Cheukting/mathqa huggingface dataset:
Question (physics): a train overtakes two persons who are walking in the same direction in which the train is going , at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively . find the length of train ?
Options: a ) 45 m , b ) 50 m , c ) 55 m , d ) 60 m , e ) 65 m
Rationale: "explanation : first person speed = 2 * ( 5 / 18 ) = 5 / 9 m / sec second person speed = 4 * ( 5 / 18 ) = 10 / 9 m / sec let the length of train is x metre and speed is y m / sec then , x / y − 5 / 9 = 9 = > 9 y − 5 = x = > 9 y − x = 5 . . . . . ( i ) also , x / y − 10 / 9 = 10 90 y − 9 x = 100 . . . . . ( ii ) from ( i ) and ( ii ) , we get , x = 50 so length of train is 50 metre option b"
Answer: b
Question (general): a number is doubled and 9 is added . if resultant is trebled , it becomes 63 . what is that number
Options: a ) 6 , b ) 10 , c ) 12 , d ) 14 , e ) 15
Rationale: "explanation : = > 3 ( 2 x + 9 ) = 63 = > 2 x + 9 = 21 = > x = 6 answer : option a"
Answer: a
Question (general): a = 5 ^ 10 - 625 ^ 2 and a / x is an integer , where x is a positive integer greater than 1 , such that it does not have a factor p such that 1 < p < x , then how many different values for x are possible ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: this is a tricky worded question and i think the answer is should be d not c . . . here is my reason : the stem says that x is a positive integer such that has no factor grater than 2 and less than x itself . the stem wants to say that x is a prime number . because any prime number has no factor grater than 1 and itself . on the other hand the stem says that x could get how many different number not must get different number ( this is very important issue ) as our friends say , if we simplify numerator more we can obtain : 5 ^ 12 ( 5 ^ 3 - 1 ) = 5 ^ 12 ( 124 ) = 5 ^ 12 ( 31 * 2 * 2 ) divided by x and we are told that this fraction is an integer . so , x could be ( not must be ) 5 , 31 , or 2 ! ! ! so , x could get 2 different values and answer is c . . . .
Answer: c
Question (physics): a 80 cm long wire is to be cut into two pieces so that one piece will be 3 / 5 th of the other , how many centimeters will the shorter piece be ?
Options: a ) a ) 30 , b ) b ) 20 , c ) c ) 83 , d ) d ) 21 , e ) e ) 52
Rationale: "explanation : 1 : 3 / 5 = 5 : 3 3 / 8 * 80 = 30 answer : option a"
Answer: a
Question (general): a library has an average of 510 visitors on sundays and 240 on other day . the average number of visitors in a month of 25 days starting with sunday is
Options: a ) 342 , b ) 285 , c ) 290 , d ) 295 , e ) 275
Rationale: "explanation : as the month begin with sunday , so there will be five sundays in the month . so result will be : = ( 510 × 5 + 240 × 25 / 30 ) = ( 8550 / 25 ) = 342 answer : option a"
Answer: a
Question (gain): a total of $ 20,000 was invested in two certificates of deposit at simple annual interest rates of 6 percent and 12 percent , respectively . if the total interest on the two certificates was $ 1,440 at the end of one year , what fractional part of the $ 20.000 was invested at the higher rate ?
Options: a ) 3 / 8 , b ) 2 / 5 , c ) 1 / 5 , d ) 3 / 5 , e ) 3 / 4
Rationale: "x * 6 / 100 * 1 + ( 20000 - x ) * 12 / 100 * 1 = 1440 6 x - 12 x = 144000 - 240000 = > - 6 x = - 96000 = > x = 16000 so 4000 / 20000 = 1 / 5 answer - c"
Answer: c
Question (geometry): the ratio , by volume , of soap to alcohol to water in a certain solution is 6 : 30 : 90 . the solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved . if the altered solution will contain 150 cubic centimeters of alcohol , how many cubic centimeters of water will it contain ?
Options: a ) 1200 , b ) 1300 , c ) 1500 , d ) 1800 , e ) 1900
Rationale: "soap : alcohol initial ratio soap : alcohol : water - - > 6 : 30 : 90 initial soap : alcohol = 6 / 30 = 6 : 30 after doubled soap : alcohol = 2 * 6 / 30 = 12 / 30 = 12 : 30 initial soap : water = 6 / 90 = 6 : 90 after halved soap : water : 1 / 2 * 6 / 90 = 3 / 90 = 3 : 90 = 12 : 360 after soap : alcohol : water - - > 12 : 30 : 360 given alcohol 150 cubic centimeter . ratio is 60 : 150 : 1800 ( 12 : 30 : 360 ) for 150 cubic centimeter of alcohol - - - 1800 cu cm water is required . answer - d"
Answer: d
Question (general): a waiter ' s salary consists of his salary and tips . during one week his tips were 7 / 4 of his salary . what fraction of his income came from tips ?
Options: a ) 4 / 9 , b ) 5 / 4 , c ) 5 / 8 , d ) 5 / 9 , e ) 7 / 11
Rationale: "income = salary ( s ) + tips = s + s * 7 / 4 = s * 11 / 4 tips = s * 7 / 4 fraction of his income came from tips = ( s * 7 / 4 ) / ( s * 11 / 4 ) = 7 / 11 answer : e"
Answer: e
Question (general): the total age of a and b is 15 years more than the total age of b and c . c is how many year younger than
Options: a ) 14 years , b ) 12 years , c ) 56 years , d ) 66 years , e ) 15 years
Rationale: "given that a + b = 15 + b + c = > a â € “ c = 15 + b â € “ b = 15 = > c is younger than a by 15 years answer : e"
Answer: e
Question (other): three numbers are in the ratio 4 : 5 : 6 and their product is 76680 . the largest number is
Options: a ) 30 , b ) 24 , c ) 26 , d ) 28 , e ) 22
Rationale: "explanation : let the number be 4 x , 5 x and 6 x . then , ( 4 x ) ( 5 x ) ( 6 x ) = 2880 = > 120 x 3 = 7680 = > x 3 = 64 = > x = 4 so , largest number is 6 x = 24 answer : option b"
Answer: b
Question (other): a bag has 9 green balls and 23 pink balls . how many green balls should be added to the bag so that the ratio of green balls and pink balls in the bag becomes 1 : 1 ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: suppose x green balls need to be added . then , the number of green balls becomes 9 + x , and the number of pink balls remains the same , 23 . but now the ratio of green and pink balls is 1 : 1 this means , ( 9 + x ) / 23 = 1 / 1 solving this we get x = 14 . ans e
Answer: e
Question (general): what is the value of 100 p 2 ?
Options: a ) 9801 , b ) 12000 , c ) 5600 , d ) 9900 , e ) none of these
Rationale: "explanation : 100 p 2 = 100 x 99 = 9900 . answer : option d"
Answer: d
Question (physics): convert 2 / 5 to a decimal
Options: a ) 0.1 , b ) 0.2 , c ) 0.3 , d ) 0.4 , e ) 0.5
Rationale: "divide 2 by 5 : 2 / 5 = 0.4 answer : 2 / 5 = 0.4 ( d )"
Answer: d
Question (general): what is remainder of the division ( 1625 * 1627 * 1629 ) / 12 ?
Options: a ) 3 , b ) 2 , c ) 1 , d ) 0 , e ) 4
Rationale: remainder will be number / 100 here as the divisor is two digit number = 12 . hence checking for the last two digits = 5 * 7 * 9 = 15 thus remainder = 3 . answer : a
Answer: a
Question (general): if henry were to add 8 gallons of water to a tank that is already 3 / 4 full of water , the tank would be 7 / 8 full . how many gallons of water would the tank hold if it were full ?
Options: a ) 25 , b ) 40 , c ) 64 , d ) 80 , e ) 96
Rationale: "7 / 8 x - 3 / 4 x = 8 galls 1 / 8 * x = 8 gallons x = 64 gallons answer c"
Answer: c
Question (gain): find compound interest on $ 4000 at 15 % per annum for 2 years 4 months , compounded annually .
Options: a ) 1554.5 , b ) 1509.5 , c ) 1108.5 , d ) 1107.5 , e ) 1100.5
Rationale: "time = 2 years 4 months = 2 ( 4 / 12 ) years = 2 ( 1 / 3 ) years . amount = $ [ 4000 x ( 1 + ­ ( 15 / 100 ) ) 2 x ( 1 + ( ( 1 / 3 ) * 15 ) / 100 ) ] = $ [ 4000 * ( 23 / 20 ) * ( 23 / 20 ) * ( 21 / 20 ) ] = $ 5554.50 . : . c . i . = rs . ( 5554.50 - 4000 ) = $ 1554.50 answer a ."
Answer: a
Question (general): if x = 1 + √ 2 , then what is the value of x 4 - 4 x 3 + 4 x 2 + 3 ?
Options: a ) - 1 , b ) 0 , c ) 4 , d ) 2 , e ) 3
Rationale: "answer x = 1 + √ 2 ∴ x 4 - 4 x 3 + 4 x 2 + 5 = x 2 ( x 2 - 4 x + 4 ) + 3 = x 2 ( x - 2 ) 2 + 3 = ( 1 + √ 2 ) 2 ( 1 + √ 2 - 2 ) 2 + 3 = ( √ 2 + 1 ) 2 ( √ 2 - 1 ) 2 + 3 = [ ( √ 2 ) 2 - ( 1 ) 2 ] 2 + 3 = ( 2 - 1 ) 2 = 1 + 3 = 4 correct option : c"
Answer: c
Question (physics): a train is 485 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length
Options: a ) 20 seconds , b ) 30 seconds , c ) 40 seconds , d ) 50 seconds , e ) none of these
Rationale: "explanation : speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 485 + 140 = 625 meter time = distance / speed = 625 ∗ 2 / 25 = 50 seconds option d"
Answer: d
Question (general): if x gets 25 % more than y and y gets 20 % more than z , the share of z out of rs . 1110 will be :
Options: a ) rs . 300 , b ) rs . 200 , c ) rs . 240 , d ) rs . 350 , e ) none of these
Rationale: "z share = z , y = 1.2 z x = 1.25 ã — 1.2 z , x + y + z = 111 ( 1.25 ã — 1.2 + 1.2 + 1 ) z = 1110 3.7 z = 1110 , z = 300 answer : . a"
Answer: a
Question (physics): a train moves with a speed of 135 kmph . its speed in metres per second is
Options: a ) 10.8 , b ) 37.5 , c ) 30 , d ) 38.8 , e ) none
Rationale: "solution speed = 135 kmph = ( 135 x 5 / 18 ) m / sec = 37.5 m / sec . answer b"
Answer: b
Question (general): a 50 ml after - shave lotion at 30 % alcohol is mixed with 30 ml of pure water . what is the percentage of alcohol in the new solution ?
Options: a ) 16.75 % , b ) 17.75 % , c ) 18.75 % , d ) 19.75 % , e ) none of these
Rationale: the amount of the final mixture is given by 50 ml + 30 ml = 80 ml the amount of alcohol is equal to the amount of alcohol in pure water ( which is 0 ) plus the amount of alcohol in the 30 % solution . let x be the percentage of alcohol in the final solution . hence 0 + 30 % 50 ml = x ( 80 ) solve for x x = 0.1817 = 18.75 % answer c
Answer: c
Question (general): what is the remainder when 1201 × 1202 × 1205 × 1207 is divided by 6 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "the remainders when dividing each number by six are : 1 , 2 , 5 , and 1 . the product is 1 * 2 * 5 * 1 = 10 the remainder when dividing 10 by 6 is 4 . the answer is d ."
Answer: d
Question (general): what is the value of 11 ^ x - 11 ^ ( x + 2 ) , where x is the largest integer such that 11 ^ x is a factor of 30030 ?
Options: a ) - 1331 , b ) - 1320 , c ) - 121 , d ) - 120 , e ) - 1
Rationale: the given expression is 11 x - 11 ( x ^ + 2 ) = 11 x ( 1 - x ) 1 x needs to be factor of 30030 and x needs to be the largest integer possible . this means 11 x needs to be the largest factor possible . the largest factor of a number is the number itself . the largest factor of 30030 is 30030 = ( 11 * 2730 ) x must be 2730 the value of 11 x ( 1 - x ) = – 1320 . answer : b
Answer: b
Question (gain): what percent of 7.2 kg is 18 gms ?
Options: a ) 25 , b ) 66 , c ) 288 , d ) 19 , e ) 17
Rationale: "explanation : required percentage = ( 18 / 7200 * 100 ) % = 1 / 4 % = 0.25 % answer : a ) . 25 %"
Answer: a
Question (general): a ’ s speed is 17 / 14 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ?
Options: a ) 1 / 14 , b ) 1 / 17 , c ) 3 / 14 , d ) 3 / 17 , e ) 1 / 31
Rationale: "let x be the fraction of the distance that b runs . let v be the speed at which b runs . the time should be the same for both runners . time = d / ( 17 v / 14 ) = xd / v ( 14 / 17 ) * d / v = x * d / v x = 14 / 17 b should have a head start of 3 / 17 of the full distance . the answer is d ."
Answer: d
Question (gain): a invested $ 100 in a business after 6 months b invested $ 200 in the business . end of the year if they got $ 100 as profit . find a shares ?
Options: a ) $ 100 , b ) $ 75 , c ) $ 20 , d ) $ 120 , e ) $ 50
Rationale: "a : b = 100 * 12 : 200 * 6 a : b = 1 : 1 a ' s share = 100 / 2 = $ 50 answer is e"
Answer: e
Question (other): in a family 13 people eat only vegetarian , 8 people eat only non veg . , 6 people eat both veg and non veg . . how many people eat veg in the family ?
Options: a ) 20 , b ) 11 , c ) 19 , d ) 31 , e ) 21
Rationale: "total people eat veg = only veg + both veg and non veg total = 13 + 6 = 19 answer = c"
Answer: c
Question (gain): a shopkeeper labeled the price of his articles so as to earn a profit of 40 % on the cost price . he then sold the articles by offering a discount of 5 % on the labeled price . what is the actual percent profit earned in the deal ?
Options: a ) 18 % , b ) 20 % , c ) 17 % , d ) 33 % , e ) none of these
Rationale: "explanation : let the cp of the article = rs . 100 . then labeled price = rs . 140 . sp = rs . 140 - 5 % of 140 = rs . 140 - 7 = rs . 133 . gain = rs . 133 â € “ rs . 100 = rs . 33 therefore , gain / profit percent = 33 % . answer : option d"
Answer: d
Question (general): the total of 336 of 20 paise and 25 paise make a sum of rs . 71 . the no of 20 paise coins is
Options: a ) 238 , b ) 277 , c ) 278 , d ) 260 , e ) 288
Rationale: "explanation : let the number of 20 paise coins be x . then the no of 25 paise coins = ( 336 - x ) . 0.20 * ( x ) + 0.25 ( 336 - x ) = 71 = > x = 260 . . answer : d ) 260"
Answer: d
Question (physics): a factory produces 6400 toys per week . if the workers at this factory work 3 days a week and if these workers make the same number of toys everyday , how many toys are produced each day ?
Options: a ) 1375 toys , b ) 2133 toys , c ) 3375 toys , d ) 4375 toys , e ) 5375 toys
Rationale: "to find the number of toys produced every day , we divide the total number of toys produced in one week ( of 3 days ) by 3 . 6400 / 3 = 2133 toys correct answer b"
Answer: b
Question (physics): walking at 5 / 6 th of its usual speed a cab is 15 mnts late . find its usual time to cover the journey ?
Options: a ) 25 m , b ) 45 m , c ) 32 m , d ) 75 m , e ) 62 m
Rationale: new speed = 5 / 6 th of usual speed new time = 6 / 5 th of usual time 6 / 5 ut - ut = 15 m ut / 5 = 15 m ut = 75 m answer is d
Answer: d
Question (general): a part - time employee whose hourly wage was increased by 20 percent decided to reduce the number of hours worked per week so that the employee ' s total weekly income would remain unchanged . by what percent should the number of hours worked be reduced ?
Options: a ) 11 , b ) 15 , c ) 16.66 , d ) 17 , e ) 18
Rationale: "let original hourly wage be x and let the no of hours worked be y total wage will be = x * y after the increment the wage will be = 1.2 x now we need to find number of hours worked so that x * y = 1.2 x * z i . e z = 1 / 1.2 y % decrease = ( y - 1 / 1.2 y ) / y * 100 = 16.66 thus my answer is c ."
Answer: c
Question (gain): a person purchased a tv set for rs . 16000 and a dvd player for rs . 6250 . he sold both the items together for rs . 35600 . what percentage of profit did he make ?
Options: a ) 80 % , b ) 49 % , c ) 40 % , d ) 60 % , e ) 90 %
Rationale: the total cp = rs . 16000 + rs . 6250 = rs . 22250 and sp = rs . 35600 profit ( % ) = ( 35600 - 22250 ) / 22250 * 100 = 60 % answer : d
Answer: d
Question (physics): two trains each 180 m in length are running on the same parallel lines in opposite directions with the speed of each 80 kmph . in what time will they cross each other completely ?
Options: a ) 7.8 sec , b ) 8.1 sec , c ) 8.3 sec , d ) 8.2 sec , e ) 8.4 sec
Rationale: d = 180 m + 180 m = 360 m * 1 / 1000 = 0.36 kms rs = 80 + 80 = 160 kmph t = ( 0.36 / 160 ) * 3600 = 8.1 sec answer : b
Answer: b
Question (physics): 20 buckets of water fill a tank when the capacity of each bucket is 13.5 litres . how many buckets will be required to fill the same tank if the capacity of each bucket is 9 litres ?
Options: a ) 30 , b ) 32 , c ) 60 , d ) data inadequate , e ) none of these
Rationale: "capacity of the tank = 20 × 13.5 = 270 litres when the capacity of each bucket = 9 litres , then the required no . of buckets = 270 ⁄ 9 = 30 answer a"
Answer: a
Question (general): the number of the members of a club is more than 50 and less than 80 . when 4 people sit at a table , other people exactly divided to 8 - people groups ( 8 people sit at a table ) or 7 - people groups ( 7 people sit at a table ) . if the members are divided to 9 - people groups , how many people will be left ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "the number of members is 7 k + 4 = 8 j + 4 the only number in this range which satisfies this is 60 . 60 / 9 = 6 ( 9 ) + 6 the answer is d ."
Answer: d
Question (physics): a train running at the speed of 72 km / hr crosses a pole in 9 seconds . find the length of the train .
Options: a ) 150 meter , b ) 286 meter , c ) 180 meter , d ) 288 meter , e ) 265 meter
Rationale: "speed = 72 * ( 5 / 18 ) m / sec = 20 m / sec length of train ( distance ) = speed * time ( 20 ) * 9 = 180 meter answer : c"
Answer: c
Question (physics): two clocks are set correctly at 1 0 ' clock in the afternoon . one keeps correct time . the other gains 5 seconds per minute . that evening , when the fast clock shows 6 : 20 , what does the correct clock show ?
Options: a ) 4.0 , b ) 5.0 , c ) 6.0 , d ) 7.2 , e ) 3.5
Rationale: faster clock gains 5 seconds per minute or 5 * 60 = 300 seconds or 5 minutes per hour . both clocks are set at 1 : 00 at 2 : 00 correct clock is at 2 : 00 faster clock is at 2 : 05 : 00 ( 1 hour + gained 5 minutes ) at 3 : 00 - correct clock is at 3 : 00 faster clock is at 3 : 10 : 00 ( 2 hours + gained 10 minutes ) . in 5 hours , faster clock would gain 20 minutes . it will show 6 : 20 . at that point , the correct clock would show 6 : 00 . answer is c
Answer: c
Question (other): the triplicate ratio of 1 : 3 is ?
Options: a ) 1 : 27 , b ) 1 : 8 , c ) 1 : 3 , d ) 1 : 1 , e ) 1 : 2
Rationale: "1 ^ 3 : 3 ^ 3 = 1 : 27 answer : a"
Answer: a
Question (gain): a shopkeeper sold an article offering a discount of 5 % and earned a profit of 22.55 % . what would have been the percentage of profit earned if no discount was offered ?
Options: a ) 60 % , b ) 29 % , c ) 39 % , d ) 56 % , e ) 73 %
Rationale: "let c . p . be rs . 100 . then , s . p . = rs . 122.55 let marked price be rs . x . then , 95 / 100 x = 122.55 x = 12255 / 95 = rs . 129 now , s . p . = rs . 129 , c . p . = rs . 100 profit % = 29 % . answer : b"
Answer: b
Question (general): 5 men are equal to as many women as are equal to 8 boys . all of them earn $ 90 only . men ’ s wages are ?
Options: a ) $ 4 , b ) $ 6 , c ) $ 7 , d ) $ 9 , e ) $ 3
Rationale: "b $ 6 5 m = xw = 8 b 5 m + xw + 8 b - - - - - $ 90 rs . 5 m + 5 m + 5 m - - - - - $ 90 rs . 15 m - - - - - - $ 90 = > 1 m = $ 6 ."
Answer: b
Question (general): two trains of equal are running on parallel lines in the same direction at 48 km / hr and 36 km / hr . the faster train passes the slower train in 36 sec . the length of each train is ?
Options: a ) 60 m , b ) 72 m , c ) 80 m , d ) 82 m , e ) 84 m
Rationale: "let the length of each train be x m . then , distance covered = 2 x m . relative speed = 48 - 36 = 12 km / hr . = 12 * 5 / 18 = 10 / 3 m / sec . 2 x / 36 = 10 / 3 = > x = 60 . answer : a"
Answer: a
Question (general): how many positive integers less than 20 can be expressed as the sum of a positive multiple of 2 and a positive multiple of 3 ?
Options: a ) 14 , b ) 13 , c ) 12 , d ) 11 , e ) 10
Rationale: "the numbers must be of the form 2 a + 3 b , 2 a + 3 b , where aa and bb are positive integers . the smallest number is 5 = 2 ∗ 1 + 3 ∗ 1.5 = 2 ∗ 1 + 3 ∗ 1 . starting with 55 , we can get all the other numbers by adding either 22 or 33 to the already existing numbers on our list . adding either 22 or 33 to 2 a + 3 b 2 a + 3 b will give another number of the same form . so , after 55 , we get 5 + 2 = 7,5 + 3 = 8,7 + 2 = 9,8 + 2 = 10 , . . . 5 + 2 = 7,5 + 3 = 8,7 + 2 = 9,8 + 2 = 10 , . . . we will get all the numbers up to 1919 inclusive , except 1,2 , 3,4 , 1,2 , 3,4 , and 6,6 , because once we have 77 and 8,8 , by adding 22 all the time we can get any odd or even number . we get a total of 19 − 5 = 1419 − 5 = 14 numbers . answer a"
Answer: a
Question (other): a number is said to be prime saturated if the product of all the different positive prime factors of t is less than the square root of t . what is the greatest two digit prime saturated integer ?
Options: a ) 99 , b ) 98 , c ) 97 , d ) 96 , e ) 95
Rationale: "t = 96 = 3 * 32 = 3 * 2 ^ 5 answer is d ."
Answer: d
Question (gain): a cycle is bought for rs . 1500 and sold for rs . 1620 , find the gain percent ?
Options: a ) 11 , b ) 8 , c ) 10 , d ) 20 , e ) 12
Rationale: "1500 - - - - 120 100 - - - - ? = > 8 % answer : b"
Answer: b
Question (general): a teacher grades students ’ tests by subtracting twice the number of incorrect responses from the number of correct responses . if student a answers each of the 100 questions on her test and receives a score of 76 , how many questions did student a answer correctly ?
Options: a ) 92 , b ) 60 , c ) 73 , d ) 82 , e ) 91
Rationale: "let the number of correct responses be x then the number of incorrect responses = 100 - x according to question x - 2 ( 100 - x ) = 76 ( subtracting twice of incorrect from correct ) 3 x = 276 x = 92 answer : a"
Answer: a
Question (gain): ravi purchased a refrigerator and a mobile phone for rs . 15000 and rs . 8000 respectively . he sold the refrigerator at a loss of 4 percent and the mobile phone at a profit of 11 percent . overall he make a .
Options: a ) 228 , b ) 288 , c ) 27 , d ) 200 , e ) 280
Rationale: "let the sp of the refrigerator and the mobile phone be rs . r and rs . m respectively . r = 15000 ( 1 - 4 / 100 ) = 15000 - 600 m = 8000 ( 1 + 11 / 100 ) = 8000 + 880 total sp - total cp = r + m - ( 15000 + 8000 ) = - 600 + 880 = rs . 280 as this is positive , an overall profit of rs . 280 was made . answer : e"
Answer: e
Question (gain): in a certain candy store , 22 % of the customers are caught sampling the candy and are charged a small fine , but 5 % of the customers who sample the candy are not caught . what is the total percent of all customers who sample candy ?
Options: a ) 22 % , b ) 23 % , c ) 24 % , d ) 25 % , e ) 34 %
Rationale: "since 5 % of the customers who sample the candyare notcaught , then 88 % of the customers who sample the candyarecaught : { % of customers who sample candy } * 0.95 = 0.22 ; { % of customers who sample candy } = 0.231 . answer : b ."
Answer: b
Question (general): the average of first 22 natural numbers is ?
Options: a ) 11.6 , b ) 11.5 , c ) 12.9 , d ) 15.4 , e ) 15.1
Rationale: "sum of 22 natural no . = 506 / 2 = 253 average = 253 / 22 = 11.5 answer : b"
Answer: b
Question (general): in a certain deck of cards , each card has a positive integer written on it , in a multiplication game a child draws a card and multiplies the integer on the card with the next large integer . if the each possible product is between 10 and 400 , then the least and greatest integer on the card would be
Options: a ) 3 and 15 , b ) 3 and 20 , c ) 4 and 13 , d ) 4 and 14 , e ) 5 and 14
Rationale: "given : 10 < x ( x + 1 ) < 400 . now , it ' s better to test the answer choices here rather than to solve : if x = 3 then x ( x + 1 ) = 12 > 10 - - > so , the least value is 3 . test for the largest value : if x = 20 then x ( x + 1 ) = 20 * 21 = 420 > 400 answer : b ."
Answer: b
Question (general): p , q and r have $ 4000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?
Options: a ) 2400 , b ) 2403 , c ) 3998 , d ) 2539 , e ) 1600
Rationale: "e 1600 let the amount with r be $ r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 4000 - r ) = > 3 r = 8000 - 2 r = > 5 r = 8000 = > r = 1600 ."
Answer: e
Question (physics): rahul and sham together can complete a task in 35 days , but rahul alone can complete same work in 60 days . calculate in how many days sham can complete this work ?
Options: a ) 84 days , b ) 82 days , c ) 76 days , d ) 68 days , e ) 60 days
Rationale: explanation : as rahul and sham together can finish work in 35 days . 1 days work of rahul and sham is 1 / 35 rahul can alone complete this work in 60 days , so , rahul one day work is 1 / 60 clearly , sham one day work will be = ( rahul and sham one day work ) - ( rahul one day work ) = 1 / 35 - 1 / 60 = 1 / 84 hence sham will complete the given work in 84 days . answer is a
Answer: a
Question (physics): a train running at the speed of 60 km / hr crosses a pole in 6 sec . what is the length of the train ?
Options: a ) 356 , b ) 278 , c ) 127 , d ) 100 , e ) 150
Rationale: "speed = 60 * 5 / 18 = 50 / 3 m / sec length of the train = speed * time = 50 / 3 * 6 = 100 m answer : d"
Answer: d