Cheukting/mathqa huggingface dataset:
Question (geometry): two cubes have their volumes are in the ratio 1 : 27 . find the ratio of their surface area ?
Options: a ) 1 : 2
b ) 2 : 3
c ) 1 : 9
d ) 2 : 7
e ) 3 : 11
Rationale: let their edges be a and b then , a ^ 3 / b ^ 3 = 1 / 27 ( a / b ) ^ 3 = ( 1 / 3 ) ^ 3 a / b = 1 / 3 ratio of their surface areas = 6 a ^ 2 / 6 b ^ 2 = ( a / b ) ^ 2 = 1 / 9 = 1 : 9 answer is c
Answer: c
Question (general): if the integer n has exactly 4 positive divisors , including 1 and n , how many positive divisors does n ^ 3 have ?
Options: a ) 16 , b ) 11 , c ) 10 , d ) 20 , e ) 9
Rationale: take the example of 6 . . . it has 4 positive divisors ( 1,2 , 3,4 ) now , take the example of 216 . . . it has 16 divisors . . so a is the ans
Answer: a
Question (general): the number 181 can be written as sum of the squares of 2 different positive integers . what is the difference of these 2 different integers ?
Options: a ) 3 , b ) 2 , c ) 1 , d ) 4 , e ) 5
Rationale: "sum of the squares of 2 different positive integers = 181 10 ^ 2 + 9 ^ 2 = 181 now , differene of these 2 different integers = 10 - 9 = 1 ans - c"
Answer: c
Question (general): if you roll a fair - sided die twice , what is the probability of getting a double ( 5,5 ) ?
Options: a ) 1 / 24 , b ) 1 / 36 , c ) 1 / 12 , d ) 1 / 18 , e ) 1 / 3 !
Rationale: "total no . in two dice ( 1,1 ) , ( 2,2 ) . . . . . ( 6 , ) total number of events = 6 * 6 total events of getting same pair ( 5,5 ) = 6 probability = 6 / 6 * 6 = 1 / 6 = 1 / 3 ! e"
Answer: e
Question (physics): a father and his son are waiting at a bus stop in the evening . there is a lamp post behind them . the lamp post , the father and his son stand on the same straight line . the father observes that the shadows of his head and his son ’ s head are incident at the same point on the ground . if the heights of the lamp post , the father and his son are 6 metres , 1.8 metres and 0.9 metres respectively , and the father is standing 2.1 metres away from the post , then how far ( in metres ) is the son standing from his father ?
Options: a ) 0.9 , b ) 0.75 , c ) 0.6 , d ) 0.45 , e ) none of these
Rationale: explanation : l is the lamp post position , f is father and s is son ’ s position . x is the point where the shadow falls . ld = 0.9 = son ’ s height , lb = 1.8 = father ’ s height . so ab = 6 – 1.8 = 4.2 also bc = lf = 2.1 we observe that ∆ abc ~ ∆ ade ( two triangles are similar ) . hence , the corresponding sides are proportional . so , ab / ad = dc / de . 4.2 / 5.1 = 2.1 / de . de = 5.1 * 2.1 / 4.2 = 5.1 / 2 = 2.55 . ls = de = 2.55 fs = ls – lf = 2.55 – 2.1 = 0.45 . answer : d
Answer: d
Question (general): a collection of books went on sale , and 2 / 3 of them were sold for $ 2.25 each . if none of the 40 remaining books were sold , what was the total amount received for the books that were sold ?
Options: a ) $ 160 , b ) $ 150 , c ) $ 280 , d ) $ 200 , e ) $ 180
Rationale: "if 40 books constitute 1 / 3 rd of the total , then 2 / 3 rd of the total = 80 books amount received for sold books = 80 * 2.25 = $ 180 answer : e"
Answer: e
Question (geometry): a rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn , one parallel to the length and the other parallel to the breadth . what is the cost of traveling the two roads at rs . 5 per sq m ?
Options: a ) 6500 , b ) 2779 , c ) 2779 , d ) 3900 , e ) 2781
Rationale: "area = ( l + b â € “ d ) d ( 80 + 60 â € “ 10 ) 10 = > 1300 m 2 1300 * 5 = rs . 6500 answer : a"
Answer: a
Question (physics): at their respective rates , pump a , b , and c can fulfill an empty tank , or pump - out the full tank in 2 , 3 , and 6 hours . if a and b are used to pump - out water from the half - full tank , while c is used to fill water into the tank , in how many hours , the tank will be empty ?
Options: a ) 2 / 3 , b ) 1 , c ) 3 / 4 , d ) 3 / 2 , e ) 2
Rationale: rate of a = 1 / 2 tank / hour ; rate of b = 1 / 3 tank / hour ; rate of c = 1 / 6 tank / hour . combined rate when a and b are used to pump - out water , while c is used to fill water into the tank is 1 / 2 + 1 / 3 - 1 / 6 = 2 / 3 tank hour . so , to empty the full tank 3 / 2 hours ( reciprocal of rate ) are needed . to empty the half - full tank half of that time would be needed : 1 / 2 * 3 / 2 = 3 / 4 hours . answer : c .
Answer: c
Question (physics): a boat can travel with a speed of 22 km / hr in still water . if the speed of the stream is 5 km / hr , find the time taken by the boat to go 108 km downstream
Options: a ) 5 hours , b ) 4 hours , c ) 3 hours , d ) 2 hours , e ) none of these
Rationale: "explanation : speed of the boat in still water = 22 km / hr speed of the stream = 5 km / hr speed downstream = ( 22 + 5 ) = 27 km / hr distance travelled downstream = 108 km time taken = distance / speed = 108 / 27 = 4 hours . answer : option b"
Answer: b
Question (general): company c sells a line of 25 products with an average retail price of $ 1,200 . if none of these products sells for less than $ 400 , and exactly 10 of the products sell for less than $ 1,000 , what is the greatest possible selling price of the most expensive product ?
Options: a ) 12000 , b ) 13000 , c ) 14000 , d ) 15000 , e ) 16000
Rationale: "the average price of 25 products is $ 1,200 means that the total price of 25 products is 25 * 1,200 = $ 30,000 . next , since exactly 10 of the products sell for less than $ 1,000 , then let ' s make these 10 items to be at $ 400 each ( min possible ) . now , the remaining 14 items can not be priced less than $ 1,000 , thus the minimum possible price of each of these 14 items is $ 1,000 . thus the minimum possible value of 24 products is 10 * 400 + 14 * 1,000 = $ 18,000 . therefore , the greatest possible selling price of the most expensive product is $ 30,000 - $ 18,000 = $ 12,000 . answer : a ."
Answer: a
Question (general): a man purchased earphone on friday . but he forgot how much it cost . the data he have are mean expenditure of all 7 days is 500 . expenditure on mon , tue , wed , thurs , sat , sun are 450600 , 400500 , 550300 . on friday he purchased 3 things one earphone , one pen and one notebook . pen cost 30 and notebook cost 50 . then what is cost of earphone ?
Options: a ) 620 , b ) 530 , c ) 450 , d ) 470 , e ) 500
Rationale: solution let expenditure on friday be x ( 450 + 600 + 400 + 500 + x + 550 + 300 ) / 7 = 500 2800 + x = 3500 x = 700 pen + notebook + earphone = 700 earphone = 700 - 80 = 620 answer a
Answer: a
Question (gain): what percent is 6 gm of 1 kg ?
Options: a ) 1.5 % , b ) 0.5 % , c ) 0.6 % , d ) 3.5 % , e ) 4 %
Rationale: "1 kg = 1000 gm 6 / 1000 × 100 = 600 / 1000 = 3 / 5 = 0.6 % c )"
Answer: c
Question (physics): a train 300 m long is running with a speed of 68 kmph . in what time will it pass a man who is running at 8 kmph in the same direction in which the train is going ?
Options: a ) 6 sec . , b ) 7 sec . , c ) 9 sec . , d ) 18 sec . , e ) none
Rationale: "solution speed of the train relative to man = ( 68 - 8 ) = 60 kmph = 60 x 5 / 18 = 50 / 3 m / sec . time taken by it to cover 300 m at ( 50 / 3 ) m / sec = ( 300 x 3 / 50 ) sec = 18 sec . answer d"
Answer: d
Question (general): how many prime numbers are between 51 / 13 and 89 / 9 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "51 / 13 = 4 - 89 / 9 = 10 - prime numbers between 4 and 10 are 5 and 7 - sign signifies that the number is marginally less . answer c"
Answer: c
Question (general): company c sells a line of 25 products with an average retail price of $ 1,400 . if none of these products sells for less than $ 420 , and exactly 10 of the products sell for less than $ 1,000 , what is the greatest possible selling price of the most expensive product ?
Options: a ) 16000 , b ) 11400 , c ) 13200 , d ) 15400 , e ) 16800
Rationale: "the average price of 25 products is $ 1,400 means that the total price of 25 products is 25 * 1,200 = $ 35,000 . next , since exactly 10 of the products sell for less than $ 1,000 , then let ' s make these 10 items to be at $ 420 each ( min possible ) . now , the remaining 14 items can not be priced less than $ 1,000 , thus the minimum possible price of each of these 14 items is $ 1,000 . thus the minimum possible value of 24 products is 10 * 420 + 14 * 1,000 = $ 18,200 . therefore , the greatest possible selling price of the most expensive product is $ 35,000 - $ 18,200 = $ 16,800 . answer : e"
Answer: e
Question (gain): a soccer team played 130 games and won 60 percent of them . how many games did it win ?
Options: a ) 84 , b ) 94 , c ) 100 , d ) 125 , e ) 78
Rationale: "60 % of 130 = x 0.60 * 130 = x 78 = x answer : e"
Answer: e
Question (general): what least no . must be subtracted from 5026 so that remaining no . is divisible by 5 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 1
Rationale: explanation : on dividing 5026 by 5 we get the remainder 1 , so 1 should be subtracted option e
Answer: e
Question (gain): a gambler has won 40 % of his 40 poker games for the week so far . if , all of a sudden , his luck changes and he begins winning 70 % of the time , how many more games must he play to end up winning 60 % of all his games for the week ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "let x be the number of additional games the gambler needs to play . 0.4 ( 40 ) + 0.7 x = 0.6 ( x + 40 ) 0.1 x = 8 x = 80 the answer is d ."
Answer: d
Question (gain): 50 % of a number is added to 200 , the result is the same number . find the number ?
Options: a ) 300 , b ) 288 , c ) 400 , d ) 129 , e ) 281
Rationale: "( 50 / 100 ) * x + 200 = x x / 2 + 200 = x x + 400 = 2 x x = 400 answer : c"
Answer: c
Question (geometry): there is a square with side ‘ a ’ and one octagon is inscribed in it . what will be perimeter of octagon .
Options: a ) 8 a / 3
b ) 7 a / 3
c ) 5 a / 3
d ) a / 3
e ) 11 a / 3
Rationale: well if it ' s a regular octagon then it actually trisects each side of the square in which 1 / 3 of the lenght of the side of the square is the length of one side of the octagon . if any one has a doubt he can draw the figure and see it going this way lenght of a side of a octagon is a / 3 and thus perimeter would be 8 a / 3 . answer : a
Answer: a
Question (general): when 2 / 9 of the votes on a certain resolution have been counted , 3 / 4 of those counted are in favor of the resolution . what fraction x of the remaining votes must be against the resolution so that the total count will result in a vote of 2 to 1 against the resolution ?
Options: a ) 11 / 14 , b ) 13 / 18 , c ) 4 / 7 , d ) 3 / 7 , e ) 3 / 14
Rationale: "if we use variable for total votes there will be too many fractions to manipulate with , so pick some smart # : let set total # of votes is 18 . 2 / 9 of the votes on a certain resolution have been counted - - > 4 counted and 18 - 4 = 14 votes left to be counted ; 3 / 4 of those counted are in favor of the resolution - - > 3 in favor and 1 against ; ratio of those who voted against to those who voted for to be 2 to 1 there should be total of 18 * 2 / 3 = 12 people who voted against , so in the remaining 14 votes there should be 12 - 1 = 11 people who voted against . thus x = 11 / 14 of the remaining votes must be against . answer : a ."
Answer: a
Question (physics): the speed of the boat in still water in 12 kmph . it can travel downstream through 54 kms in 3 hrs . in what time would it cover the same distance upstream ?
Options: a ) 8 hours , b ) 6 hours , c ) 4 hours , d ) 5 hours , e ) 9 hours
Rationale: "still water = 12 km / hr downstream = 54 / 3 = 18 km / hr upstream = > > still water = ( u + v / 2 ) = > > 12 = u + 18 / 2 = 6 km / hr so time taken in upstream = 545 / 6 = 9 hrs answer : e"
Answer: e
Question (other): if shares of two persons in profits are rs . 400 and rs . 600 then ratio of their capitals is
Options: a ) 3 : 4 , b ) 2 : 3 , c ) 4 : 3 , d ) 1 : 3 , e ) 1 : 2
Rationale: "profit = time * capital so 400 : 600 = 2 : 3 answer : b"
Answer: b
Question (gain): each light bulb at a hotel is either incandescent or fluorescent . at a certain moment , thirty percent of the incandescent bulbs are switched on , and eighty percent of the fluorescent bulbs are switched on . if 40 percent of all the bulbs are switched on at this moment , what percent of the bulbs that are switched on are incandescent ?
Options: a ) 20 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 80 %
Rationale: "let i be the number of incandescent bulbs . let f be the number of fluorescent bulbs . 0.3 i + 0.8 f = 0.4 ( i + f ) 0.4 f = 0.1 i f = 0.25 i this means that for every 4 incandescent bulbs , there is 1 fluorescent bulb . the percent of bulbs that are switched on which are incandescent is : 0.3 i / ( 0.3 i + 0.8 f ) = 0.3 i / ( 0.3 i + 0.8 * 0.25 i ) = 0.3 i / 0.5 i = 3 / 5 = 60 % . the answer is d ."
Answer: d
Question (physics): a train 300 m long is running at a speed of 99 km / hr . in what time will it pass a bridge 195 m long ?
Options: a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 21
Rationale: "speed = 99 * 5 / 18 = 55 / 2 m / sec total distance covered = 300 + 195 = 495 m required time = 495 * 2 / 55 = 18 sec answer : b"
Answer: b
Question (general): f ( x ) is a function such that f ( 2 x + 1 ) = 2 f ( x ) + 1 for all real numbers x and f ( 0 ) = 2 . find the value of f ( 3 ) .
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: f ( 2 x + 1 ) = 2 f ( x ) + 1 : given f ( 3 ) = 2 f ( 1 ) + 1 : x = 1 in a f ( 1 ) = 2 f ( 0 ) + 1 : x = 0 in a f ( 3 ) = 11 : substitute correct answer b
Answer: b
Question (gain): evaluate 28 % of 450 + 45 % of 260
Options: a ) 232 , b ) 243 , c ) 252 , d ) 262 , e ) 282
Rationale: "explanation : = ( 28 / 100 ) * 450 + ( 45 / 100 ) * 260 = 126 + 117 = 243 answer : option b"
Answer: b
Question (general): what is the units digit of ( 44 ^ 4 ) ( 33 ^ 5 ) ( 21 ^ 6 ) ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "the units digit of 44 ^ 4 is the units digit of 4 ^ 4 which is 6 . the units digit of 33 ^ 5 is the units digit of 3 ^ 5 which is 3 . the units digit of 21 ^ 6 is the units digit of 1 ^ 6 which is 1 . the units digit of 6 * 3 * 1 is 8 . the answer is e ."
Answer: e
Question (general): the largest 4 digit number exactly divisible by 55 is ?
Options: a ) 9935 , b ) 9939 , c ) 9944 , d ) 9955 , e ) 9960
Rationale: "largest 4 - digit number = 9999 55 ) 9999 ( 181 9955 answer : d"
Answer: d
Question (gain): a sum of money deposited at c . i . amounts to rs . 2420 in 2 years and to rs . 2662 in 3 years . find the rate percent ?
Options: a ) 23 % , b ) 10 % , c ) 32 % , d ) 98 % , e ) 31 %
Rationale: "2420 - - - 242 100 - - - ? = > 10 % answer : b"
Answer: b
Question (physics): a car started running at a speed of 36 km / hr and the speed of the car was increased by 2 km / hr at the end of every hour . find the total distance covered by the car in the first 10 hours of the journey .
Options: a ) 45 km , b ) 76 km , c ) 25 km , d ) 15 km , e ) 30 km
Rationale: "a 45 km the total distance covered by the car in the first 10 hours = 36 + 38 + 40 + 42 + 44 + 46 + 48 + 50 + 52 + 54 = sum of 10 terms in ap whose first term is 36 and last term is 54 = 10 / 2 [ 36 + 54 ] = 450 km ."
Answer: a
Question (general): the average age of a class of 20 students is 18 years . the average increased by 2 when the teacher ' s age also included . what is the age of the teacher ?
Options: a ) 40 years , b ) 41 years , c ) 42 years , d ) 43 years , e ) 44 years
Rationale: "if age of the teacher was 18 , average would not have changed . since average increased by 2 , age of the teacher = 18 + 22 × 1 = 40 answer : a"
Answer: a
Question (gain): the profits of qrs company rose 30 % from march to april , then dropped 20 % from april to may , then rose 50 % from may to june . what was the percent increase for the whole quarter , from march to june ?
Options: a ) 15 % , b ) 32 % , c ) 56 % , d ) 62 % , e ) 80 %
Rationale: "assume 100 in march , then 130 in april as 30 % increase , then 104 in may as 20 % decrease from april , and then 156 in june which is 150 % of 104 . so overall increase is from 100 to 156 is 56 % answer c"
Answer: c
Question (geometry): if the radius of a circle is increased by 20 % then the area is increased by :
Options: a ) 44 % , b ) 120 % , c ) 144 % , d ) 40 % , e ) none of the above
Rationale: "initially a = pi * r 2 now r 2 = 120 / 100 r then area = pi * ( 120 r / 100 ) 2 area = 144 r / 100 that is area increases from 100 to 144 = increase in area = 44 % answer : a"
Answer: a
Question (general): one half of a two digit number exceeds its one third by 7 . what is the sum of the digits of the number ?
Options: a ) a ) 3 , b ) b ) 5 , c ) c ) 7 , d ) d ) 9 , e ) e ) 10
Rationale: "x / 2 – x / 3 = 7 = > x = 46 4 + 6 = 10 answer : e"
Answer: e
Question (physics): the sum of two consecutive numbers is 37 . what are they ?
Options: a ) 18 and 19 , b ) 18 and 21 , c ) 18 and 23 , d ) 19 and 20 , e ) none
Rationale: "two consecutive numbers are like 8 and 9 , or 51 and 52 . let x , then , be the first number . then the number after it is x + 1 . the problem states that their sum is 37 : word problem = 37 2 x = 37 − 1 = 36 . x = 36 2 = 18 . the two numbers are 18 and 19 . option is a"
Answer: a
Question (general): a pupil ' s marks were wrongly entered as 83 instead of 63 . due to that the average marks for the class got increased by half . the number of pupils in the class is :
Options: a ) 45 , b ) 40 , c ) 39 , d ) 37 , e ) 38
Rationale: "explanation : let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 . x / 2 = ( 83 - 63 ) = > x / 2 = 20 = > x = 40 . answer : b"
Answer: b
Question (general): if 40 % of ( x - y ) = 30 % of ( x + y ) then what percent of x is y ?
Options: a ) 2.5 % , b ) 10 % , c ) 5 % , d ) 14 % , e ) 25 %
Rationale: 40 % of ( x - y ) = 30 % of ( x + y ) ( 40 / 100 ) ( x - y ) = ( 30 / 100 ) ( x + y ) 4 ( x - y ) = 3 ( x + y ) x = 7 y x = 7 y therefore required percentage = ( ( y / x ) x 100 ) % = ( ( y / 7 y ) x 100 ) = 14 % answer is d .
Answer: d
Question (other): one fast typist type some matter in 4 hrs and another slow typist type the same matter in 6 hrs . if both do combine in how much time they will take to finish .
Options: a ) 10 hr , b ) 1 hr , c ) 2 hr 24 mins , d ) 3 hr 4 mins , e ) 4 hr 10 mins
Rationale: "fast ' s 1 hr work = 1 / 4 slow ' s 1 hr work = 1 / 6 1 / 4 + 1 / 6 = 5 / 12 they ll finish in 12 / 5 hrs = 2 2 / 5 = = > 2 hr 24 mins answer : c"
Answer: c
Question (general): there are 20 players on a rugby team . if the average weight of the players is 180 pounds , what will be the new average height if a 210 pound player will join the team ?
Options: a ) 185 , b ) 183.22 , c ) 184.96 , d ) 181.43 , e ) 182.78
Rationale: ( sum of the 20 weights ) / 20 = 180 sum of the 20 weights = 3600 new sum = 3600 + 210 = 3810 new average = 3810 / 21 = 181.43 ans : d
Answer: d
Question (general): if in a 20 over cricket match , there were no wide balls , no wides , no extras and no overthrows . what is the maximum number of runs that a batsman can score in an ideal case scenario ?
Options: a ) 663 , b ) 720 , c ) 625 , d ) 640 , e ) none
Rationale: solution : 663 explanation : for an ideal case , the batsman will hit a six on each ball . but if he hits six on the last ball of the over , the strike will change in the next over . thus , the best he can do in the last ball is run 3 runs so that he retains the strike even in the next over . thus the total runs that he can score in each over : 6 * 5 + 3 = 33 but this will have to go like it only till the 19 th over . in the last over , he can hit a six in the last ball as well as that will be the last ball of the match . thus runs for the last over will be 6 * 6 = 36 . hence the maximum runs = 33 * 19 + 36 = 663 answer a
Answer: a
Question (gain): what annual payment will discharge a debt of rs . 1025 due in 2 years at the rate of 5 % compound interest ?
Options: a ) rs . 550 , b ) rs . 551.25 , c ) rs . 560 , d ) rs . 560.75 , e ) rs . 660.75
Rationale: "let each installment be rs . x . then , x / ( 1 + 5 / 100 ) + x / ( 1 + 5 / 100 ) 2 = 1025 820 x + 1025 * 441 x = 551.25 so , value of each installment = rs . 551.25 answer : b"
Answer: b
Question (gain): after 10 % of the inhabitants of a village disappeared , a panic set in during which 25 % of the remaining inhabitants left the village . at that time , the population was reduced to 5130 . what was the number of original inhabitants ?
Options: a ) 7300 , b ) 7600 , c ) 7900 , d ) 8200 , e ) 8500
Rationale: "let the total number of original inhabitants be x . ( 75 / 100 ) * ( 90 / 100 ) * x = 5130 ( 27 / 40 ) * x = 5130 x = 5130 * 40 / 27 = 7600 the answer is b ."
Answer: b
Question (gain): 40 is subtracted from 70 % of a number , the result is 30 . find the number ?
Options: a ) 150 , b ) 997 , c ) 266 , d ) 288 , e ) 100
Rationale: "( 70 / 100 ) * x – 40 = 30 7 x = 700 x = 100 answer : e"
Answer: e
Question (general): find the greatest number that will divide 28 , 128 and 147 leaving 10 , 2 and 3 as remainders respectively
Options: a ) 19 , b ) 17 , c ) 13 , d ) 9 , e ) 18
Rationale: "explanation : answer will be hcf of ( 28 - 10 , 128 - 2 , 147 - 3 ) hcf of ( 18 , 126 , 144 ) = 18 option e"
Answer: e
Question (physics): if a train , travelling at a speed of 120 kmph , crosses a pole in 6 sec , then the length of train is ?
Options: a ) 281 , b ) 125 , c ) 200 , d ) 266 , e ) 121
Rationale: "d = 120 * 5 / 18 * 6 = 200 m answer : c"
Answer: c
Question (physics): sakshi can do a piece of work in 5 days . tanya is 25 % more efficient than sakshi . the number of days taken by tanya to do the same piece of work :
Options: a ) 4 , b ) 16 , c ) 18 , d ) 25 , e ) 10
Rationale: "solution ratio of times taken by sakshi and tanya = 125 : 100 = 5 : 4 . suppose tanya taken x days to do the work . 5 : 4 : : 5 : x ⇒ x = ( 5 x 4 / 5 ) ⇒ x = 4 days . hence , tanya takes 16 days is complete the work . answer a"
Answer: a
Question (physics): two pipes a and b can separately fill a cistern in 60 minutes and 80 minutes respectively . there is a third pipe in the bottom of the cistern to empty it . if all the three pipes are simultaneously opened , then the cistern is full in 40 minutes . in how much time , the third pipe alone can empty the cistern ?
Options: a ) 90 min , b ) 100 min , c ) 240 min , d ) 120 min , e ) 130 min
Rationale: 1 / 40 - ( 1 / 60 + 1 / 80 ) = - 1 / 240 third pipe can empty in 240 minutes answer : c
Answer: c
Question (physics): 13 buckets of water fill a tank when the capacity of each bucket is 51 litres . how many buckets will be needed to fill the same tank , if the capacity of each bucket is 17 litres ?
Options: a ) 39 , b ) 28 , c ) 23 , d ) 12 , e ) 24
Rationale: "capacity of the tank = ( 13 × 51 ) litre number of buckets required of capacity of each bucket is 17 litre = 13 × 51 / 17 = 13 × 3 = 39 answer is a"
Answer: a
Question (gain): a candidate appearing for an examination has to secure 55 % marks to pass paper i . but he secured only 45 marks and failed by 25 marks . what is the maximum mark for paper i ?
Options: a ) 127 , b ) 120 , c ) 130 , d ) 140 , e ) 150
Rationale: he secured 45 marks nd fail by 25 marks so total marks for pass the examinatn = 70 let toal marks x x * 55 / 100 = 70 x = 127 answer : a
Answer: a
Question (gain): by selling 15 pencils for a rupee a man loses 20 % . how many for a rupee should he sell in order to gain 20 % ?
Options: a ) 8 , b ) 7 , c ) 6 , d ) 4 , e ) 10
Rationale: "80 % - - - 15 120 % - - - ? 80 / 120 * 15 = 10 answer : e"
Answer: e
Question (physics): find the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 10 cm ?
Options: a ) 827 cm 2 , b ) 216 cm 2 , c ) 285 cm 2 , d ) 178 cm 2 , e ) 190 cm 2
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 10 ) = 190 cm 2 answer : e"
Answer: e