Cheukting/mathqa huggingface dataset:
Question (general): 324 ã · ? ã — 15 + 270 = 405
Options: a ) 24 , b ) 25 , c ) 36 , d ) 39 , e ) 43
Rationale: "explanation : 324 ã · ? ã — 15 = 405 - 270 = 135 ( 324 ã — 15 ) / ? = 135 ? = ( 324 ã — 15 ) / 135 = 36 answer : option c"
Answer: c
Question (gain): the cash difference between the selling prices of an article at a profit of 4 % and 6 % is rs . 3 . the ratio of the two selling prices is ?
Options: a ) 52 : 56 , b ) 52 : 53 , c ) 52 : 50 , d ) 22 : 56 , e ) 52 : 51
Rationale: "let c . p . of the article be rs . x . then , required ratio = 104 % of x / 106 % of x = 104 / 106 = 52 / 53 = 52 : 53 answer : b"
Answer: b
Question (other): lovely shop runs a sale on goldfish and platys . if one customer buys 13 goldfish and 12 platys for $ 5.60 , and another buys 14 goldfish and 21 platys for $ 8.05 , what is the ratio of the price of goldfish to platys ?
Options: a ) 0.8 , b ) 0.75 , c ) c ) 8 / 9 , d ) 5 / 7 , e ) 6 / 8
Rationale: the approach of plugging in the numbers is a fine approach . but , in this case , the answer was the first option and thus , by plugging in a number in the ration given , we arrived at the answer quickly ! however , what if the correct ratio was option d or c ? in any case , the algebraic solution is n ' t that complex if you realize a key concept : the number 7 can be factored out of the second equation ! here ' s the working : lovely shop runs a sale on goldfish and platys . 13 x + 12 y = 5.60 < < < < < equation 1 14 x + 21 y = 8.05 < < < < < equation 2 2 x + 3 y = 1.15 [ factor out 7 from equation 2 ] < < < < < equation 3 8 x + 12 y = 4.6 [ multiply equation 3 with 4 ] 5 x = 1.0 [ equation 1 - equation 2 ] x = 0.2 3 y = 1.15 - 0.4 = 0.75 [ substitute for x in equation 1 ] y = 0.25 x / y = 0.2 / 0.25 = 20 / 25 = 4 / 5 = 0.8 [ answer a ] the whole thing must have taken me about 45 s : d
Answer: d
Question (gain): a football team lost 5 yards and then gained 9 . what is the team ' s progress ?
Options: a ) 1 , b ) 3 , c ) 2 , d ) 4 , e ) 5
Rationale: "for lost , use negative . for gain , use positive . progress = - 5 + 9 = 4 yards correct answer is d ) 4"
Answer: d
Question (general): in expressing a length 810472 km as nearly as possible with 3 significant digits , find the percentage error .
Options: a ) 0.034 , b ) 0.024 , c ) 0.352 , d ) 0.063 , e ) 0.026
Rationale: error = ( 81.5 – 81.472 ) km = 0.028 . required percentage = [ ( 0.028 / 81.472 ) * 100 ] % = 0.034 % . answer a .
Answer: a
Question (general): the amount of an investment will double in approximately 70 / p years , where p is the percent interest , compounded annually . if thelma invests $ 40,000 in a long - term cd that pays 5 percent interest , compounded annually , what will be the approximate total value of the investment when thelma is ready to retire 42 years later ?
Options: a ) $ 280,000 , b ) $ 320,000 , c ) $ 360,000 , d ) $ 450,000 , e ) $ 540,000
Rationale: "the amount of an investment will double in approximately 70 / p years , where p is the percent interest , compounded annually . if thelma invests $ 40,000 in a long - term cd that pays 5 percent interest , compounded annually , what will be the approximate total value of the investment when thelma is ready to retire 42 years later ? the investment gets doubled in 70 / p years . therefore , the investment gets doubled in 70 / 5 = every 14 years . after 42 years , the investment will get doubled 42 / 14 = 3 times . so the amount invested will get doubled thrice . so , 40000 * 2 = 80000 80000 * 2 = 160000 160000 * 2 = 320000 hence , the answer is b ."
Answer: b
Question (other): 140 college students were asked in a survey if they preferred windows or mac brand computers . 80 students claimed that they preferred mac to windows brand computers . one third as many of the students who preferred mac to windows , equally preferred both brands . 50 of the students had no preference . how many of the students in the survey preferred windows to mac brand computers ?
Options: a ) 25 , b ) 10 , c ) 50 , d ) 60 , e ) 75
Rationale: "140 = 80 ( mac ) + x ( window ) + 50 ( both ) = > x = 10 answer : b"
Answer: b
Question (general): there are 5 more women than there are men on a local co - ed softball team . if there are a total of 15 players on the team , what is the ratio of men to women ?
Options: a ) 10 / 16 , b ) 6 / 16 , c ) 5 / 10 , d ) 6 / 10 , e ) 4 / 10
Rationale: w = m + 5 w + m = 15 m + 5 + m = 15 2 m = 10 m = 5 w = 10 ratio : 5 : 10 ans : c
Answer: c
Question (other): each factor of 210 is inscribed on its own plastic ball , and all of the balls are placed in a jar . if a ball is randomly selected from the jar , what is the probability that the ball is inscribed with a multiple of 42 ?
Options: a ) 1 / 16 , b ) 5 / 42 , c ) 1 / 8 , d ) 3 / 16 , e ) 1 / 4
Rationale: "210 = 2 * 3 * 5 * 7 , so the # of factors 210 has is ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 16 ( see below ) ; 42 = 2 * 3 * 7 , so out of 16 factors only two are multiples of 42 : 42 and 210 , itself ; so , the probability is 2 / 16 = 1 / 8 . answer : c ."
Answer: c
Question (physics): a can do a work in 3 days . b can do in 6 days . if both a & b are working together in how many days they can finish the work ?
Options: a ) 1 , b ) 3 , c ) 2 , d ) 4 , e ) 5
Rationale: "1 day work of a = 1 / 3 1 day work of b = 1 / 6 1 day work of a & b = 1 / 3 + 1 / 6 = 1 / 2 a & b finish the work in 2 days answer is c"
Answer: c
Question (gain): the population of a village is 6000 . it decreases annually at the rate of 10 % p . a . what will be its population after 2 years ?
Options: a ) 5000 , b ) 4860 , c ) 5400 , d ) 4800 , e ) 5120
Rationale: formula : ( after = 100 denominator ago = 100 numerator ) 6000 ã — 90 / 100 ã — 90 / 100 = 4860 b
Answer: b
Question (general): what is the value of 3 x ^ 2 − 2 x + 0.3 for x = 0.5 ?
Options: a ) − 0.3 , b ) 0 , c ) 0.05 , d ) 1.08 , e ) 2.46
Rationale: "3 x ^ 2 - 2 x + 0.3 for x = 0.6 = 3 ( 0.5 * 0.5 ) - 4 * 0.5 * ( 0.5 ) + 0.3 = - 0.5 * 0.5 + 0.3 = - 0.25 + 0.3 = 0.05 correct option : c"
Answer: c
Question (physics): excluding the stoppages , the speed of a bus is 64 km / hr and including the stoppages the speed of the bus is 48 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 15 min , b ) 10 min , c ) 12 min , d ) 20 min , e ) 18 min
Rationale: "speed of the bus without stoppage = 64 km / hr speed of the bus with stoppage = 48 km / hr difference in speed = 16 km / hr so , the time taken in the stoppages = time taken to cover 16 km = ( 16 / 64 ) hr = 1 / 4 hr = 15 min answer : a"
Answer: a
Question (general): an analysis of the monthly incentives received by 5 salesmen : the mean and median of the incentives is $ 7000 . the only mode among the observations is $ 12000 . incentives paid to each salesman were in full thousands . what is the difference z between the highest and the lowest incentive received by the 5 salesmen in the month ?
Options: a ) $ 4000 , b ) $ 5000 , c ) $ 9000 , d ) $ 11000 , e ) $ 13000
Rationale: break down the question in to steps : step # 1 : incentives received by 5 salesmen - - > abcde step # 2 : mean and median of the incentives is $ 7000 : via number properties - - > total incentives = 7000 * 5 = 35000 ab 7000 de step # 3 : only mode among the observations is $ 12000 : mode is the value that appears most often in a set of data . therefore 12000 must occur more then once and since 12000 is larger than the mean ( 7000 ) the most it can occur is twice in our list . if we place the numbers in ascending order we haveab 70001200012000 step # 4 : what is the difference z between the highest and the lowest incentive : - the total paid has to equal mean * # of numbers = 7000 * 5 = 35 000 . - the three values we have so far ( 12000 12000 and 7000 ) equal 31000 . - therefore the first two numbers ( ab ) must equal 4000 - there is only one mode which is 12000 , therefore 4000 must be equal to a set of two numbers that are not the and a < b if a = 1000 b = 3000 - - > difference between the highest and the lowest incentive = 12000 - 1000 = 11000 no other options for a or b to fit the criteria final list : 1000300070001200012000 answer d
Answer: d
Question (general): 6000 , 1200 , 300 , 60 . . .
Options: a ) 30 , b ) 15 , c ) 20 , d ) 36 , e ) 46
Rationale: "6000 / 5 = 1200 1200 / 4 = 300 300 / 5 = 60 60 / 4 = 15 answer : b"
Answer: b
Question (other): the ratio of 2 numbers is 10 : 20 and their h . c . f . is 100 . their l . c . m . is ?
Options: a ) 1100 , b ) 3000 , c ) 2100 , d ) 1000 , e ) 2000
Rationale: "let the numbers be 10 x and 20 x their h . c . f . = 100 so the numbers are 10 * 100 , 20 * 100 = 1000 , 2000 l . c . m = 2000 answer is e"
Answer: e
Question (other): if the numbers 1 to 97 are written on 97 pieces of paper , ( one on each ) and one piece is picked at random , then what is the probability that the number drawn is neither prime nor composite ?
Options: a ) 1 / 50 , b ) 1 / 25 , c ) 1 / 97 , d ) 1 , e ) 2
Rationale: "there are 25 primes , 71 composite numbers from 1 to 97 . the number which is neither prime nor composite is 1 . therefore , required probability = 1 / 97 . answer : c"
Answer: c
Question (general): 3.5 can be expressed in terms of percentage as ?
Options: a ) 0.35 % , b ) 3.5 % , c ) 35 % , d ) 350 % , e ) 0.0035 %
Rationale: "answer : option d 3.5 = 35 / 10 = ( 35 / 10 * 100 ) = 350 %"
Answer: d
Question (geometry): a rectangular photograph is surrounded by a border that is 2 inch wide on each side . the total area of the photograph and the border is m square inches . if the border had been 4 inches wide on each side , the total area would have been ( m + 94 ) square inches . what is the perimeter of the photograph , in inches ?
Options: a ) 34 , b ) 36 , c ) 23 , d ) 40 , e ) 42
Rationale: "let length and breadth of photograph be l and b respectively . perimeter is given by 2 * ( l + b ) - - - - - ( 1 ) according to the question : ( l + 4 ) ( b + 4 ) = m - - - - ( 2 ) and ( l + 8 ) ( b + 8 ) = m + 94 - - - - - - - - - > ( l + 8 ) ( b + 8 ) - 94 = m - - - - - - ( 3 ) equating ( 2 ) and ( 3 ) ( l + 4 ) ( b + 4 ) = ( l + 8 ) ( b + 8 ) - 94 lb + 4 l + 4 b + 16 = lb + 8 l + 8 b + 64 - 94 simplify 4 l + 4 b = 46 - - - - - - > 2 ( l + b ) = 23 ( check eq ( 1 ) ) answer is c"
Answer: c
Question (gain): an inspector rejects 15 % of the meters as defective . how many will he examine to reject 10 ?
Options: a ) a ) 100 , b ) b ) 66.7 , c ) c ) 250 , d ) d ) 200 , e ) e ) 160
Rationale: "then , 10 % of x = 15 ( 15 / 100 ) x = 10 x = ( 10 * 100 * ) / 15 = 66.7 answer is b"
Answer: b
Question (general): the average of 10 numbers is calculated as 16 . it is discovered later on that while calculating the average , the number 35 was incorrectly read as 25 , and this incorrect number was used in the calculation . what is the correct average ?
Options: a ) 16 , b ) 17 , c ) 19 , d ) 22 , e ) 26
Rationale: the total sum of the numbers should be increased by 10 . then the average will increase by 10 / 10 = 1 . the correct average is 17 . the answer is b .
Answer: b
Question (general): a gambler bought $ 4,000 worth of chips at a casino in denominations of $ 20 and $ 100 . that evening , the gambler lost 16 chips , and then cashed in the remainder . if the number of $ 20 chips lost was 2 more or 2 less than the number of $ 100 chips lost , what is the largest amount of money that the gambler could have received back ?
Options: a ) $ 2,040 , b ) $ 2,120 , c ) $ 1,960 , d ) $ 3,120 , e ) $ 1,400
Rationale: "in order to maximize the amount of money that the gambler kept , we should maximize # of $ 20 chips lost and minimize # of $ 100 chips lost , which means that # of $ 20 chips lost must be 2 more than # of $ 100 chips lost . so , if # of $ 20 chips lost is x then # of $ 100 chips lost should be x - 2 . now , given that total # of chips lost is 16 : x + x - 2 = 16 - - > x = 9 : 9 $ 20 chips were lost and 9 - 2 = 7 $ 100 chips were lost . total worth of chips lost is 9 * 20 + 7 * 100 = $ 880 , so the gambler kept $ 4,000 - $ 880 = $ 3,120 . answer : d"
Answer: d
Question (gain): there are 600 employees in a room . 99 % are managers . how many managers must leave the room to bring down the percentage of managers to 98 % ?
Options: a ) 100 , b ) 200 , c ) 250 , d ) 300 , e ) 400
Rationale: "there are 594 managers and 6 others . the 6 others would compose 2 % of the total number of people if there were 300 people in the room . thus 300 managers must leave . the answer is d ."
Answer: d
Question (probability): when 3 fair coins are tossed together , what is the probability of getting 2 tails ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 3 / 4 , e ) 2 / 3
Rationale: we can get 2 tails in 3 c 2 ways . we can get 3 tails in exactly one way . also , there are a total out 8 possible outcomes . thus , the required probability = ( 3 + 1 ) / 8 = 1 / 2 answer : a
Answer: a
Question (other): the ratio of two cow a , b milk is 5 : 3.3 kg milk of cow a get distributed and 1 kg milk of cow b get distributed . now , 8 kg milk of cow b left . now what is the ratio of cow a and b left milk ?
Options: a ) 3 : 2 , b ) 4 : 3 , c ) 5 : 4 , d ) 6 : 5 , e ) 5 : 3
Rationale: left milk of cow b = 3 x - 1 = 8,3 x = 9 , x = 3 . left milk of cow a = 15 - 3 = 12 12 / 8 = 3 : 2 . answer a
Answer: a
Question (physics): a tank is filled by 3 pipes a , b , c in 8 hours . pipe c is twice as fast as b and b is twice as fast as a . how much will pipe a alone take to fill the tank ?
Options: a ) 25 hr , b ) 35 hr , c ) 56 hr , d ) 20 hr , e ) 50 hr
Rationale: "suppose pipe a alone take x hours to fill the tank then pipe b and c will take x / 2 and x / 4 hours respectively to fill the tank . 1 / x + 2 / x + 4 / x = 1 / 8 7 / x = 1 / 8 x = 56 hours answer is c"
Answer: c
Question (physics): a car travels at a speed of 75 miles per hour . how far will it travel in 5 hours ?
Options: a ) 425 miles , b ) 625 miles , c ) 325 miles , d ) 375 miles , e ) 625 miles
Rationale: "during each hour , the car travels 65 miles . for 5 hours it will travel 75 + 75 + 75 + 75 + 75 = 5 * 65 = 375 miles correct answer d"
Answer: d
Question (physics): angelina walked 150 meters from her home to the grocery at a constant speed . she then walked 200 meters to the gym at double the speed . she spent 10 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 ) 2 , b ) 3 , c ) 4 , d ) 10 , e ) 12
Rationale: let the speed be x . . . so time taken from home to grocery = 150 / x . . the speed to gym = 2 x . . so time taken = 200 / 2 x = 100 / x . . its given 150 / x - 100 / x = 10 50 / x = 10 x = 5 m / secs . . so grocery to gym = 2 * 5 = 10 m / s . . . answer : d
Answer: d
Question (gain): a cylinder of height h is 5 / 6 of water . when all of the water is poured into an empty cylinder whose radius is 25 percent larger than that of the original cylinder , the new cylinder is 3 / 5 full . the height of the new cylinder is what percent of h ?
Options: a ) 25 % , b ) 50 % , c ) 60 % , d ) 72 % , e ) 100 %
Rationale: "basically we can disregard the radius is 25 % information , as we are only asked about the height of the original and the new cylinder . this is becausethe new cylinder is 3 / 5 fullmeans the same as that it ' s height is 3 / 5 . original cylinder 5 / 6 new cylinder 3 / 5 so 3 / 5 / 5 / 6 = 3 / 5 * 6 / 5 = 0.72 or 72 % . answer d"
Answer: d
Question (general): a library has an average of 510 visitors on sundays and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is ?
Options: a ) 285 , b ) 227 , c ) 271 , d ) 187 , e ) 199
Rationale: "since the month begins with a sunday , so there will be five sundays in the month , required average = ( 510 * 5 + 240 * 25 ) / 30 = 8550 / 30 = 285 . answer : a"
Answer: a
Question (physics): a train running at the speed of 30 km / hr crosses a pole in 9 seconds . find the length of the train ?
Options: a ) 75 , b ) 65 , c ) 25 , d ) 288 , e ) 212
Rationale: "speed = 30 * ( 5 / 18 ) m / sec = 25 / 3 m / sec length of train ( distance ) = speed * time ( 25 / 3 ) * 9 = 75 meter answer : a"
Answer: a
Question (physics): if 8 men or 12 women can do a piece of work in 15 days , in how many days can the same work be done by 6 men and 11 women ?
Options: a ) 9 days , b ) 11 days , c ) 13 days , d ) 15 days , e ) 17 days
Rationale: "8 men = 12 women ( i . e 2 men = 3 women ) 12 women 1 day work = 1 / 15 soln : 6 men ( 9 women ) + 11 women = 20 women = ? 1 women 1 day work = 12 * 15 = 1 / 180 so , 20 women work = 20 / 180 = 1 / 9 ans : 9 days answer : a"
Answer: a
Question (physics): a train 200 m long running at 72 kmph crosses a platform in 25 sec . what is the length of the platform ?
Options: a ) 443 m , b ) 354 m , c ) 450 m , d ) 350 m , e ) 300 m
Rationale: "e 300 e = 72 * 5 / 18 = 25 = 500 â € “ 200 = 300"
Answer: e
Question (gain): what is the rate percent when the simple interest on rs . 9100 amount to rs . 455 in 3 years ?
Options: a ) 3.7 % , b ) 5.7 % , c ) 6.7 % , d ) 8.7 % , e ) 9.7 %
Rationale: "455 = ( 4100 * 3 * r ) / 100 r = 3.7 % answer : a"
Answer: a
Question (physics): the length of a train and that of a platform are equal . if with a speed of 126 k / hr , the train crosses the platform in one minute , then the length of the train ( in meters ) is ?
Options: a ) 227 , b ) 299 , c ) 1050 , d ) 750 , e ) 211
Rationale: "speed = [ 126 * 5 / 18 ] m / sec = 35 m / sec ; time = 1 min . = 60 sec . let the length of the train and that of the platform be x meters . then , 2 x / 60 = 35 è x = 35 * 60 / 2 = 1050 answer : c"
Answer: c
Question (general): laura took out a charge account at the general store and agreed to pay 7 % simple annual interest . if she charges $ 35 on her account in january , how much will she owe a year later , assuming she does not make any additional charges or payments ?
Options: a ) $ 2.10 , b ) $ 37.10 , c ) $ 37.45 , d ) $ 38.10 , e ) $ 38.80
Rationale: "principal that is amount taken by laura at year beginning = 35 $ rate of interest = 7 % interest = ( 7 / 100 ) * 35 = 2.45 $ total amount that laura owes a year later = 35 + 2.45 = 37.45 $ answer c"
Answer: c
Question (gain): a dishonest dealer professes to sell goods at the cost price but uses a weight of 852 grams per kg , what is his percent ?
Options: a ) 22 % , b ) 25 % , c ) 17.37 % , d ) 99 % , e ) 12 %
Rationale: "852 - - - 148 100 - - - ? = > 17.37 % answer : c"
Answer: c
Question (physics): a man walks at a rate of 10 mph . after every ten miles , he rests for 6 minutes . how much time does he take to walk 60 miles ?
Options: a ) 300 , b ) 318 , c ) 322 , d ) 324 , e ) 390
Rationale: "to cover 60 miles the man needs ( time ) = ( distance ) / ( rate ) = 60 / 10 = 6 hours = 360 minutes . he will also rest 5 times ( after 10 , 20 , 30,40 and 50 miles ) , so total resting time = 5 * 6 = 30 minutes . total time = 360 + 30 = 390 minutes . answer : e ."
Answer: e
Question (gain): the difference between compound interest and simple interest on a certain amount of money at 5 % per annum for 2 years is 15 . find the sum :
Options: a ) 4500 , b ) 7500 , c ) 5000 , d ) 6000 , e ) none of these
Rationale: "sol . ( d ) let the sum be 100 . therefore , si = 100 × 5 × 2100 = 10100 × 5 × 2100 = 10 and ci = 100 ( 1 + 5100 ) 2 − 100100 ( 1 + 5100 ) 2 − 100 ∴ = 100 × 21 × 2120 × 20 − 100 = 414 = 100 × 21 × 2120 × 20 − 100 = 414 difference of ci and si = 41 ⁄ 4 - 10 = 1 ⁄ 4 if the difference is 1 ⁄ 4 , the sum = 100 = > if the difference is 15 , the sum = 400 × 15 = 6000 answer d"
Answer: d
Question (physics): r is the set of positive odd integers less than 40 , and s is the set of the squares of the integers in r . how many elements does the intersection of r and s contain ?
Options: a ) none , b ) three , c ) four , d ) five , e ) seven
Rationale: "squares < 40 { 1,4 , 9,16 , 25,36 } s = { 1 , 9,25 } r = { 1,3 , . . . . . 40 } hence b ."
Answer: b
Question (geometry): a square and an equilateral triangle have the same perimeter . what is the ratio of the area of the circle circumscribing the square to the area of the circle inscribed in the triangle ?
Options: a ) 9 : 8
b ) 15 : 8
c ) 27 : 8
d ) 8 : 9
e ) 8 : 15
Rationale: let x be side of square perimeter of square = 4 x = perimeter of triangle = 3 * side of triangle so side of eq . triangle = ( 4 / 3 ) * x diameter of circle circumscribing the square = sqrt ( 2 ) * x area of circle circumscribing the square = pi * ( sqrt ( 2 ) * x ) ^ 2 / 4 = ( pi / 2 ) * x ^ 2 - - - - ( 1 ) to find radius of the circle inscribed in the triangle area of triangle = r * s = sqrt ( 3 ) / 4 * ( 4 x / 3 ) ^ 2 now s = ( 4 / 3 ) * x + ( 4 / 3 ) * x + ( 4 / 3 ) * x / 2 = 2 x so sqrt ( 3 ) / 4 * ( 4 x / 3 ) ^ 2 = r * 2 x gives r = { 2 / 3 * ( 3 ^ 1 / 2 ) } * x area of the circle inscribed in the triangle = pi * [ { 2 / 3 * ( 3 ^ 1 / 2 ) } * x ] ^ 2 = pi * ( 4 / 27 ) * x ^ 2 - - - - - - - ( 2 ) so reqd ratio = eqn ( 1 ) / eqn ( 2 ) = [ ( pi / 2 ) * x ^ 2 ] / [ pi * ( 4 / 27 ) * x ^ 2 ] = 27 / 8 so reqd ratio = 27 : 8 answer : c
Answer: c
Question (gain): 10 is subtracted from 50 % of a number , the result is 25 . find the number ?
Options: a ) 75 , b ) 70 , c ) 35 , d ) 170 , e ) 50
Rationale: "( 50 / 100 ) * x â € “ 10 = 25 5 x = 350 x = 70 answer : b"
Answer: b
Question (other): a bag holds 3 red marbles and 3 green marbles . if you removed two randomly selected marbles from the bag , without replacement , what is the probability that both would be red ?
Options: a ) 1 / 10 , b ) 1 / 5 , c ) 3 / 10 , d ) 2 / 5 , e ) 1 / 2
Rationale: "given : 3 r and 3 g marbles required : probability that 2 marbles removed without replacement are both red initially we have to pick one red from a total of 3 red and 3 green marbles after one red has been picked , we need to pick 1 red from a total of 2 red and 3 green marbles . p ( both red ) = ( 3 / 6 ) * ( 2 / 5 ) = 1 / 5 option b"
Answer: b
Question (physics): a cistern can be filled by a tap in 3 hours while it can be emptied by another tap in 5 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
Options: a ) 5.2 hrs , b ) 2.9 hrs , c ) 1.9 hrs , d ) 7.5 hrs , e ) 1.4 hrs
Rationale: "net part filled in 1 hour = ( 1 / 3 - 1 / 5 ) = 2 / 15 the cistern will be filled in 15 / 2 hrs i . e . , 7.5 hrs . answer : d"
Answer: d
Question (gain): the value of a machine depreciates at 20 % per annum . if its present value is rs . 1 , 50,000 , at what price should it be sold after two years such that a profit of rs . 24,000 is made ?
Options: a ) 328897 , b ) 120000 , c ) 877888 , d ) 277768 , e ) 188871
Rationale: "the value of the machine after two years = 0.8 * 0.8 * 1 , 50,000 = rs . 96,000 sp such that a profit of rs . 24,000 is made = 96,000 + 24,000 = rs . 1 , 20,000 answer : b"
Answer: b
Question (physics): a tank can supply water to a village for 100 days . if a leak at the bottom of the tank drains out 10 liters per day , the supply lasts for 75 days only . for how many days will the supply last if the leak drains out 20 liters per day ?
Options: a ) 50 , b ) 60 , c ) 65 , d ) 70 , e ) 72
Rationale: "losing 10 liters per day results in a loss of 750 liters in 75 days . so , those 750 liters were for 25 days , making daily consumption of the village 30 liters per day . thus the capacity of the tank is 30 * 100 = 3000 liters . losing 20 liters plus 30 liters gives 50 liters per day . at this rate the supply will last 3000 / 50 = 60 days . the answer is b ."
Answer: b
Question (general): if x + y = 2 x + 2 z , x - 2 y = 2 z and x + y + z = 21 , what is the value of y / z ?
Options: a ) - 4 . , b ) - 2 . , c ) - 1.7 . , d ) 3 . , e ) 2.5 .
Rationale: x + y = 2 x + 2 z y = x + 2 z - - - - - - - - - - 1 x - 2 y = 2 z x - 2 z = 2 y - - - - - - - - - 2 subtracting equation 1 from equation 2 - 4 z = y y / z = - 4 a is the answer
Answer: a
Question (physics): a 300 meter long train crosses a platform in 36 seconds while it crosses a signal pole in 18 seconds . what is the length of the platform ?
Options: a ) 300 m , b ) 278 m , c ) 350 m , d ) 228 m , e ) 282 m
Rationale: "speed = [ 300 / 18 ] m / sec = 50 / 3 m / sec . let the length of the platform be x meters . then , x + 300 / 36 = 50 / 3 3 ( x + 300 ) = 1800 è x = 300 m . answer : a"
Answer: a