Cheukting/mathqa huggingface dataset:
Question (physics): two trains are moving in the same direction at 72 kmph and 36 kmph . the faster train crosses a man in the slower train in 10 seconds . find the length of the faster train ?
Options: a ) 270 , b ) 288 , c ) 100 , d ) 299 , e ) 126
Rationale: "relative speed = ( 72 - 36 ) * 5 / 18 = 2 * 5 = 10 mps . distance covered in 27 sec = 10 * 10 = 100 m . the length of the faster train = 100 m . answer : c"
Answer: c
Question (physics): a trader sells 78 meters of cloth for rs . 6788 at the profit of rs . 29 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) 22 , b ) 75 , c ) 60 , d ) 58 , e ) 11
Rationale: "sp of 1 m of cloth = 6788 / 78 = rs . 87 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 87 - rs . 29 = rs . 58 . answer : d"
Answer: d
Question (gain): by selling an article at rs . 800 , a shopkeeper makes a profit of 25 % . at what price should he sell the article so as to make a loss of 50 % ?
Options: a ) s . 429 , b ) s . 480 , c ) s . 320 , d ) s . 128 , e ) s . 419
Rationale: "sp = 800 profit = 25 % cp = ( sp ) * [ 100 / ( 100 + p ) ] = 800 * [ 100 / 125 ] = 640 loss = 50 % = 50 % of 640 = rs . 320 sp = cp - loss = 640 - 320 = rs . 320 answer : c"
Answer: c
Question (general): a ( 8 , w ^ 2 ) is the ( x , y ) coordinate of point located on the parabola y = x ^ 2 + 17 . what is the value of w ?
Options: a ) 3 . , b ) 4 . , c ) 5 . , d ) 6 . , e ) 9 .
Rationale: "y = x ^ 2 + 17 w ^ 2 = 8 ^ 2 + 17 w ^ 2 = 81 w = 9 answer e"
Answer: e
Question (gain): on a certain transatlantic crossing , 40 percent of a ship ’ s passengers held round - trip tickets and also took their cars abroad the ship . if 50 percent of the passengers with round - trip tickets did not take their cars abroad the ship , what percent of the ship ’ s passengers held round - trip tickets ?
Options: a ) 40 % , b ) 50 % , c ) 60 % , d ) 80 % , e ) 90 %
Rationale: let t be the total number of passengers . let x be the number of people with round trip tickets . 0.4 t had round trip tickets and took their cars . 0.5 x had round trip tickets and took their cars . 0.5 x = 0.4 t x = 0.8 t the answer is d .
Answer: d
Question (other): if log 2 = 0.30103 , the number of digits in 2128 is .
Options: a ) 38 , b ) 39 , c ) 40 , d ) 41 , e ) 56
Rationale: log ( 2128 ) = 128 log ( 2 ) = 128 × 0.30103 ≈ 38.4 ie , its characteristic = 38 hence , number of digits in 2128 = 38 + 1 = 39 answer : option b
Answer: b
Question (other): bag a contains red , white and blue marbles such that the red to white marble ratio is 1 : 3 and the white to blue marble ratio is 2 : 3 . bag b contains red and white marbles in the ratio of 1 : 4 . together , the two bags contain 40 white marbles . how many red marbles could be in bag a ?
Options: a ) 8 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: "6 is the answer . bag a - r : w : b = 2 : 6 : 9 let w in bag a be 6 k bab b - r : w = 1 : 3 let w in bag b be 4 k w = 30 = 6 k + 4 k = > k = 40 / 10 = 4 total red ' s in bag a will be 2 k = 8 a"
Answer: a
Question (general): if a person walks at 5 km / hr instead of 4 km / hr , he would have walked 6 km more . the actual distance traveled by him is ?
Options: a ) 14 , b ) 20 , c ) 18 , d ) 24 , e ) 21
Rationale: "let the actual distance traveled be x km . then , x / 4 = ( x + 6 ) / 5 x - 24 = > x = 24 km . answer : d"
Answer: d
Question (gain): if tim had lunch at $ 60.80 and he gave 20 % tip , how much did he spend ?
Options: a ) $ 30.60 , b ) $ 60.60 , c ) $ 72.96 , d ) $ 40.60 , e ) $ 50.60
Rationale: the tip is 20 % of what he paid for lunch . hence tip = 20 % of 60.80 = ( 20 / 100 ) * 60.80 = $ 12.16 total spent 60.80 + 12.16 = $ 72.96 correct answer c
Answer: c
Question (general): when asked what the time is , a person answered that the amount of time left is 1 / 3 of the time already completed . what is the time .
Options: a ) 2 pm , b ) 9 pm , c ) 3 pm , d ) 8 pm , e ) 6 pm
Rationale: "a day has 24 hrs . assume x hours have passed . remaining time is ( 24 - x ) 24 − x = 1 / 3 x ⇒ x = 18 time is 6 pm answer : e"
Answer: e
Question (gain): a ladder 18 feet long is leaning against a wall that is perpendicular to level ground . the bottom of the ladder is 6 feet from the base of the wall . if the top of the ladder slips down 4 feet , how many feet will the bottom of the ladder slip ?
Options: a ) 12.5 , b ) 15 , c ) 18 , d ) 19 , e ) 25
Rationale: "18 ^ 2 - 6 ^ 2 = 288 it means that the height is equal to 16.9 . since the top of the ladder slips down 4 feet , then the height of the wall = 16.9 - 4 = 12.9 the bottom = sqrt ( 18 ^ 2 - 12.9 ^ 2 ) = sqrt ( 324 - 166.41 ) = 12.5 ans is a"
Answer: a
Question (probability): if x is to be chosen at random from the set { 1 , 2 , 3 , 4 } and y is to be chosen at random from the set { 5 , 6 , 7 } , what is the probability that xy will be even ?
Options: a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6
Rationale: "in order to make even nos . by multiplication , we should have even * odd , odd * even or even * even total even nos . possible by multiplying nos . from the 2 sets : ( 1 * 6 ) ; 2 * any of the three from set b ; 3 * 6 ; & 4 * any of the three from set b 1 + 3 + 1 + 3 = 8 total possibilities = 4 * 3 = 12 p ( event ) = 8 / 12 or 2 / 3 ans d"
Answer: d
Question (physics): johnny makes $ 3.25 per hour at his work . if he works 8 hours , how much money will he earn ?
Options: a ) $ 30 , b ) $ 54 , c ) $ 26 , d ) $ 12 , e ) $ 9.60
Rationale: 3.25 * 8 = 26 . answer is c .
Answer: c
Question (gain): an article is bought for rs . 1280 and sold for rs . 900 , find the loss percent ?
Options: a ) 28 % , b ) 29 % , c ) 16 % , d ) 26 % , e ) 32 %
Rationale: "1280 - - - - 380 100 - - - - ? = > 29 % answer : b"
Answer: b
Question (gain): what is the rate percent when the simple interest on rs . 800 amount to rs . 160 in 3 years ?
Options: a ) 5 % , b ) 6.6 % , c ) 9 % , d ) 2 % , e ) 4 %
Rationale: "160 = ( 800 * 3 * r ) / 100 r = 6.6 % answer : b"
Answer: b
Question (general): solve below question 2 x + 1 = - 17
Options: a ) - 8 , b ) - 9 , c ) 9 , d ) 8 , e ) - 7
Rationale: "1 . subtract 1 from both sides : 2 x + 1 - 1 = - 17 - 1 2 . simplify both sides : 2 x = - 18 3 . divide both sides by 2 : 4 . simplify both sides : x = - 9 b"
Answer: b
Question (general): what is the difference between the largest number and the least number written with the digits 9 , 3 , 1 , 2 ?
Options: a ) 6084 , b ) 3788 , c ) 2077 , d ) 8082 , e ) 1812
Rationale: "explanation : 1239 9321 - - - - - - - - - - - - 8082 answer : d"
Answer: d
Question (general): if m and n are positive integer , and 1800 m = n ^ 3 , what is the least possible value of m ?
Options: a ) 2 , b ) 3 , c ) 15 , d ) 30 , e ) 45
Rationale: 1800 * m = n ^ 3 m = n ^ 3 / 1800 = n ^ 3 / ( 3 ^ 2 * 5 ^ 2 * 2 ^ 3 ) so n has to be 3 * 5 * 2 so that n ^ 3 is divisible by 1800 . so m = ( 2 * 3 * 5 ) ^ 3 / ( 3 ^ 2 * 5 ^ 2 * 2 ^ 3 ) m = 15 answer : c
Answer: c
Question (physics): the moon revolves around the earth at a speed of approximately 1.04 kilometers per second . this approximate speed is how many kilometers per hour ?
Options: a ) 60 , b ) 61.2 , c ) 3,744 , d ) 3,600 , e ) 3,672
Rationale: "moon revolves around the earth at a speed of 1.02 kilometers per second . one hour equal to 60 minutes . one minute equals to 60 seconds . so one hour equals to 3600 seconds . so one hour , speed = 1.04 * 3600 = 3744 kilometers per hour . option c is correct"
Answer: c
Question (general): rates for having a manuscript typed at a certain typing service are $ 6 per page for the first time a page is typed and $ 3 per page each time a page is revised . if a certain manuscript has 100 pages , of which 30 were revised only once , 10 were revised twice , and the rest required no revisions , what was the total cost of having the manuscript typed ?
Options: a ) $ 690 , b ) $ 620 , c ) $ 650 , d ) $ 640 , e ) $ 770
Rationale: "for 100 - 30 - 10 = 60 pages only cost is 6 $ per page for the first time page is typed - 60 * 5 = 300 $ ; for 30 pages the cost is : first time 6 $ + 3 $ of the first revision - 30 * ( 6 + 3 ) = 270 $ ; for 10 pages the cost is : first time 5 $ + 3 $ of the first revision + 3 $ of the second revision - 10 ( 6 + 3 + 3 ) = 120 $ ; total : 300 + 270 + 120 = 690 $ . answer : a ."
Answer: a
Question (physics): a trader sells 85 meters of cloth for rs . 8925 at the profit of rs . 15 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) rs . 90 , b ) rs . 76 , c ) rs . 98 , d ) rs . 18 , e ) rs . 02
Rationale: "sp of 1 m of cloth = 8925 / 85 = rs . 105 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 105 - rs . 15 = rs . 90 . answer : c"
Answer: c
Question (gain): 20 % of a number is added to 120 , the result is the same number . find the number ?
Options: a ) 150 , b ) 288 , c ) 1687 , d ) 997 , e ) 121
Rationale: "( 20 / 100 ) * x + 120 = x 2 x = 300 x = 150 answer : a"
Answer: a
Question (physics): the length of a rectangular plot is 20 metres more than its breadth . if the cost of fencing the plot @ rs . 26.50 per metre is rs . 5830 , what is the length of the plot in metres ?
Options: a ) 333 , b ) 200 , c ) 288 , d ) 276 , e ) 220
Rationale: "let length of plot = l meters , then breadth = l - 20 meters and perimeter = 2 [ l + l - 20 ] = [ 4 l - 40 ] meters [ 4 l - 40 ] * 26.50 = 5830 [ 4 l - 40 ] = 5830 / 26.50 = 220 4 l = 260 l = 260 / 4 = 65 meters . answer : e"
Answer: e
Question (physics): there is a train and car . the ratio between the speed of a train & a car is 16 : 15 respectively . also , a bus covered a distance of 480 km in 8 hours . the speed of the bus is 3 / 4 th of the speed of the train . how much distance will the car cover in 5 hours ?
Options: a ) 300 km , b ) 325 km , c ) 375 km , d ) 425 km , e ) 450 km
Rationale: "the speed of the bus is 480 / 8 = 60 km / hr the speed of the train is ( 60 * 4 ) / 3 = 80 km / hr the speed of the car is 80 / 16 * 15 = 75 km / hr the distance covered by the car in 5 hours is 75 × 5 = 375 km the answer is c ."
Answer: c
Question (gain): if a town of 65,000 people is growing at a rate of approx . 1 % per year , the population of the town in 5 years will be closest to ?
Options: a ) a . 66000 , b ) b . 67000 , c ) c . 68000 , d ) d . 69000 , e ) e . 70000
Rationale: 1 % is quite small and hence the answer is a )
Answer: a
Question (physics): two trains , a and b , started simultaneously from opposite ends of a 75 - mile route and traveled toward each other on parallel tracks . train a , traveling at a constant rate , completed the 75 - mile trip in 3 hours ; train b , traveling at a constant rate , completed the 75 - mile trip in 2 hours . how many miles had train a traveled when it met train b ?
Options: a ) 20 , b ) 22.5 , c ) 30 , d ) 37.5 , e ) 45
Rationale: "as the ratio of the rates of a and b is 2 to 3 then the distance covered at the time of the meeting ( so after traveling the same time interval ) would also be in that ratio , which means that x would cover 2 / ( 2 + 3 ) = 2 / 5 of 75 miles : 75 * 2 / 5 = 30 miles . answer : c ."
Answer: c
Question (gain): in one alloy there is 12 % chromium while in another alloy it is 8 % . 15 kg of the first alloy was melted together with 30 kg of the second one to form a third alloy . find the percentage of chromium in the new alloy .
Options: a ) 9.4 % , b ) 9.33 % , c ) 9.6 % , d ) 9.8 % , e ) 10 %
Rationale: "the amount of chromium in the new 15 + 30 = 45 kg alloy is 0.12 * 15 + 0.08 * 30 = 4.2 kg , so the percentage is 4.2 / 45 * 100 = 9.33 % . answer : b ."
Answer: b
Question (general): what is the remainder when 135 ^ 77 is divided by 7 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "( 15 ^ 77 * 9 ^ 77 ) / 7 ; ( 15 ^ 77 ) / 7 * ( 9 ^ 77 ) / 7 ; 1 * 2 ^ 77 / 7 ; ( ( 2 ^ 3 ) ^ 25 * 2 ^ 2 ) / 7 ; 1 * 4 = 4 answer : e"
Answer: e
Question (general): the difference between a two - digit number and the number obtained by interchanging the positions of its digits is 45 . what is the difference between the two digits of that number ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: "sol . let the ten ’ s digit be x and unit ’ s digit be y , then , ( 10 x + y ) - ( 10 y + x ) = 45 ⇔ 9 ( x - y ) = 45 ⇔ x - y = 5 answer b"
Answer: b
Question (general): if 42.30 = k ( 14 + m / 50 ) , where k and m are positive integers and m < 50 , then what is the value of k + m ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "42.30 = 14 k + km / 50 . . . we can rewrite the number as follows : 42 + 0.30 = 14 k + km / 50 . . . . . . . . since k is integer , then 42 = 14 k . . . . . . . . . . k = 3 0.30 = km / 50 . . . . . . 40 / 100 = 3 m / 50 . . . . . . m = 5 k + m = 3 + 5 = 8 answer : c"
Answer: c
Question (geometry): a cube is painted red on all faces . it is then cut into 27 equal smaller cubes . how many j cubes are painted on only 2 faces ?
Options: a ) 12 , b ) 8 , c ) 6 , d ) 10 , e ) 16
Rationale: "1 ) draw a simple cube 2 ) draw 9 squares on each face of the cube ( so that it looks like a rubik ' s cube ) - this is what the cube will look like when it ' s cut into 27 equal smaller cubes . 3 ) remember that the outside of the cube is the part that ' s painted . . . . the mini - cubes with 2 painted sides are all on the edge of the cube , in themiddleof the edge . there are 4 in front , 4 in back and 4 more on thestripthat runs around the left / top / right / bottom of the cube . j = 4 + 4 + 4 = 12 . answer a"
Answer: a
Question (other): at present the ratio between the ages of arun and deepak is 5 : 7 . after 6 years , arun ' s age will be 36 years . what is the age of deepak at present ?
Options: a ) 35 years , b ) 25 years , c ) 42 years , d ) 39 years , e ) 40 years
Rationale: "let the present ages of arun and deepak be 5 x years and 7 x years respectively 5 x + 6 = 36 5 x = 30 x = 6 deepak ' s age = 7 x = 42 years answer is c"
Answer: c
Question (general): the average age of 15 students of a class is 16 years . out of these , the average age of 5 students is 14 years and that of the other 10 students is 16 years . tee age of the 15 th student is ?
Options: a ) 18 years , b ) 16 years , c ) 14 years , d ) 12 years , e ) 10 years
Rationale: "age of the 15 th student = [ 15 * 16 - ( 14 * 5 + 16 * 10 ) ] = ( 240 - 230 ) = 10 years . answer : e"
Answer: e
Question (physics): excluding stoppages , the speed of a bus is 75 kmph and including stoppages , it is 45 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 15 , b ) 24 , c ) 17 , d ) 19 , e ) none of these
Rationale: "due to stoppages , it covers 30 km less . time taken to cover 30 km = ( ( 30 / 75 ) ã — 60 ) = 24 min . option ( b ) is correct"
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 130 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 ) 520
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 ) = 130 group # 2 = ( like understood ) = 3 / 4 ( 1 / 4 ) n = 130 n = 520 answer = ( e )
Answer: e
Question (geometry): when a certain perfect square is increased by 148 , the result is another perfect square . what is the value of the original perfect square ?
Options: a ) 1296
b ) 1369
c ) 1681
d ) 1764
e ) 2500
Rationale: let ’ s call the two perfect squares x ^ 2 and y ^ 2 , respectively . then the given information translates as x ^ 2 + 148 = y ^ 2 . subtracting x ^ 2 gives 148 = y ^ 2 − x ^ 2 , a difference of squares . this , in turn , factors as ( y + x ) ( y − x ) = 148 . the next step is tricky . it begins with factoring 148 , which breaks down as 2 ∗ 2 ∗ 37 . since we ’ re dealing with perfect squares , x and y are positive integers , and ( y + x ) and ( y − x ) must be paired integer factors of 148 . the options are 148 ∗ 1,74 ∗ 2 , and 37 ∗ 4 . but our number properties establish that ( y + x ) and ( y − x ) must be either both odd or both even , so only 74 ∗ 2 is an actual possibility . and because for any positive integers ( y + x ) > ( y − x ) , we can conclude that y + x = 74 and y – x = 2 . solving by elimination , 2 y = 76 , y = 38 , and x = 36 . finally , we just need to square 36 . but rather than multiplying it out , note that 36 ^ 2 ends in 6 – as does only one answer , choice a . this answer must be the one we want .
Answer: a
Question (physics): train a is 13 miles ahead of train b , which is traveling the same direction along the same route as train a . if train a is traveling at an average speed of 37 miles per hour and train b is traveling at an average speed of 43 miles per hour , how long will it take train b to overtake and drive 17 miles ahead of train a ?
Options: a ) 4 hours , b ) 2 hours , c ) 2 hours 30 minutes , d ) 5 hours , e ) 3 hours 20 minutes
Rationale: relative speed = 43 - 37 = 6 miles per hour dist required = 13 + 17 = 30 miles time taken to overtake = 30 / 6 = 5 hours . d is the answer .
Answer: d
Question (probability): x , y , and z are all unique numbers . if x is chosen randomly from the set { 9 , 10 , 11 } and y and z are chosen randomly from the set { 20 , 21 , 22 , 23 } , what is the probability that x and y are prime and z is not ?
Options: a ) 1 / 20 , b ) 1 / 12 , c ) 2 / 15 , d ) 3 / 10 , e ) 1 / 7
Rationale: "p ( x is prime ) = 1 / 3 p ( y is prime ) = 1 / 4 if y is prime , then z is not prime since y and z are unique . then the probability is 1 / 3 * 1 / 4 = 1 / 12 the answer is b ."
Answer: b
Question (gain): on increasing the price of t . v . sets by 30 % , their sale decreases by 20 % . what is the effect on the revenue receipts of the shop ?
Options: a ) 4 , b ) 5 , c ) 56 , d ) 2 , e ) 7
Rationale: "explanation : let the price be = rs . 100 , and number of units sold = 100 then , sale value = rs . ( 100 × 100 ) = rs . 10000 new sale value = rs . ( 130 × 80 ) = rs . 10400 increase % = 4001000040010000 × 100 = 4 % answer : a"
Answer: a
Question (general): if sharon ' s weekly salary increased by 16 percent , she would earn $ 348 per week . if instead , her weekly salary were to increase by 10 percent , how much would she earn per week ?
Options: a ) $ 374 , b ) $ 330 , c ) $ 385 , d ) $ 392 , e ) $ 399
Rationale: "( 348 / 116 ) 110 = 330 in this case long division does not take much time . ( 348 / 116 ) = 3 3 * 110 = 330 ( 300 + 30 ) answer b"
Answer: b
Question (general): if the charge of staying in a student youth hostel $ 18.00 / day for the first week , and $ 14.00 / day for each additional week , how much does it cost to stay for 23 days ?
Options: a ) $ 160 , b ) $ 350 , c ) $ 282 , d ) $ 274 , e ) $ 286
Rationale: "total number of days of stay = 23 charge of staying in first week = 18 * 7 = 126 $ charge of staying for additional days = ( 23 - 7 ) * 14 = 16 * 14 = 224 $ total charge = 126 + 224 = 350 $ answer b"
Answer: b
Question (gain): mr . john used to purchase certain number of mangoes for $ 360 since the price of mangoes is reduced by 10 % he got 12 more mangoes today . find the original price of 125 mangoes .
Options: a ) 360 , b ) 380 , c ) 400 , d ) 416 , e ) 412
Rationale: "mr . john used to purchase certain number of mangoes for $ 360 since the price of mangoes is reduced by 10 % he got 12 more mangoes today . find the original price of 120 mangoes . method 1 : let price per mango = x . let number of mangoes be n . then , nx = 360 . now price = 0.9 x ; number of mangoes = n + 12 . total amount = 0.9 x * ( n + 12 ) = 360 . nx = 0.9 nx + 10.8 x = > 0.1 nx = 10.8 x = > n = 108 = > x = 360 / 108 = 3.33 original price of 125 mangoes = 125 * 3.33 = 416 . answer d"
Answer: d
Question (physics): calculate the time it will take for a full tank of water to become completely empty due to a leak given that the tank could be filled in 10 hours , but due to the leak in its bottom it takes 11 hours to be filled ?
Options: a ) 90 hours , b ) 80 hours , c ) 50 hours , d ) 120 hours , e ) 110 hours
Rationale: part filled without leak in 1 hour = 1 / 10 part filled with leak in 1 hour = 1 / 11 work done by leak in 1 hour = 1 / 10 â ˆ ’ 1 / 11 = 110 hours answer : e
Answer: e
Question (gain): in the first 25 overs of a cricket game , the run rate was only 5.4 . what should be the run rate in the remaining 25 overs to reach the target of 400 runs ?
Options: a ) 16.5 , b ) 13.2 , c ) 10.6 , d ) 11.2 , e ) 7.25
Rationale: required run rate = 400 - ( 5.4 x 25 ) / 25 = 265 / 25 = 10.6 option c
Answer: c
Question (general): if one positive integer is greater than another positive integer by 3 , and the difference of their cubes is 279 , what is their sum ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 11 , e ) 13
Rationale: "1 ^ 3 = 1 2 ^ 3 = 8 3 ^ 3 = 27 4 ^ 3 = 64 5 ^ 3 = 125 6 ^ 3 = 216 7 ^ 3 = 343 the two numbers are 4 and 7 . the answer is d ."
Answer: d
Question (gain): a , b and c invested rs . 6300 , rs . 4200 and rs . 10500 respectively , in a partnership business . find the share of a in profit of rs . 12100 after a year ?
Options: a ) 3630 , b ) 3877 , c ) 2667 , d ) 2977 , e ) 2378
Rationale: "explanation : 6300 : 4200 : 10500 3 : 2 : 5 3 / 10 * 12100 = 3630 answer : a"
Answer: a
Question (general): what is the unit digit in 4 ^ 100 ?
Options: a ) 0 , b ) 1 , c ) 6 , d ) 3 , e ) 5
Rationale: unit digit in 4 ^ 100 = unit digit in [ ( 4 ^ 4 ) ^ 25 ] but unit digit in 4 ^ 4 = 6 unit digit 4 ^ 100 = 6 answer is c
Answer: c
Question (general): the average age of 37 students in a group is 14 years . when teacher ' s age is included to it , the average increases by one . what is the teacher ' s age in years ?
Options: a ) 35 years , b ) 45 years , c ) 51 years , d ) 52 years , e ) none of these
Rationale: "explanation : age of the teacher = ( 38 * 15 - 37 * 14 ) years = 52 years . answer : d"
Answer: d
Question (physics): pipe a can fill a tank in 12 hours . due to a leak at the bottom , it takes 18 hours for the pipe a to fill the tank . in what time can the leak alone empty the full tank ?
Options: a ) 36 , b ) 87 , c ) 40 , d ) 37 , e ) 86
Rationale: "let the leak can empty the full tank in x hours 1 / 12 - 1 / x = 1 / 18 = > 1 / x = 1 / 12 - 1 / 18 = ( 3 - 2 ) / 36 = 1 / 36 = > x = 36 . answer : a"
Answer: a
Question (physics): if one and a half women , drink one and a half tea in one and a half minutes . how many tea can 9 women drink in 3 minutes ?
Options: a ) 11 , b ) 8 , c ) 37 , d ) 15 , e ) 18
Rationale: e 18 explanation : more minutes implies more tea . more women implies more tea . the time become twice ( 3 minutes / 1.5 minutes ) . women become six times ( 9 / 1.5 ) . number of tea = 2 * 6 * original ( 1.5 )
Answer: e
Question (physics): a can run 2 km distance in 2 min 20 seconds , while b can run this distance in 3 min 5 sec . . by how much distance can a beat b ?
Options: a ) 900 m , b ) 500 m , c ) 120 m , d ) 180 m , e ) 190 m
Rationale: a takes time 2.20 minutes = 140 sec b takes time 3 minutes = 185 sec difference = 185 - 140 = 45 sec now we are to find distance covered in 40 sec by b 180 sec = 2000 m 1 sec = 100 / 9 m 45 sec = 45 x 100 / 9 = 500 m answer : b
Answer: b
Question (general): the price of 10 chairs is equal to that of 4 tables . the price of 15 chairs and 2 tables together is rs . 4000 . the total price of 12 chairs and 3 tables is :
Options: a ) rs . 3900 , b ) rs . 3990 , c ) rs . 4000 , d ) rs . 4100 , e ) rs . 4200
Rationale: "let the cost of a chair and that of a table be rs . x and rs . y respectively . then , 10 x = 4 y or y = 5 x . 2 15 x + 2 y = 4000 15 x + 2 x 5 x = 4000 2 20 x = 4000 x = 200 . so , y = 5 x 200 = 500 . 2 hence , the cost of 12 chairs and 3 tables = 12 x + 3 y = rs . ( 2400 + 1500 ) = rs . 3900 . a"
Answer: a