Cheukting/mathqa huggingface dataset:
Question (general): a batsman scored 80 runs which included 2 boundaries and 2 sixes . what percent of his total score did he make by running between the wickets ?
Options: a ) 45 % , b ) 500 / 11 , c ) 75 % , d ) 55 % , e ) 35 %
Rationale: "explanation : number of runs made by running , = > 80 − ( 2 × 4 + 2 × 6 ) . = > 80 − 20 = > 60 hence , the required percentage is : - = > 60 / 80 * 100 = > 75 % answer : c"
Answer: c
Question (physics): a certain car can travel 20 minutes on a gallon of gasoline at 60 miles per hour . if the car had started with a full tank and had 8 gallons of gasoline left in its tank at the end , then what percent of the tank was used to travel 80 miles at 60 mph ?
Options: a ) 16.67 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 40 %
Rationale: "let , tank capacity = t gallon used fuel = ( t - 8 ) gallons distance travelled ( @ 60 miles / hr ) = 80 miles distance travelled in 1 gallon = distance travelled in 20 mins ( @ 60 miles / hr ) = ( 60 / 60 ) * 20 = 20 miles fuel used to travel 80 miles = ( 80 / 20 ) = 4 gallon i . e . used fuel = ( t - 8 ) = 4 gallon i . e . t = 12 gallons i . e . used fuel = ( 2 / 12 ) * 100 = 16,67 % a"
Answer: a
Question (physics): there is a church tower 150 feet tall and another catholic tower at a distance of 350 feet from it which is 200 feet tall . there is one each bird sitting on top of both the towers . they fly at a constant speed and time to reach a grain in b / w the towers at the same time . at what distance from the church is the grain ?
Options: a ) 170 meters , b ) 160 meters , c ) 150 meters , d ) 140 meters , e ) 130 meters
Rationale: if x ft is the distance of grain from 200 ft tall tower , then 150 ^ 2 + ( 350 - x ) ^ 2 = 200 ^ 2 + x ^ 2 then x = 150 meters answer : c
Answer: c
Question (gain): for 1 rs 4 p interest wat will be for 5000 rs ?
Options: a ) 350 rs , b ) 450 rs , c ) 200 rs , d ) 30 rs , e ) 448 rs
Rationale: for 1 rs , 4 p interest for 5000 rs , x x = 5000 / 1 * 4 p = = > 20000 paise to express in rs , 20000 / 100 = 200 rs answer : c
Answer: c
Question (physics): a train running at the speed of 60 km / hr crosses a pole in 15 seconds . find the length of the train .
Options: a ) 150 m , b ) 145 m , c ) 240 m , d ) 135 m , e ) 250 m
Rationale: "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 15 = 250 meter answer : e"
Answer: e
Question (gain): a sum was put at simple interest at a certain rate for 10 years . had it been put at 5 % higher rate , it would have fetched rs . 600 more . what was the sum ?
Options: a ) rs . 1200 , b ) rs . 1300 , c ) rs . 1400 , d ) rs . 1500 , e ) none of these
Rationale: "explanation : at 5 % more rate , the increase in s . i for 10 years = rs . 600 ( given ) so , at 5 % more rate , the increase in si for 1 year = 600 / 10 = rs . 60 / - i . e . rs . 60 is 5 % of the invested sum so , 1 % of the invested sum = 60 / 5 therefore , the invested sum = 60 × 100 / 5 = rs . 1200 answer : a"
Answer: a
Question (gain): a shop owner sells 60 mtr of cloth and gains sp of 10 mtrs . find the gain % ?
Options: a ) 20 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 70 %
Rationale: "here , selling price of 10 m cloth is obtained as profit . profit of 10 m cloth = ( s . p . of 60 m cloth ) – ( c . p . of 60 m cloth ) selling price of 50 m cloth = selling price of 60 m of cloth let cost of each metre be rs . 100 . therefore , cost price of 50 m cloth = rs . 5000 and s . p . of 50 m cloth = rs . rs . 6000 profit % = 10 / 50 × 100 = 20 % 20 profit of 20 % was made by the merchant . a"
Answer: a
Question (general): a no . when divided by 221 gives a remainder 43 , what remainder will beobtained by dividingthe same no . 17 ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 10 , e ) 12
Rationale: "221 + 43 = 264 / 17 = 9 ( remainder ) c"
Answer: c
Question (other): in a certain pet shop , the ratio of dogs to cats to bunnies in stock is 4 : 7 : 9 . if the shop carries 364 dogs and bunnies total in stock , how many dogs are there ?
Options: a ) 42 , b ) 66 , c ) 98 , d ) 112 , e ) 154
Rationale: "let us assume the number of dogs , cats and bunnies to be 4 x , 7 x and 9 x total dogs and bunnies = 13 x . and we are given that 13 x = 364 . hence x = 28 . dogs = 4 x = 4 * 28 = 112 ( option d )"
Answer: d
Question (gain): albert invested rs . 6500 in a scheme for 2 years at compound interest rate 6.5 % p . a . how much amount will albert get on maturity of the fixed deposit ?
Options: a ) s . 8829 , b ) s . 7200 , c ) s . 7200.5 , d ) s . 4000 , e ) s . 7372.46
Rationale: amount = [ 6500 * ( 1 + 6.5 / 100 ) 2 ] = 6500 * 106.5 / 100 * 106.5 / 100 = rs . 7372.46 answer : e
Answer: e
Question (general): keats library purchases a number of new books , all in the category of biography , and the library does not acquire any other books . with the addition of the new biographies , the biography collection of the library amounts to 30 % of the total number of books in the library . if prior to the purchase , only 20 % of the books in keats library were biographies , by what percent has the number of biographies in the library increased ?
Options: a ) 47 % , b ) 59 % , c ) 71 % , d ) 83 % , e ) 95 %
Rationale: "let x be the number of new biographies added to the library . let b be the original number of biographies , so the original number of books was 5 b . 0.3 ( 5 b + x ) = b + x 0.5 b = 0.7 x x = 0.71 b the answer is c ."
Answer: c
Question (general): if the average ( arithmetic mean ) of the 4 numbers 3 , 16 , 33 , and ( n + 1 ) is 20 , then n =
Options: a ) 19 , b ) 20 , c ) 21 , d ) 27 , e ) 29
Rationale: 3 + 16 + 33 + n + 1 = 20 x 4 = 80 = > n + 53 = 80 = > n = 27 answer d
Answer: d
Question (general): the mean of 50 observations is 200 . but later he found that there is decrements of 6 from each observations . what is the the updated mean is ?
Options: a ) 165 , b ) 185 , c ) 190 , d ) 198 , e ) 194
Rationale: 194 answer is e
Answer: e
Question (general): country c imposes a two - tiered tax on imported cars : the first tier imposes a tax of 12 % of the car ' s price up to a certain price level . if the car ' s price is higher than the first tier ' s level , the tax on the portion of the price that exceeds this value is 8 % . if ron imported a $ 14,000 imported car and ended up paying $ 1440 in taxes , what is the first tier ' s price level ?
Options: a ) $ 1600 , b ) $ 6000 , c ) $ 6050 , d ) $ 7050 , e ) $ 8000
Rationale: "let t be the tier price , p be total price = 14000 per the given conditions : 0.12 t + 0.08 ( p - t ) = 1440 - - - - > t = 8000 . e is the correct answer ."
Answer: e
Question (gain): a sum fetched a total simple interest of rs . 144 at the rate of 15 p . c . p . a . in 1 year 6 months . what is the sum ?
Options: a ) 490 , b ) 850 , c ) 580 , d ) 640 , e ) 760
Rationale: "sol . principal = rs . [ 100 * 144 / 15 * ( 18 / 12 ) ] = rs . [ 14400 / 22.5 ] = rs . 640 . answer d"
Answer: d
Question (physics): the ` ` racing magic ' ' takes 120 seconds to circle the racing track once . the ` ` charging bull ' ' makes 40 rounds of the track in an hour . if they left the starting point together , how many minutes will it take for them to meet at the starting point for the second time ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: time taken by racing magic to make one circle = 120 seconds = 2 mins time taken by ` ` charging bull ' ' to make one circle = 60 mins / 40 = 1.5 mins = 90 seconds lcm of 90 and 120 seconds = 360 seconds = 6 mins time taken for them to meet at the starting point for the second time = 6 mins * 2 = 12 mins answer d
Answer: d
Question (general): find the constant k so that : - x 2 - ( k + 10 ) x - 8 = - ( x - 2 ) ( x - 4 )
Options: a ) 11 , b ) 12 , c ) 16 , d ) 14 , e ) 15
Rationale: "- x 2 - ( k + 10 ) x - 8 = - ( x - 2 ) ( x - 4 ) : given - x 2 - ( k + 10 ) x - 8 = - x 2 + 6 x - 8 - ( k + 10 ) = 6 : two polynomials are equal if their corresponding coefficients are equal . k = - 16 : solve the above for k correct answer c"
Answer: c
Question (general): 102 ã — 102 + 98 ã — 98 = ?
Options: a ) 20018 , b ) 20028 , c ) 20108 , d ) 10008 , e ) 20008
Rationale: "explanation : ( a + b ) 2 + ( a â ˆ ’ b ) 2 = 2 ( a 2 + b 2 ) ( reference : basic algebraic formulas ) 1022 + 982 = ( 100 + 2 ) 2 + ( 100 â ˆ ’ 2 ) 2 = 2 ( 1002 + 22 ) = 2 ( 10000 + 4 ) = 20008 . answer : option e"
Answer: e
Question (physics): two trains 140 m and 190 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
Options: a ) 11.88 sec , b ) 13.8 sec , c ) 53.8 sec , d ) 10.8 sec , e ) 10.4 sec
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 140 + 190 = 330 m . required time = 330 * 9 / 250 = 11.88 sec . answer : a :"
Answer: a
Question (gain): mary works in a restaurant a maximum of 70 hours . for the first 20 hours , she is paid $ 8 per hour . for each overtime hour , she is paid at a rate which is 25 % higher than her regular rate . how much mary can earn in a week ?
Options: a ) 600 , b ) 620 , c ) 660 , d ) 320 , e ) 400
Rationale: "mary receives $ 8 ( 20 ) = $ 160 for the first 20 hours . for the 50 overtime hours , she receives $ 8 ( 0.25 ) + $ 8 = $ 10 per hour , that is $ 50 ( 20 ) = $ 500 . the total amount is $ 160 + $ 500 = $ 660 answer c 660 ."
Answer: c
Question (geometry): the area of a circular field is 17.56 hectares . find the cost of fencing it at the rate of rs . 4 per metre approximately
Options: a ) 4457 , b ) 4567 , c ) 5943 , d ) 4547 , e ) 4675
Rationale: "explanation : area = ( 17.56 x 10000 ) m 2 = 175600 m 2 . π r 2 = 175600 ⇔ ( r ) 2 = ( 175600 x ( 7 / 22 ) ) ⇔ r = 236.37 m . circumference = 2 π r = ( 2 x ( 22 / 7 ) x 236.37 ) m = 1485.78 m . cost of fencing = rs . ( 1485.78 x 4 ) = rs . 5943 . answer : option c"
Answer: c
Question (general): 49 × 49 × 49 × 49 = 7 ?
Options: a ) 4 , b ) 7 , c ) 8 , d ) 16 , e ) none of these
Rationale: "49 × 49 × 49 × 49 = 7 ? or , 7 ( 2 ) × 7 ( 2 ) × 7 ( 2 ) × 7 ( 2 ) = 7 ? or 7 ( 8 ) = 7 ? or , ? = 8 answer c"
Answer: c
Question (general): 30 pens and 75 pencils were purchased for 750 . if the average price of a pencil was 2.00 , find the average price of a pen .
Options: a ) 20 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "since average price of a pencil = 2 ∴ price of 75 pencils = 150 ∴ price of 30 pens = ( 750 – 150 ) = 600 ∴ average price of a pen = 600 ⁄ 60 = 20 answer a"
Answer: a
Question (other): the h . c . f of two numbers is 23 and the other two factors of their l . c . m are 16 and 17 . the larger of the two numbers is :
Options: a ) 338 , b ) 278 , c ) 322 , d ) 231 , e ) 391
Rationale: "clearly , the numbers are ( 23 * 16 ) and ( 23 * 17 ) . larger number = ( 23 * 17 ) = 391 . answer : e"
Answer: e
Question (physics): to fill a tank , 25 buckets of water is required . how many buckets of water will be required to fill the same tank if the capacity of bucket is reduced to two - fifth of its present ?
Options: a ) 52.5 , b ) 62.5 , c ) 72.5 , d ) 82.5 , e ) 81.5
Rationale: explanation : let the capacity of 1 bucket = x . then , capacity of tank = 25 x . new capacity of bucket = 2 / 5 x . required no of buckets = 25 x / ( 2 x / 5 ) = 62.5 answer is b
Answer: b
Question (general): the visitors of a modern art museum who watched a certain picasso painting were asked to fill in a short questionnaire indicating whether they had enjoyed looking at the picture and whether they felt they had understood it . according to the results of the survey , all 110 visitors who did not enjoy the painting also did not feel they had understood the painting , and the number of visitors who enjoyed the painting was equal to the number of visitors who felt they had understood the painting . if 3 / 4 of the visitors who answered the questionnaire both enjoyed the painting and felt they had understood the painting , then how many visitors answered the questionnaire ?
Options: a ) 90 , b ) 120 , c ) 160 , d ) 360 , e ) 440
Rationale: "if we exclude those cases and take the question at face value , then it seems straightforward . group # 1 = ( did n ' t like , did n ' t understand ) = 110 group # 2 = ( like understood ) = 3 / 4 ( 1 / 4 ) n = 110 n = 440 answer = ( e )"
Answer: e
Question (geometry): a rectangular lawn of length 200 m by 120 m has two roads running along its center , one along the length and the other along the width . if the width of the roads is 5 m what is the area r covered by the two roads ?
Options: a ) 400 , b ) 1550 , c ) 1575 , d ) 1600 , e ) 1625
Rationale: "area covered by road along the length = 5 * 200 = 1000 square meter area covered by road along the width = 5 * 120 = 600 square meter common area in both roads ( where the roads intersect ) = square with side 5 meter = 5 * 5 = 25 total area of the roads r = 1000 + 600 - 25 = 1575 answer : option c"
Answer: c
Question (physics): a and b can together finish a work in 40 days . they worked together for 10 days and then b left . after another 21 days , a finished the remaining work . in how many days a alone can finish the job ?
Options: a ) 10 , b ) 25 , c ) 60 , d ) 30 , e ) 28
Rationale: "a + b 10 days work = 10 * 1 / 40 = 1 / 4 remaining work = 1 - 1 / 4 = 3 / 4 3 / 4 work is done by a in 21 days whole work will be done by a in 21 * 4 / 3 = 28 days answer is e"
Answer: e
Question (general): how many integers are between 6 and 74 / 5 , inclusive ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 9
Rationale: "74 / 5 = 14 . xx we are not concerned about the exact value of 74 / 5 as we just need the integers . since the values are small , we can write down the integers . the different integers between 6 and 74 / 5 would be 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13,14 total number of integers = 9 option e"
Answer: e
Question (general): what is the smallest positive integer x such that 180 - x is the cube of a positive integer
Options: a ) 50 , b ) 52 , c ) 60 , d ) 55 , e ) 12
Rationale: "given 180 - x is a perfect cube so we will take 125 = 5 * 5 * 5 180 - x = 125 x = 180 - 125 = 55 correct option is d"
Answer: d
Question (geometry): what will be the cost of building to paint which area equal to 196 sq ft , if the price per foot of building is rs . 15 ?
Options: a ) 120
b ) 240
c ) 360
d ) 380
e ) 840
Rationale: let the side of the square plot be a ft . a 2 = 196 = > a = 14 length of the fence = perimeter of the plot = 4 a = 56 ft . cost of building the fence = 56 * 15 = rs . 840 . answer : e
Answer: e
Question (general): in the youth summer village there are 175 people , 100 of them are not working , 75 of them have families and 125 of them like to sing in the shower . what is the largest possible number of people in the village , which are working , that do n ' t have families and that are singing in the shower ?
Options: a ) 70 , b ) 75 , c ) 85 , d ) 80 , e ) 100
Rationale: "total = 175 not working = 100 having family = 75 like to sing in shower = 125 working = 175 - 100 = 75 not having family = 175 - 75 = 100 like to sing in shower = 100 largest possible number is the lowest possible among the above thus 75 b"
Answer: b
Question (general): if it takes a tub 3 minutes to drain 6 / 7 of its content , how much more time will it take for the tub to be empty ?
Options: a ) 30 seconds , b ) 1 minute , 12 seconds , c ) 1 minute , 50 seconds , d ) 2 minutes , 14 seconds , e ) 4 minutes , 12 seconds
Rationale: "if 6 / 7 of tub ' s content is drained 1 / 7 th of tub still needs to be drained . if it takes 3 minutes to drain 6 / 7 th of tub it takes 3 * ( 7 / 6 ) minutes to drain the entire tub and 3 * ( 7 / 6 ) * ( 1 / 7 ) min to drain 1 / 7 th of the tub which is 6 / 5 minutes or 0.5 minutes or 30 seconds so answer is a"
Answer: a
Question (general): exactly 3 sides of a certain 10 - sided die are red . what is the probability that kumar rolls the die 3 times and the die lands with a red side up for the first time on the third roll ?
Options: a ) 0.184 , b ) 0.16 , c ) 0.18 , d ) 0.147 , e ) 0.148
Rationale: total no . of sides = 10 sides that are red = 3 probability that the die lands with red side up = 3 / 10 therefore , probability that the die does not land with red side up = 1 - 3 / 10 = 7 / 10 probability that kumar rolls the die 3 times and the die lands with a red side up for the first time on the third roll = ( 1 st roll - non red face ) x ( 2 nd roll - non red face ) x ( 3 rd roll - red face ) = ( 7 / 10 ) x ( 7 / 10 ) x ( 3 / 10 ) = 128 / 1000 = 0.147 d
Answer: d
Question (general): the average runs scored by a batsman in 25 matches is 45 . in the next 7 matches the batsman scored an average of 15 runs . find his average in all the 32 matches ?
Options: a ) 31355 , b ) 38.44 , c ) 29.55 , d ) 97.66 , e ) 45.66
Rationale: total score of the batsman in 25 matches = 1125 . total score of the batsman in the next 7 matches = 105 . total score of the batsman in the 32 matches = 1230 . average score of the batsman = 1230 / 32 = 38.44 . answer : b
Answer: b
Question (gain): carl is facing very difficult financial times and can only pay the interest on a $ 10,000 loan he has taken . the bank charges him a quarterly compound rate of 4 % . what is the approximate interest he pays annually ?
Options: a ) $ 1750 , b ) $ 2000 , c ) $ 2150 , d ) $ 2500 , e ) $ 12000
Rationale: "an easy way too attempt this is by approximation : for the first quarter , he pays 4 % of 10,000 which is $ 400 . so for the four quarters in the year , he will approximately play 400 * 4 = 1600 over the entire year . because of compound interest it will be more than 1600 . approx . option a is correct . answer : a"
Answer: a
Question (physics): jack and jill work at a hospital with 7 other workers . for an internal review , 2 of the 9 workers will be randomly chosen to be interviewed . what is the probability that jack and jill will both be chosen ?
Options: a ) 1 / 3 , b ) 1 / 4 , c ) 1 / 15 , d ) 3 / 8 , e ) 1 / 36
Rationale: "1 / 9 c 2 = 1 / 36 . answer : e ."
Answer: e
Question (general): a student has to obtain 50 % of the total marks to pass . he got 200 marks and failed by 20 marks . the maximum marks are ?
Options: a ) 510 , b ) 520 , c ) 530 , d ) 540 , e ) 440
Rationale: "let the maximum marks be x then , 50 % of x = 200 + 20 50 x / 100 = 220 50 x = 220 * 100 = 22000 x = 440 answer is e"
Answer: e
Question (other): the cost of 3 pens and 5 pencils is rs . 150 . also the cost of one pen and one pencil is in the ratio of 5 : 1 respectively . what is the cost of one dozen pens ?
Options: a ) rs . 200 , b ) rs . 250 , c ) rs . 300 , d ) rs . 450 , e ) none of these
Rationale: "explanation : let the cost of one pen is ‘ 5 x ’ and pencil is ‘ x ’ 3 x 5 x + 5 x = rs . 150 15 x + 5 x = rs . 150 x = 150 / 20 = 7.50 : . cost of 1 pen = 5 x = 5 x 7.50 = 37.50 : . cost of 12 pens , i . e . ( one dozen ) = 37.50 x 12 = rs . 450 answer : option d"
Answer: d
Question (general): car dealership x , the total profit from sales increased by 8 percent over the previous years , while the number of cars sold decreased by 8 percent over the previous years . approximately what was the average percent increase in profit per car over the previous year .
Options: a ) 17.39 % , b ) 20 % , c ) 22 % , d ) 23 % , e ) 25 %
Rationale: "let profit be x and cars sold be y originally profit / car = x / y now it is 1.08 x / 0.92 y = 108 / 92 ( x / y ) increase in profit per car = ( ( 16 / 92 ) ( x / y ) ) / ( x / y ) * 100 = 17.39 % answer = a"
Answer: a
Question (general): the product z of two prime numbers is between 16 and 40 . if one of the prime numbers is greater than 2 but less than 6 and the other is greater than 12 but less than 30 then what is z ?
Options: a ) 21 , b ) 22 , c ) 28 , d ) 35 , e ) 39
Rationale: "the smallest possible product is 39 which is 3 * 13 . all other products are too big . the answer is e ."
Answer: e
Question (probability): if 4 people are selected from a group of 8 married couples , what is the probability that none of them would be married to each other ?
Options: a ) 1 / 33 , b ) 2 / 33 , c ) 8 / 13 , d ) 16 / 33 , e ) 11 / 12
Rationale: "if we are to select 4 people from 8 couples without any restriction , how many ways can we make the selection ? 16 ! / 4 ! 12 ! = 1820 if we are to select 4 people from 8 couples with restriction that no married couple can both make it to the group , only a representative ? 8 ! / 4 ! 4 ! = 70 but we know that to select a person from each couple , take 2 possibilities 70 * 2 * 2 * 2 * 2 = 1120 probability = desired / all possibilities = 1120 / 1820 = 8 / 13 answer : c"
Answer: c
Question (general): the tax on a commodity is diminished by 20 % but its consumption is increased by 10 % . find the decrease percent in the revenue derived from it ?
Options: a ) 20 % , b ) 19 % , c ) 15 % , d ) 12 % , e ) 24 %
Rationale: "answer : option d 100 * 100 = 10000 80 * 110 = 8800 10000 - - - - - - - 1200 100 - - - - - - - ? = 12 %"
Answer: d
Question (gain): a store sells chairs and tables . if the price of 2 chairs and 1 table is 60 % of the price of 1 chair and 2 tables , and the price of 1 table and 1 chair is $ 72 , what is the price , in dollars , of 1 table ? ( assume that every chair has the same price and every table has the same price . )
Options: a ) 55 , b ) 84 , c ) 63 , d ) 75 , e ) 70
Rationale: "let c = chair ; t = table 2 c + 1 t = 0.6 ( 1 c + 2 t ) or c ( 2 - 0.6 ) = 1.2 t - 1 t or 1.4 c = 0.2 t therefore c = 0.2 / 1.4 t = 1 / 7 t ic + 1 t = 72 or 1 / 7 t + 1 t = 60 therefore t = 72 * 7 / 8 = 63 c"
Answer: c
Question (general): a small pool filled only with water will require an additional 300 gallons of water in order to be filled to 80 % of its capacity . if pumping in these additional 300 gallons of water will increase the amount of water in the pool by 25 % , what is the total capacity of the pool in gallons ?
Options: a ) 1875 , b ) 1250 , c ) 1300 , d ) 1600 , e ) 1625
Rationale: "300 gallons of water increases capacity by 25 % that means 25 % is 300 gallons , so 100 % would be = 300 * 100 / 25 = 1200 gallons now 1200 + 300 gallons is 80 % capacity of tank . so 100 % capacity would be = 1500 * 100 / 80 = 1875 a is the answer"
Answer: a
Question (physics): at 3 : 40 , the hour hand and the minute hand of a clock form an angle of
Options: a ) 160 ° , b ) 180 ° , c ) 130 ° , d ) 110 ° , e ) 150 °
Rationale: "angle between hands of a clock when the minute hand is behind the hour hand , the angle between the two hands at m minutes past h ' o clock = 30 ( h − m / 5 ) + m / 2 degree when the minute hand is ahead of the hour hand , the angle between the two hands at m minutes past h ' o clock = 30 ( m / 5 − h ) − m / 2 degree here h = 3 , m = 40 and minute hand is ahead of the hour hand . hence the angle = 30 ( m / 5 − h ) − m / 2 = 30 ( 40 / 5 − 3 ) − 40 / 2 = 30 ( 8 − 3 ) − 20 = 30 × 5 − 20 = 130 ° answer is c ."
Answer: c
Question (gain): heinz produces tomato puree by boiling tomato juice . the tomato puree has only 20 % water while the tomato juice has 90 % water . how many liters of tomato puree will be obtained from 20 litres of tomato juice ?
Options: a ) 2.8 liters . , b ) 2.5 liters . , c ) 8.5 liters . , d ) 2.6 liters . , e ) 2.1 liters .
Rationale: "answer : explanation : in each of the solutions , there is a pure tomato component and some water . so while boiling , water evaporates but tomato not . so we equate tomato part in the both equations . ⇒ ⇒ 10 % ( 20 ) = 80 % ( x ) ⇒ ⇒ x = 2.5 liters . answer : b"
Answer: b
Question (general): if 2 ^ 5 , 3 ^ 3 , and 14 ^ 2 are all factors of the product of 936 and w where w is a positive integer , what is the smallest possible value of w ?
Options: a ) 26 , b ) 39 , c ) 42 , d ) 65 , e ) 168
Rationale: here 156 has three two ' s two three ' s and one 14 rest of them must be in w so w = 14 * 3 * 4 = 168 smash e
Answer: e