Cheukting/mathqa huggingface dataset:
Question (geometry): the parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 14 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places
Options: a ) 34 , b ) 35 , c ) 56 , d ) 67 , e ) 23.57
Rationale: "let the side of the square be a cm . parameter of the rectangle = 2 ( 16 + 14 ) = 60 cm parameter of the square = 60 cm i . e . 4 a = 60 a = 15 diameter of the semicircle = 15 cm circimference of the semicircle = 1 / 2 ( ∏ ) ( 15 ) = 1 / 2 ( 22 / 7 ) ( 15 ) = 330 / 14 = 23.57 cm to two decimal places answer : option e"
Answer: e
Question (physics): a flagstaff 17.5 m high casts a shadow of length 40.25 m . the height of the building , which casts a shadow of length 28.75 m under similar conditions will be :
Options: a ) 10 m , b ) 12.5 m , c ) 17.5 m , d ) 21.25 m , e ) none
Rationale: "let height of the building be x meters 40.25 : 28.75 : : 17.5 < = > 40.25 x x = 28.75 x 17.5 x = 28.75 x 17.5 / 40.25 x = 12.5 answer : option b"
Answer: b
Question (physics): x can do a piece of work in 4 hours ; y and z together can do it in 3 hours , while x and z together can do it in 2 hours . how long will y alone take to do it ?
Options: a ) 5 hours , b ) 10 hours , c ) 12 hours , d ) 24 hours , e ) 15 hours
Rationale: x 1 hour ' s work = 1 / 4 ; y + z ' s hour ' s work = 1 / 3 x + y + z ' s 1 hour ' s work = 1 / 4 + 1 / 3 = 7 / 12 y ' s 1 hour ' s work = ( 7 / 12 - 1 / 2 ) = 1 / 12 . y alone will take 12 hours to do the work . c
Answer: c
Question (gain): how many liters of water must be evaporated from 50 liters of a 6 - percent sugar solution to get a 10 - percent solution ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 28
Rationale: "6 % of a 50 liter solution is 3 l which is 10 % of the solution at the end . the solution at the end must be 30 l . we need to evaporate 20 liters . the answer is a ."
Answer: a
Question (gain): in a certain company 20 % of the men and 40 % of the women attended the annual company picnic . if 40 % of all the employees are men . what % of all the employee went to the picnic ?
Options: a ) 32 % , b ) 34 % , c ) 35 % , d ) 36 % , e ) 37 %
Rationale: "total men in company 40 % means total women in company 60 % ( assume total people in company 100 % ) no of men employees attended picnic = 40 x ( 20 / 100 ) = 8 no of women employees attended picnic = 60 x ( 40 / 100 ) = 24 total percentage of employees attended the picnic = 8 + 24 = 32 % answer : a"
Answer: a
Question (other): 7 log 7 ( 8 ) = ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 8
Rationale: "exponential and log functions are inverse of each other . hence aloga ( x ) = x , for all x real and positive . and therefore 7 log 7 ( 8 ) = 8 correct answer e"
Answer: e
Question (physics): excluding stoppages , the speed of a bus is 84 kmph and including stoppages , it is 70 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 12 min , b ) 10 min , c ) 15 min , d ) 14 min , e ) 13 min
Rationale: "due to stoppages , it covers 14 km less . time taken to cover 14 km = ( 14 / 84 x 60 ) min = 10 min answer : b"
Answer: b
Question (gain): 40 is what percent of 160 ?
Options: a ) 35 % , b ) 40 % , c ) 45 % , d ) 50 % , e ) 25 %
Rationale: 40 / 160 × 100 = 25 % answer : e
Answer: e
Question (general): in a fuel station the service costs $ 1.75 per car , every liter of fuel costs 0.65 $ . assuming that a company owns 12 cars and that every fuel tank contains 57 liters and they are all empty , how much money total will it cost to fuel all cars ?
Options: a ) 320.50 $ , b ) 380.50 $ , c ) 425.50 $ , d ) 450.50 $ , e ) 465.60 $
Rationale: "total cost = ( 1.75 * 12 ) + ( 0.65 * 12 * 57 ) = 465.60 hence answer will be ( e )"
Answer: e
Question (physics): the l . c . m of 22 , 54 , 108 , 135 and 198 is
Options: a ) 5942 , b ) 2887 , c ) 5940 , d ) 2888 , e ) 28881
Rationale: answer : c ) 5940
Answer: c
Question (gain): the sale price sarees listed for rs . 280 after successive discount is 12 % and 8 % is ?
Options: a ) 288 , b ) 226 , c ) 250 , d ) 230 , e ) 262
Rationale: "280 * ( 88 / 100 ) * ( 92 / 100 ) = 226 answer : b"
Answer: b
Question (physics): a girl sitting in a train which is travelling at 40 kmph observes that a goods train travelling in a opposite direction , takes 12 seconds to pass him . if the goods train is 1120 m long , find its speed .
Options: a ) 295 , b ) 296 , c ) 297 , d ) 298 , e ) 299
Rationale: relative speed = ( 1120 / 12 ) m / s = ( 1120 / 12 ) * ( 18 / 5 ) = 336 kmph speed of goods train = 336 - 40 = 296 kmph answer is b
Answer: b
Question (general): a certain list consists of 21 different numbers . if n is in the list and n is 4 times the average ( arithmetic mean ) of the other 20 numbers in the list , then n is what fraction t of the sum of the 21 numbers in the list ?
Options: a ) 1 / 20 , b ) 1 / 6 , c ) 1 / 5 , d ) 4 / 21 , e ) 5 / 21
Rationale: "this is how i used to calculate which i think works pretty well : if you let the average of the 20 other numbers equal a , can you write this equation for sum of the list ( s ) n + 20 a = s the question tells us that n = 4 a plug this back into the first equation and you get that the sum is 24 a 4 a + 20 a = 24 a therefore fraction t of n to the total would be 4 a / 24 a or 1 / 6 answer b"
Answer: b
Question (general): 107 x 107 + 93 x 93 = ?
Options: a ) 19578 , b ) 19418 , c ) 20098 , d ) 21908 , e ) none of them
Rationale: "= ( 107 ) ^ 2 + ( 93 ) ^ 2 = ( 100 + 7 ) ^ 2 + ( 100 - 7 ) ^ 2 = 2 x [ ( 100 ) ^ 2 + 7 ^ 2 ] = 2 [ 10000 + 49 ] = 2 x 10049 = 20098 answer is c"
Answer: c
Question (gain): a sum was put at simple interest at certain rate for 3 years . had it been put at 1 % higher rate it would have fetched rs . 66 more . the sum is : a . rs . 2,400 b . rs . 2,100 c . rs . 2,200 d . rs . 2,480
Options: a ) 2000 , b ) 2100 , c ) 2200 , d ) 2300 , e ) 2400
Rationale: "1 percent for 3 years = 66 1 percent for 1 year = 22 = > 100 percent = 2200 answer : c"
Answer: c
Question (general): the difference between the place value and the face value of 6 in the numeral 856973 is
Options: a ) 973 , b ) 6973 , c ) 5994 , d ) 6084 , e ) none of these
Rationale: "( place value of 6 ) - ( face value of 6 ) = ( 6000 - 6 ) = 5994 answer : option c"
Answer: c
Question (gain): 60 % of a number is added to 180 , the result is the same number . find the number ?
Options: a ) 300 , b ) 277 , c ) 266 , d ) 99 , e ) 450
Rationale: ": ( 60 / 100 ) * x + 180 = x 2 x = 900 x = 450 answer : e"
Answer: e
Question (general): andrew travelling to 7 cities . gasoline prices varied from city to city . $ 1.75 , $ 1.61 , $ 1.79 , $ 2.11 , $ 1.96 , $ 2.09 , $ 1.82 . what is the median gasoline price ?
Options: a ) $ 1 , b ) $ 1.82 , c ) $ 1.92 , d ) $ 2.13 , e ) $ 2.15
Rationale: ordering the data from least to greatest , we get : $ 1.61 , $ 1.75 , $ 1.79 , $ 1.82 , $ 1.96 , $ 2.09 , $ 2.11 the median gasoline price is $ 1.82 . ( there were 3 states with higher gasoline prices and 3 with lower prices . ) b
Answer: b
Question (general): if 625 ( 5 ^ x ) = 1 then x =
Options: a ) – 2 , b ) - 4 , c ) 0 , d ) - 1 , e ) 2
Rationale: "5 ^ x = 1 / 625 5 ^ x = 1 / 5 ^ 4 5 ^ x = 5 ^ - 4 x = - 4 b"
Answer: b
Question (general): find the least number of complete years in which a sum of money put out at 45 % compound interest will be more than double of itself ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "2 years answer : a"
Answer: a
Question (physics): the speed of the boat in still water in 12 kmph . it can travel downstream through 45 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 ) 6 hours
Rationale: still water = 12 km / hr downstream = 45 / 3 = 15 km / hr upstream = > > still water = ( u + v / 2 ) = > > 12 = u + 15 / 2 = 9 km / hr so time taken in upstream = 45 / 9 = 5 hrs answer : d
Answer: d
Question (general): the avg weight of a , b & c is 55 kg . if d joins the group , the avg weight of the group becomes 60 kg . if another man e who weights is 3 kg more than d replaces a , then the avgof b , c , d & e becomes 58 kg . what is the weight of a ?
Options: a ) 56 , b ) 65 , c ) 75 , d ) 86 , e ) 90
Rationale: "a + b + c = 3 * 55 = 165 a + b + c + d = 4 * 60 = 240 - - - - ( i ) so , d = 75 & e = 75 + 3 = 78 b + c + d + e = 58 * 4 = 232 - - - ( ii ) from eq . ( i ) & ( ii ) a - e = 240 – 232 = 8 a = e + 8 = 78 + 8 = 86 answer : d"
Answer: d
Question (physics): a train 120 m in length crosses a telegraph post in 12 seconds . the speed of the train is ?
Options: a ) 16 kmph , b ) 88 kmph , c ) 36 kmph , d ) 18 kmph , e ) 19 kmph
Rationale: "s = 120 / 12 * 18 / 5 = 36 kmph answer : c"
Answer: c
Question (geometry): a small table has a length of 12 inches and a breadth of b inches . cubes are placed on the surface of the table so as to cover the entire surface . the maximum side of such cubes is found to be 4 inches . also , a few such tables are arranged to form a square . the minimum length of side possible for such a square is 32 inches . find b .
Options: a ) 8 , b ) 16 , c ) 24 , d ) 32 , e ) 48
Rationale: "from the info that the maximum sides of the cubes is 4 , we know that the gcf of 12 ( = 2 ^ 2 * 3 ) andbis 4 ( = 2 ^ 2 ) , sob = 2 ^ x , where x > = 2 . from the second premise , we know that the lcm of 12 ( 2 ^ 2 * 3 ) andbis 32 ( 2 ^ 5 ) , sob = 2 ^ 5 combining 2 premises shows the answer is d ( 32 ) ."
Answer: d
Question (physics): if ' a ' completes a piece of work in 3 days , which ' b ' completes it in 5 days and ' c ' takes 10 days to complete the same work . how long will they take to complete the work , if they work together ?
Options: a ) 1.5 days , b ) 4.5 days , c ) 7 days , d ) 9.8 days , e ) 9 days
Rationale: explanation : hint : a ' s one day work = 1 / 3 b ' s one day work = 1 / 5 c ' s one day work = 1 / 10 ( a + b + c ) ' s one day work = 1 / 3 + 1 / 5 + 1 / 10 = 1 / 1.5 hence , a , b & c together will take 1.5 days to complete the work . answer is a
Answer: a
Question (general): a certain drink of type a is prepared by mixing 4 parts milk with 3 parts fruit juice . another drink of type b is prepared by mixing 4 parts of fruit juice and 3 parts of milk . how many liters of fruit juice must be added to 105 liters of drink a to convert it to drink b ?
Options: a ) 14 , b ) 21 , c ) 28 , d ) 35 , e ) 42
Rationale: "in 105 liters of drink a , there are 60 liters of milk and 45 liters of juice . with 60 liters of milk , we need a total of 80 liters of juice to make drink b . we need to add 35 liters of juice . the answer is d ."
Answer: d
Question (gain): at what rate percent per annum will a sum of money double in 9 years .
Options: a ) 12.5 % , b ) 13.5 % , c ) 11.5 % , d ) 11.1 % , e ) 21.5 %
Rationale: "let principal = p , then , s . i . = p and time = 8 years rate = [ ( 100 x p ) / ( p x 9 ) ] % = 11.1 % per annum . answer : d"
Answer: d
Question (general): evaluate : 30 - 12 ÷ 3 × 2 =
Options: a ) 11 , b ) 22 , c ) 33 , d ) 44 , e ) 55
Rationale: "according to order of operations , 12 ÷ 3 × 2 ( division and multiplication ) is done first from left to right 12 ÷ 3 × 2 = 4 × 2 = 8 hence 30 - 12 ÷ 3 × 2 = 30 - 8 = 22 correct answer is b ) 22"
Answer: b
Question (general): if n is a prime number greater than 11 , what is the remainder when n ^ 2 is divided by 12 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5
Rationale: "there are several algebraic ways to solve this question , but the easiest way is as follows : since we can not have two correct answers just pick a prime greater than 11 , square it and see what would be the remainder upon division of it by 12 . n = 17 - - > n ^ 2 = 289 - - > remainder upon division 289 by 12 is 1 . answer : b ."
Answer: b
Question (general): if a * b = 2 a - 3 b + ab , then 3 * 5 + 5 * 3 is equal to :
Options: a ) 22 , b ) 37 , c ) 38 , d ) 398 , e ) 72
Rationale: "explanation : 3 * 5 + 5 * 3 = ( 2 * 3 - 3 * 5 + 3 * 5 ) + ( 2 * 5 - 3 * 3 + 5 * 3 ) = ( 6 + 10 - 9 + 15 ) = 22 . answer : a ) 22"
Answer: a
Question (physics): noelle walks from point a to point b at an average speed of 3 kilometers per hour . at what speed , in kilometers per hour , must noelle walk from point b to point a so that her average speed for the entire trip is 4 kilometers per hour ?
Options: a ) 5.75 , b ) 6 , c ) 7.25 , d ) 7.5 , e ) 7.75
Rationale: "let ' s suppose that speed while returning was xkm / h since the distance is same , we can apply the formula of avg speed avg speed = 2 s 1 s 2 / s 1 + s 2 4 = 2 * 3 * x / 3 + x x = 6 b is the answer"
Answer: b
Question (general): the product of x and y is a constant . if the value of x is increased by 40 % , by what percentage must the value of y be decreased ?
Options: a ) 34 % , b ) 36 % , c ) 28.57 % , d ) 30 % , e ) 32 %
Rationale: x * y = constt . let x = y = 100 in beginning i . e . x * y = 100 * 100 = 10000 x ( 100 ) - - - becomes - - - > 1.4 x ( 140 ) i . e . 140 * new ' y ' = 10000 i . e . new ' y ' = 10000 / 140 = 71.43 i . e . y decreases from 100 to 71.43 i . e . decrease of 28.57 % c
Answer: c
Question (general): if a and b are the roots of the equation x 2 - 6 x + 6 = 0 , then the value of a 2 + b 2 is :
Options: a ) 36 , b ) 24 , c ) 17 , d ) 6 , e ) 5
Rationale: "sol . ( b ) the sum of roots = a + b = 6 product of roots = ab = 6 now , a 2 + b 2 = ( a + b ) 2 - 2 ab = 36 - 12 = 24 answer b"
Answer: b
Question (physics): a honey bee flies for 10 seconds , from a daisy to a rose . it immediately continues to a poppy , flying for 6 additional seconds . the distance the bee passed , flying from the daisy to the rose is 3 meters longer than the distance it passed flying from the rose to the poppy . the bee flies to the poppy at 3 meters per second faster than her speed flying to the rose . the bee flies how many meters per second from the daisy to the rose ?
Options: a ) 4.2 , b ) 5.2 , c ) 6 , d ) 8 , e ) 10
Rationale: "let the speed be ' s ' and let the distance between rose and poppy be ' x ' the problem boils down to : rose to poppy : s + 3 = x / 6 - - - - - - - 1 daisy to rose : s = ( x + 3 ) / 10 - - - - - - 2 so from 1 we can re write x as x = 6 s + 18 substitute the value of x in 2 gives us s = 4.2 m / s a"
Answer: a
Question (general): 6 persons in an organization including x and y were to be divided in two groups of 3 members each . the total number of groups containing both x and y is what fraction of the total number of groups which can be formed ?
Options: a ) 1 / 4 , b ) 1 / 70 , c ) 3 / 14 , d ) 3 / 10 , e ) 11 / 14
Rationale: the fraction is nothing but the probability . . number to choose 3 out of 6 = 6 c 3 number to choose x and y and 2 from remaining 4 = 4 c 2 . . prob of a and b choosen = 4 c 2 / 6 c 3 = 3 / 10 answer : d
Answer: d
Question (general): having scored 94 runs in the 19 th inning , a cricketer increases his average score by 4 . what will be his average score after 19 innings ?
Options: a ) 28 , b ) 27 , c ) 26 , d ) 22 , e ) 24
Rationale: "explanation : let the average score of the first 18 innings be n 18 n + 94 = 19 ( n + 4 ) = > n = 18 so , average score after 19 th innings = x + 4 = 22 . answer : d"
Answer: d
Question (other): ratio between rahul and deepak is 4 : 2 , after 6 years rahul age will be 22 years . what is deepak present age
Options: a ) 9 , b ) 3 , c ) 5 , d ) 2 , e ) 7
Rationale: "explanation : present age is 4 x and 2 x , = > 4 x + 22 = 26 = > x = 1 so deepak age is = 2 ( 1 ) = 2 answer : option d"
Answer: d
Question (physics): a train 150 m long running at 72 kmph crosses a platform in 25 sec . what is the length of the platform ?
Options: a ) 288 , b ) 236 , c ) 350 , d ) 299 , e ) 266
Rationale: d = 72 * 5 / 18 = 25 = 500 – 150 = 299 . answer : c
Answer: c
Question (gain): the present worth of a certain bill due sometime hence is rs . 1296 and the true discount is rs . 72 . what is the banker ' s discount ?
Options: a ) rs . 76 , b ) rs . 72 , c ) rs . 74 , d ) rs . 4 , e ) none of these
Rationale: explanation : bg = ( td ) 2 / pw = 722 / 1296 = 72 × 72 / 1296 = 12 × 12 / 36 = 12 / 3 = rs . 4 bg = bd – td = > 4 = bd - 72 = > bd = 72 + 4 = rs . 76 answer : option a
Answer: a
Question (general): the grade point average of the entire class is 88 . if the average of one third of the class is 94 , what is the average of the rest of the class ?
Options: a ) 82 , b ) 83 , c ) 84 , d ) 85 , e ) 86
Rationale: "let x be the number of students in the class . let p be the average of the rest of the class . 88 x = ( 1 / 3 ) 94 x + ( 2 / 3 ) ( p ) x 264 = 94 + 2 p 2 p = 170 p = 85 . the answer is d ."
Answer: d
Question (physics): a truck covers a distance of 376 km at a certain speed in 8 hours . how much time would a car take at an average speed which is 18 kmph more than that of the speed of the truck to cover a distance which is 14 km more than that travelled by the truck ?
Options: a ) 6 hours , b ) 5 hours , c ) 7 hours , d ) 8 hours , e ) none
Rationale: "explanation : speed of the truck = distance / time = 376 / 8 = 47 kmph now , speed of car = ( speed of truck + 18 ) kmph = ( 47 + 18 ) = 65 kmph distance travelled by car = 376 + 14 = 390 km time taken by car = distance / speed = 390 / 65 = 6 hours . answer – a"
Answer: a
Question (general): the ratio of the ages of maala and kala is 3 : 5 . the total of their ages is 3.2 decades . the proportion of their ages after 0.8 decades will be [ 1 decade = 10 years ]
Options: a ) 6 : 5 , b ) 5 : 7 , c ) 4 : 5 , d ) 7 : 9 , e ) 3 : 6
Rationale: let , maala ’ s age = 3 a and kala ’ s age = 5 a then 3 a + 5 a = 32 a = 4 maala ’ s age = 12 years and kala ’ s age = 20 years proportion of their ages after 8 is = ( 12 + 8 ) : ( 20 + 8 ) = 20 : 28 = 5 : 7 answer : b
Answer: b
Question (general): mike took a taxi to the airport and paid $ 2.50 to start plus $ 0.25 per mile . annie took a different route to the airport and paid $ 2.50 plus $ 5.00 in bridge toll fees plus $ 0.25 per mile . if each was charged exactly the same amount , and annie ' s ride was 18 miles , how many miles was mike ' s ride ?
Options: a ) 30 , b ) 34 , c ) 38 , d ) 42 , e ) 48
Rationale: "the cost of annie ' s ride was 2.5 + 5 + ( 0.25 * 18 ) = $ 12 let x be the distance of mike ' s ride . the cost of mike ' s ride is 2.5 + ( 0.25 * x ) = 12 0.25 * x = 9.5 x = 38 miles the answer is c ."
Answer: c
Question (physics): a mobile battery in 1 hour charges to 20 percent . how much time ( in minute ) will it require more to charge to 55 percent .
Options: a ) 145 , b ) 150 , c ) 175 , d ) 165 , e ) 130
Rationale: 1 hr = 20 percent . thus 15 min = 5 percent . now to charge 55 percent 165 min . answer : d
Answer: d
Question (general): in a box of 11 pens , a total of 3 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ?
Options: a ) 28 / 55 , b ) 19 / 33 , c ) 7 / 11 , d ) 4 / 7 , e ) 3 / 5
Rationale: "p ( neither pen is defective ) = 8 / 11 * 7 / 10 = 28 / 55 the answer is a ."
Answer: a
Question (general): an engineer designed a ball so that when it was dropped , it rose with each bounce exactly one - half as high as it had fallen . the engineer dropped the ball from a 32 - meter platform and caught it after it had traveled 46.5 meters . how many times did the ball bounce ?
Options: a ) 4 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "going down = 32 m going up = 16 - - > total = 48 going down = 16 - - > total = 64 going up = 8 - - > total = 72 going down = 8 - - > total = 80 going up = 4 - - > total = 84 going down = 4 - - > total = 86 going up = 2 - - > total = 88 ( caught ) no of bounces = 4 answer : a"
Answer: a
Question (physics): there are two cars . one is 90 miles north of the other . simultaneously , the car to the north is driven westward at 25 miles per hour and the other car is driven eastward at 35 miles per hour . how many miles apart are the cars after 2 hours ?
Options: a ) 120 , b ) 130 , c ) 140 , d ) 150 , e ) 160
Rationale: "here , drawing a quick sketch of the ' actions ' described will end in a diagonal line that you canbuilda right triangle around : the right triangle will have a base of 90 and a height of 120 . the hidden pattern here is a 3 / 4 / 5 right triangle ( the 90 lines up with the ' 3 ' and the 120 lines up with the ' 4 ' ) . in this way , you can deduce that each side is ' 30 times ' bigger than it ' s corresponding side : 3 / 4 / 5 becomes 90 / 120 / 150 thus the distance between the two cars is the length of the hypotenuse of this larger right triangle . . . final answer : d"
Answer: d
Question (physics): a rectangular box measures internally 1.6 m long , 1 m broad and 60 cm deep . the number of cubical box each of edge 20 cm that can be packed inside the box is :
Options: a ) 30 , b ) 60 , c ) 90 , d ) 120 , e ) 140
Rationale: "explanation : number of blocks = ( 160 x 100 x 60 / 20 x 20 x 20 ) = 120 answer : d"
Answer: d
Question (general): a certain meter records voltage between 0 and 10 volts inclusive . if the average value of 3 recordings on the meter was 9 volts , what was the smallest possible recording in volts ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 7
Rationale: "if average of 3 is 9 so sum of 3 should be 27 3 recording can be from 0 - 10 inclusive to find one smallest other two should be highest so , lets assume three var are a , b , c say a is smallest and give b and c greatest readings say 10 and 10 so a has to be 7 e"
Answer: e
Question (other): bucket p has thrice the capacity as bucket q . it takes 60 turns for bucket p to fill the empty drum . how many turns it will take for both the buckets p & q , having each turn together to fill the empty drum ?
Options: a ) 45 , b ) 53 , c ) 54 , d ) 46 , e ) 63
Rationale: if caoacity of q is x units , then capacity of p is 3 x and capacity of drum is 60 * 3 x = 180 x . it will take 180 x / 4 x = 45 turns it will take for both the buckets p & q , having each turn together to fill the empty drum . answer : a
Answer: a
Question (general): a father said his son , ` ` i was as old as you are at present at the time of your birth . ` ` if the father age is 40 now , the son age 5 years back was
Options: a ) 14 , b ) 17 , c ) 15 , d ) 19 , e ) 99
Rationale: "let the son ' s present age be x years . then , ( 40 - x ) = x x = 20 . son ' s age 5 years back = ( 20 - 5 ) = 15 years answer : c"
Answer: c
Question (other): the h . c . f . of two numbers is 30 and the other two factors of their l . c . m . are 13 and 14 . the larger of the two numbers is :
Options: a ) 276 , b ) 299 , c ) 420 , d ) 345 , e ) 365
Rationale: "clearly , the numbers are ( 30 x 13 ) and ( 30 x 14 ) . larger number = ( 30 x 14 ) = 420 . answer : option c"
Answer: c
Question (gain): find compound interest on rs . 7500 at 4 % per year for 2 years , compounded annually .
Options: a ) 812 , b ) 712 , c ) 412 , d ) 512 , e ) 612
Rationale: "amount = rs [ 7500 * ( 1 + ( 4 / 100 ) 2 ] = rs ( 7500 * ( 26 / 25 ) * ( 26 / 25 ) ) = rs . 8112 . therefore , compound interest = rs . ( 8112 - 7500 ) = rs . 612 . answer is e ."
Answer: e
Question (general): a man whose speed is 5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph , find his average speed for the total journey ?
Options: a ) 7 , b ) 4 , c ) 6 , d ) 9 , e ) 4.55
Rationale: "m = 5.0 s = 1.5 ds = 6.5 us = 3.5 as = ( 2 * 6 * 3 ) / 10 = 4.55 answer : e"
Answer: e
Question (gain): in an election only two candidates contested . a candidate secured 70 % of the valid votes and won by a majority of 178 votes . find the total number of valid votes ?
Options: a ) 445 , b ) 570 , c ) 480 , d ) 520 , e ) 550
Rationale: let the total number of valid votes be x . 70 % of x = 70 / 100 * x = 7 x / 10 number of votes secured by the other candidate = x - 7 x / 100 = 3 x / 10 given , 7 x / 10 - 3 x / 10 = 178 = > 4 x / 10 = 178 = > 4 x = 1780 = > x = 445 . answer : a
Answer: a
Question (geometry): what is the angle between the hands of a clock when time is 10 : 30 ?
Options: a ) 65 deg , b ) 75 deg , c ) 45 deg , d ) 15 deg , e ) 135 deg
Rationale: "angle between two hands = 30 h - 11 / 2 m = 30 * 10 - 30 * 11 / 2 = 300 - 165 = 135 deg answer : e"
Answer: e