multiples ! correct option is a"
Answer: a
Question (general): find the average of all the numbers between 6 and 29 which are divisible by 5 ?
Options: a ) 17 , b ) 20 , c ) 25 , d ) 30 , e ) 15
Rationale: average = ( 10 + 15 + 20 + 25 ) 4 = 70 / 4 = 17 answer is a
Answer: a
Question (physics): train a leaves the station traveling at 30 miles per hour . two hours later train в leaves the same station traveling in the same direction at 36 miles per hour . how many miles from the station was train a overtaken by train b ?
Options: a ) 320 , b ) 360 , c ) 400 , d ) 440 , e ) 480
Rationale: "after two hours , train a is ahead by 60 miles . train b can catch up at a rate of 6 miles per hour . the time to catch up is 60 / 6 = 10 hours . in 10 hours , train a travels another 30 * 10 = 300 miles for a total of 360 miles . the answer is b ."
Answer: b
Question (general): in a flight of 600 km , an aircraft was slowed down due to bad weather . its average speed for the trip was reduced by 200 km / hr and the time of flight increased by 30 minutes . the duration of the flight is ?
Options: a ) 1 hr , b ) 2 hr , c ) 6 hr , d ) 8 hr , e ) 7 hr
Rationale: let the duration of the flight be x hours . then , 600 / x - 600 / ( x + 1 / 2 ) = 200 x ( 2 x + 1 ) = 3 2 x 2 + x - 3 = 0 ( 2 x + 3 ) ( x - 1 ) = 0 x = 1 hr . answer : a
Answer: a
Question (gain): solve the quickfire maths brain teaser √ 9 % = ?
Options: a ) 30 % , b ) 40 % , c ) 85 % , d ) 19 % , e ) 29 %
Rationale: "a 30 % √ 9 % = > √ 9 / √ 100 = > 3 / 10 = > 30 / 100 = > 30 %"
Answer: a
Question (general): balls of equal size are arranged in rows to form an equilateral triangle . the top most row consists of one ball , the 2 nd row of two balls and so on . if 789 balls are added , then all the balls can be arranged in the shape of square and each of the sides of the square contain 8 balls less than the each side of the triangle did . how many balls made up the triangle ?
Options: a ) 1711 , b ) 2209 , c ) 2878 , d ) 1210 , e ) 1560
Rationale: "as expected , this question boils down to 2 equation , consider total number of balls in triangle = t and number of balls in last row = x . 1 + 2 + 3 + . . . + x = t x ( x + 1 ) / 2 = t - - - - ( a ) as mentioned in the question , side of a square will be ( x - 8 ) and total number of balls in square will be ( t + 789 ) ( x - 8 ) ^ 2 = t + 789 - - - - - ( b ) now the hardest part of the question will be to solve these 2 equations and this looks like time consuming but the easy way will be plug and play . also , we ' ve to find a value of t ( from 5 optiosn given below ) which can make a square of a a number . one we know this , it will be a cake walk . we can see that option a fits this criteria in eq ( b ) . add - 1711 + 789 = 2500 = 50 ^ 2 = ( x - 8 ) ^ 2 hence , x = 58 . cross check by putting in eq ( a ) = x ( x + 1 ) / 2 = t = > 58 * 59 / 2 = 1711 hence , answer is a ."
Answer: a
Question (general): the average of 20 numbers is calculated as 30 . it is discovered later on that while calculating the average , one number namely 36 was wrongly read as 26 . the correct average is ?
Options: a ) 40 , b ) 26 , c ) 60 , d ) 97 , e ) 12
Rationale: "20 * 30 + 36 – 26 = 160 / 10 = 60 answer : 60 answer is c"
Answer: c
Question (general): when n is divided by 12 , the remainder is 2 . what is the remainder when 4 n is divided by 5 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "let n = 2 ( leaves a remainder of 2 when divided by 15 ) 4 n = 4 ( 2 ) = 8 , which leaves a remainder of 3 when divided by 5 . answer c"
Answer: c
Question (general): s is a set of 64 consecutive multiples of 4 . if the smallest number in s is 68 , then the greatest number in s is
Options: a ) 198 , b ) 297 , c ) 320 , d ) 402 , e ) 405
Rationale: last term = first term + ( total no . of terms - 1 ) consecutive difference s is a set of 64 consecutive multiples of 4 . if the smallest number in s is 68 , then the greatest number in s is first term = 68 ; total terms = 64 ; difference = 4 68 + ( 63 ) 4 = 320 ans c
Answer: c
Question (general): the “ s - number ” of a number x is defined as the ones digit of 2 ^ x . antony rolls a die with 6 sides labeled with the integers from 1 to 6 , each of which has an equal probability of landing face - up . he then takes 3 ^ s , where s is the s - number of the result of his die roll , and plots 3 ^ s on a number line as the point a . finally , he repeats this entire process , this time plotting the result as the point b . what is the probability that the distance between a and b is greater than the value of b ?
Options: a ) 3 / 8 , b ) 13 / 36 , c ) 17 / 36 , d ) 19 / 36 , e ) 23 / 36
Rationale: if you calculate 3 ^ s for 1 st roll , all 6 results will be 9 , 81 , 6561 , 729 , 9 , 81 . this result is the same for 2 nd roll . 9 , 81 , 6561 , 729 , 9 , 81 . about distance : if the first result is 9 and the second is also 9 , the distance is 9 - 9 = 0 which is smaller than 9 . if the first result is 9 and the second is 81 , the distance is 81 - 9 = 72 which is also smaller than b which has the value of 81 . if the first result is 81 and the second is 9 , the distance will be greater than b . distance 81 - 9 = 72 > 9 . on the first roll , the probability of getting result 9 is 2 / 6 . in this case no other alternative values for second roll which would make the distance greater than b . so probability is 0 . so next estimations are : probability of getting 81 on the first roll ( 2 / 6 ) * probability of getting 9 on the second roll ( 2 / 6 ) = 1 / 9 probability of getting 729 on the first roll ( 1 / 6 ) * probability of getting 9 , 81 on the second roll ( 4 / 6 ) = 1 / 9 probability of getting 6561 on the first roll ( 1 / 6 ) * probability of getting 9 , 81 , 729 on the first roll ( 5 / 6 ) = 5 / 36 all together : 1 / 9 + 1 / 9 + 5 / 36 = 13 / 36 = b
Answer: b
Question (gain): two numbers are respectively 20 % and 50 % more than a third number . what percentage is the first of the second ?
Options: a ) 25 % , b ) 60 % , c ) 80 % , d ) 55 % , e ) 74 %
Rationale: "required answer = ( 100 + x ) / ( 100 + y ) * 100 = 120 * 100 / 150 = 80 % answer is c"
Answer: c
Question (physics): calculate how much time could be saved if the train would run at its usual speed , given that it ran at 3 / 4 of its own speed and got to its destination in 10 hours ?
Options: a ) 1.5 hrs , b ) 2.5 hrs , c ) 3.5 hrs , d ) 1.2 hrs , e ) 2.9 hrs
Rationale: "new speed = 3 / 4 of usual speed new time = 3 / 4 of usual time 3 / 4 of usual time = 10 hrs usual time = 10 * 3 / 4 = 7.5 hrs time saved = 10 - 7.5 = 2.5 hrs answer is b"
Answer: b
Question (physics): angelina walked 1200 meters from her home to the grocery at a constant speed . she then walked 480 meters to the gym at double the speed . she spent 40 seconds less on her way from the grocery to the gym than on her way from home to the grocery . what was angelina ' s speed , in meters per second , from the grocery to the gym ?
Options: a ) 12 , b ) 23 , c ) 34 , d ) 48 , e ) 52
Rationale: "let the speed be x . . . so time taken from home to grocery = 1200 / x . . the speed to gym = 2 x . . so time taken = 480 / 2 x = 240 / x . . its given 1200 / x - 240 / x = 40 . . 960 / x = 40 . . x = 24 m / secs . . so grocery to gym = 2 * 24 = 48 m / s . . . d"
Answer: d
Question (general): a waiter ' s salary consists of his salary and tips . during one week his tips were 5 / 2 of his salary . what fraction of his income came from tips ?
Options: a ) 4 / 9 , b ) 5 / 4 , c ) 5 / 8 , d ) 5 / 7 , e ) 6 / 9
Rationale: income = salary ( s ) + tips = s + s * 5 / 2 = s * 7 / 2 tips = s * 7 / 2 fraction of his income came from tips = ( s * 5 / 2 ) / ( s * 7 / 2 ) = 5 / 7 answer : d
Answer: d
Question (general): if a certain number x is divided by 82 , the reminder is 5 . what is the reminder when x + 7 is divided by 41 ?
Options: a ) 12 , b ) 5 , c ) 6 , d ) 16 , e ) 18
Rationale: "x can be written as 82 k + 5 or x = 5 , 87,169 , etc . when k = 0 , 1,2 etc x + 7 = 82 k + 5 + 7 = 82 k + 12 or x + 7 = 12,94 , 176 etc . k = 0 , 1,2 when divided by 41 , we will get the remainder 12 . a"
Answer: a
Question (gain): a reduction of 50 % in the price of apples would enable a man to obtain 80 more for rs . 55 , what is reduced price per dozen ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 7 , e ) 10
Rationale: c 55 * ( 50 / 100 ) = 28 - - - 64 ? - - - 12 = > rs . 4
Answer: c
Question (general): what is the next number : 3 , 18 , 258 , __
Options: a ) 2928 , b ) 3638 , c ) 4098 , d ) 4418 , e ) 5378
Rationale: "4 ^ 0 + 2 = 3 4 ^ 2 + 2 = 18 4 ^ 4 + 2 = 258 4 ^ 6 + 2 = 4098 the answer is c ."
Answer: c
Question (general): cindy has her eye on a sundress but thinks it is too expensive . it goes on sale for 15 % less than the original price . before cindy can buy the dress , however , the store raises the new price by 25 % . if the dress cost $ 85 after it went on sale for 15 % off , what is the difference between the original price and the final price ?
Options: a ) $ 0.00 , b ) $ 1.00 , c ) $ 3.40 , d ) $ 5.00 , e ) $ 6.25
Rationale: "0.85 * { original price } = $ 85 - - > { original price } = $ 100 . { final price } = $ 85 * 1.25 = $ 106.25 . the difference = $ 106.25 - $ 100 = $ 6.25 . answer : e ."
Answer: e
Question (geometry): how many books each of volume 200 meter cube can be packed into a crate of volume 4000 meter cube ?
Options: a ) 20 , b ) 40 , c ) 60 , d ) 80 , e ) can not be determined
Rationale: "gud question with a simple concept . in geo if we want to insert one shape into another we need to know the dimensions of the two shapes . in above with volume given , we can come up with different shapes , so we cant know the answer for ex : 4000 m 3 can be 400 * 10 or 40 * 100 or just 4000 * 1 we do n ' t know , so we cant calculate answer : e"
Answer: e
Question (general): a committee is reviewing a total of 20 x black - and - white films and 6 y color films for a festival . if the committee selects y / x % of the black - and - white films and all of the color films , what fraction q of the selected films are in color ?
Options: a ) 1 / 130 , b ) 1 / 5 , c ) 3 / 13 , d ) 10 / 13 , e ) 30 / 31
Rationale: it ' s y / xpercentnot y / x . if x = 20 and y = 10 . then : 20 x = 400 black - and - white films ; 6 y = 60 color films . y / x % = 10 / 20 % = 0.5 % of the black - and - white films , so 2 black - and - white films and all 60 color films , thus total of 62 films were selected . color films thus compose q = 60 / 62 = 30 / 31 of the selected films . answer : e .
Answer: e
Question (physics): a train travels 125 km in 2.5 hours and 270 km in 3 hours . find the average speed of train .
Options: a ) 80 kmph , b ) 60 kmph , c ) 72 kmph , d ) 90 kmph , e ) none of these
Rationale: "as we know that speed = distance / time for average speed = total distance / total time taken thus , total distance = 125 + 270 = 395 km thus , total speed = 5.5 hrs or , average speed = 5 = 395 / 5.5 or , 72 kmph . answer : c"
Answer: c
Question (general): if 4 x = 6 y = z , what is x + y , in terms of z ?
Options: a ) z / 2 , b ) 5 z / 12 , c ) z / 3 , d ) 3 z / 5 , e ) z / 9
Rationale: "4 x = 6 y = z x = z / 4 and y = z / 6 x + y = z / 4 + z / 6 = 5 z / 12 answer is b"
Answer: b
Question (general): when x is even , [ x ] = x / 2 + 1 , when x is odd [ x ] = 2 x + 1 then [ 7 ] * [ 8 ] = ?
Options: a ) [ 22 ] , b ) [ 44 ] , c ) [ 75 ] , d ) [ 88 ] , e ) [ 90 ]
Rationale: "[ 7 ] * [ 8 ] = ( 7 * 2 + 1 ) ( 8 / 2 + 1 ) = [ 75 ] . ans - c"
Answer: c
Question (gain): the price of a car is marked at $ 12,000 . if the car has successive discounts of 20 % , 15 % and 5 % , then at what price does a customer buy the car ?
Options: a ) $ 7524 , b ) $ 7752 , c ) $ 7880 , d ) $ 8196 , e ) $ 8324
Rationale: 0.95 * 0.85 * 0.8 * 12000 = $ 7752 the answer is b .
Answer: b
Question (gain): a dealer offers a cash discount of 10 % and still makes a profit of 20 % when he further allows 45 articles to be sold at the cost price of 40 articles to a particular sticky bargainer . how much percent above the cost price were his articles listed ?
Options: a ) 40 % , b ) 50 % , c ) 55 % , d ) 80 % , e ) 90 %
Rationale: "given cash discount - 10 % profit - 20 % items sold - 45 price sold at = list price of 40 assume list price = $ 10 total invoice = $ 400 - 10 % cash discount = $ 360 let cost price of 45 items be x so total cost = 45 * x given the shopkeeper had a profit of 20 % 45 * x * 120 / 100 = 360 or x = $ 20 / 3 = $ 6 + ( 2 / 3 ) which means his products were listed at $ 10 which is a 50 % markup over $ 6 + ( 2 / 3 ) answer b"
Answer: b