Cheukting/mathqa huggingface dataset:
Question (gain): a library branch originally contained 18360 volumes , 30 % of which were fiction novels . 1 / 3 of the volumes were transferred to another location and 1 / 3 of the volumes transferred were fiction novels . what percent of the remaining collection was fiction novels ?
Options: a ) 2.5 % , b ) 17.67 % , c ) 28.3 % , d ) 45.2 % , e ) 73.6 %
Rationale: "as everything is either fraction or percentage , the given figure 18360 is just a false alarm . we can do this by assuming that originally the branch had 100 volumes . originally : total - 100 fiction - 30 transferred : total - 33 ( one third of original total ) fiction - 11 ( one third of those transferred ) remaining : total - 100 − 33 = 67100 − 33 = 67 fiction - 30 − 11 = 1930 − 11 = 19 to find : 19 is what percent of 67 28.3 option c"
Answer: c
Question (physics): the distance between 2 cities a and b is 1000 km . a train starts from a at 1 p . m . and travels towards b at 100 km / hr . another starts from b at 2 p . m . and travels towards a at 150 km / hr . at what time do they meet ?
Options: a ) 11 am . , b ) 6 p . m . , c ) 3 pm . , d ) 2 p . m . , e ) 1 p . m .
Rationale: "suppose they meet x hrs after 1 p . m . distance moved by first in x hrs + distance moved by second in ( x - 1 ) hrs = 1000 100 x + 150 ( x - 1 ) = 1000 x = 4.60 = 5 hrs they meet at 1 + 5 = 6 p . m . answer is b"
Answer: b
Question (general): in a certain brick wall , each row of bricks above the bottom row contains one less brick than the row just below it . if there are 5 rows in all and a total of 50 bricks in the wall , how many bricks does the bottom row contain ?
Options: a ) 12 , b ) 10 , c ) 9 , d ) 8 , e ) 11
Rationale: the bottom row has x bricks x + x - 1 + x - 2 + x - 3 + x - 4 = 50 5 x - 10 = 50 5 x = 40 x = 8 answer : d
Answer: d
Question (general): if 17 ^ 4 * 13 ^ 4 * 9 ^ 4 * 8 ^ 4 = x , what is the units digit of x ?
Options: a ) 8 , b ) 3 , c ) 6 , d ) 7 , e ) 9
Rationale: "17 ^ 4 * 13 ^ 4 * 9 ^ 4 * 8 ^ 4 = x units digit of x will be 7 ^ 4 * 3 ^ 4 * 9 ^ 4 * 8 ^ 4 = 1 * 1 * 1 * 6 = 6 therefore , units digit of x = 6 answer c"
Answer: c
Question (general): mark bought a set of 6 flower pots of different sizes at a total cost of $ 8.25 . each pot cost 0.15 more than the next one below it in size . what was the cost , in dollars , of the largest pot ?
Options: a ) $ 1.75 , b ) $ 1.85 , c ) $ 2.00 , d ) $ 2.15 , e ) $ 2.30
Rationale: "this question can be solved with a handful of different algebra approaches ( as has been shown in the various posts ) . since the question asks for the price of the largest pot , and the answers are prices , we can test the answers . we ' re told that there are 6 pots and that each pot costs 25 cents more than the next . the total price of the pots is $ 8.25 . we ' re asked for the price of the largest ( most expensive ) pot . since the total price is $ 8.25 ( a 15 - cent increment ) and the the difference in sequential prices of the pots is 15 cents , the largest pot probably has a price that is a 15 - cent increment . from the answer choices , i would then test answer a first if . . . . the largest pot = $ 1.75 1 1.15 1.3 1.45 1.6 1.75 total = $ 8.25 so this must be the answer . a"
Answer: a
Question (physics): a pipe can fill a cistern in 66 minutes . find the time in which 1 / 11 part of the cistern will be filled ?
Options: a ) 5 min , b ) 2 min , c ) 6 min , d ) 1 min , e ) 10 min
Rationale: "full cistern filled in = 66 minutes 1 / 11 part filled in = 66 * 1 / 11 = 6 minutes answer is c"
Answer: c
Question (physics): a train crosses a platform of 160 m in 15 sec , same train crosses another platform of length 250 m in 20 sec . then find the length of the train ?
Options: a ) 110 , b ) 887 , c ) 167 , d ) 197 , e ) 161
Rationale: "length of the train be ‘ x ’ x + 160 / 15 = x + 250 / 20 20 x + 3200 = 15 x + 3750 5 x = 550 x = 110 m answer : a"
Answer: a
Question (general): if a = 1 , what is the value of – ( a ^ 2 + a ^ 3 + a ^ 4 + a ^ 5 + a ^ 6 ) ?
Options: a ) - 14 , b ) - 4 , c ) 0 , d ) 4 , e ) - 5
Rationale: "if a = - 1 , then putting values in equation = - [ ( 1 ) ^ 2 + ( 1 ) ^ 3 + ( 1 ^ 4 ) + ( 1 ^ 5 ) + ( 1 ^ 6 ) ] = - [ 1 + 1 + 1 + 1 + 1 ] = - 5 answer = e = - 5"
Answer: e
Question (general): a positive number x is multiplied by 2 , and this product is then divided by 5 . if the positive square root of the result of these two operations equals x , what is the value of x ?
Options: a ) 9 / 4 , b ) 3 / 2 , c ) 4 / 3 , d ) 2 / 3 , e ) 1 / 2
Rationale: "we need to produce an equation from the information given in the problem stem . we are first given that x is multiplied by 2 and then the product is divided by 3 . this gives us : 2 x / 3 next we are given that the positive square root of the result ( which is 2 x / 3 ) is equal to x . this gives us √ ( 2 x / 3 ) = x 2 x / 3 = x ^ 2 2 x = 3 x ^ 2 3 x ^ 2 – 2 x = 0 x ( 3 x – 2 ) = 0 x = 0 or 3 x – 2 = 0 3 x = 2 x = 3 / 2 because x is positive , x = 3 / 2 . the answer is b ."
Answer: b
Question (general): if the number 892 , 132,26 x is divisible by 11 , what must be the value of x ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "multiplication rule of 11 : ( sum of digits at odd places - sum of digits at even places ) should be divisible by 11 given number : 892 , 132,24 x sum of digits at odd places = 8 + 2 + 3 + 2 + x = 15 + x ( i ) sum of digits at even places = 9 + 1 + 2 + 6 = 18 ( ii ) ( i ) - ( ii ) = 15 + x - 18 = x - 3 hence x should be = 3 to make this a multiple of 11 ( 0 ) option c"
Answer: c
Question (physics): two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.75 km and 1.10 km respectively . the time taken by the slower train to cross the faster train in seconds is ?
Options: a ) 48 , b ) 9 , c ) 7 , d ) 66 , e ) 15
Rationale: ": relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 1.75 + 1.10 = 2.75 km = 2750 m . required time = 2750 * 3 / 125 = 66 sec . answer : d"
Answer: d
Question (gain): a and b put in rs . 300 and rs . 400 respectively into a business . a reinvests into the business his share of the first year ' s profit of rs . 210 where as b does not . in what ratio should they divide the second year ' s profit ?
Options: a ) 39 : 40 , b ) 39 : 45 , c ) 39 : 40 , d ) 39 : 41 , e ) 39 : 42
Rationale: "3 : 4 a = 3 / 7 * 210 = 90 390 : 400 39 : 40 answer : a"
Answer: a
Question (other): tea worth rs . 126 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs . 153 per kg , the price of the third variety per kg will be
Options: a ) rs . 169.50 , b ) rs . 1700 , c ) rs . 175.50 , d ) rs . 180 , e ) none
Rationale: "solution since first second varieties are mixed in equal proportions , so their average price = rs . ( 126 + 135 / 2 ) = rs . 130.50 so , the mixture is formed by mixing two varieties , one at rs . 130.50 per kg and the other at say , rs . x per kg in the ratio 2 : 2 , i . e . , 1 : 1 . we have to find x . x - 153 / 22.50 = 1 = › x - 153 = 22.50 = › x = 175.50 . hence , price of the third variety = rs . 175.50 per kg . answer c"
Answer: c
Question (general): if a and b are integers and ( a * b ) ^ 5 = 144 y , y could be :
Options: a ) 40 , b ) 48 , c ) 56 , d ) 62 , e ) 54
Rationale: "distribute the exponent . a ^ 5 * b ^ 5 = 144 y find the prime factorization of 144 . this is 2 ^ 4 * 3 ^ 2 . we need 2 ^ 1 and 3 ^ 3 i . e 2 * 27 = 54 the answer is e ."
Answer: e
Question (general): on dividing 23 by a number , the quotient is 4 and the remainder is 3 . find the divisor .
Options: a ) 1 , b ) 2 , c ) 4 , d ) 5 , e ) 7
Rationale: "d = ( d - r ) / q = ( 23 - 3 ) / 4 = 20 / 4 = 5 d"
Answer: d
Question (geometry): the diagonal of a rectangle is 41 cm and its area is 20 sq . cm . the perimeter of the rectangle must be :
Options: a ) 18 cm
b ) 28 cm
c ) 30 cm
d ) 38 cm
e ) 42 cm
Rationale: l 2 + b 2 = 41 . also , lb = 20 . ( l + b ) 2 = ( l 2 + b 2 ) + 2 lb = 41 + 40 = 81 ( l + b ) = 9 . perimeter = 2 ( l + b ) = 18 cm . a )
Answer: a
Question (physics): a boy is travelling from his home to school at 12 km / hr and reached 7 min late . next day he traveled at 16 km / hr and reached 8 min early . distance between home and school ?
Options: a ) 12 km , b ) 13 km , c ) 14 km , d ) 15 km , e ) 16 km
Rationale: "let the distance be x t 1 = x / 12 hr t 2 = x / 16 hr difference in time = 7 + 8 = 15 = 1 / 4 hr x / 12 - x / 16 = 1 / 4 x / 48 = 1 / 4 x = 12 km answer is a"
Answer: a
Question (gain): if a and b get profits of rs . 15,000 and rs . 5,000 respectively at the end of year then ratio of their investments are
Options: a ) 4 : 1 , b ) 1 : 4 , c ) 3 : 1 , d ) 2 : 3 , e ) 2 : 5
Rationale: "ratio = 15000 / 5000 = 3 : 1 answer : c"
Answer: c
Question (physics): after an ice began to melt out from the freezer , in the first hour lost 3 / 4 , in the second hour lost 3 / 4 of its remaining . if after two hours , the volume is 0.4 cubic inches , what is the original volume of the cubic ice , in cubic inches ?
Options: a ) 2.5
b ) 3.0
c ) 4.0
d ) 6.4
e ) 8.0
Rationale: let initial volume of ice be = x ice remaining after 1 hour = x - 0.75 x = 0.25 x ice remaining after 2 hour = ( 1 / 4 ) x - ( 3 / 4 * 1 / 4 * x ) = ( 1 / 16 ) x ( 1 / 16 ) x = 0.4 x = 6.4 alternate solution : try to backsolve . initial volume = 6.4 after one hour - - > ( 1 / 4 ) 6.4 = 1.6 after two hours - - > ( 1 / 4 ) 1.6 = 0.4 answer : d
Answer: d
Question (physics): the speed of a car is 10 km in the first hour and 60 km in the second hour . what is the average speed of the car ?
Options: a ) 79 kmph , b ) 85 kmph , c ) 35 kmph , d ) 23 kmph , e ) 14 kmph
Rationale: "s = ( 10 + 60 ) / 2 = 35 kmph answer : c"
Answer: c
Question (general): how many integers between 324,700 and 436,600 have tens digit 1 and units digit 3 ?
Options: a ) 327 , b ) 645 , c ) 987 , d ) 1119 , e ) 1339
Rationale: "the integers are : 324,713 324,813 etc . . . 436,513 the number of integers is 4366 - 3247 = 1119 the answer is d ."
Answer: d
Question (general): plaudia can choose any two of 4 different candles and any 8 of 9 different flowers for a centerpiece arrangement . given these choices , how many candle + flower groupings can she select ?
Options: a ) 54 , b ) 72 , c ) 96 , d ) 144 , e ) 432
Rationale: plaudia can choose any two of four different candles and any 8 of 9 different flowers for a centerpiece arrangement . 2 candles from 4 candles : 4 c 2 : 6 8 flowers from 9 flowers : 9 c 8 : 9 so total grouping 9 * 6 = 54 . answer is a .
Answer: a
Question (gain): in town x , 64 percent of the population are employed , and 55 percent of the population are employed males . what percent of the employed people in town x are females ?
Options: a ) 14 % , b ) 25 % , c ) 32 % , d ) 40 % , e ) 52 %
Rationale: "we are asked to find the percentage of females in employed people . total employed people 64 % , out of which 55 are employed males , hence 9 % are employed females . ( employed females ) / ( total employed people ) = 9 / 64 = 14 % answer : a ."
Answer: a
Question (general): for an agricultural experiment , 300 seeds were planted in one plot and 200 were planted in a second plot . if exactly 30 percent of the seeds in the first plot germinated and exactly 35 percent of the seeds in the second plot germinated , what percent of the total number of seeds germinated ?
Options: a ) 12 % , b ) 26 % , c ) 29 % , d ) 32 % , e ) 60 %
Rationale: "in the first plot 30 % of 300 seeds germinated , so 0.3 x 300 = 90 seeds germinated . in the second plot , 35 % of 200 seeds germinated , so 0.35 x 200 = 70 seeds germinated . since 90 + 70 = 260 seeds germinated out of a total of 300 + 200 = 500 seeds , the percent of seeds that germinated is ( 160 / 500 ) x 100 % , or 32 % . answer : d ."
Answer: d
Question (general): ifaequals the sum of the even integers from 2 to 20 , inclusive , andbequals the sum of the odd integers from 1 to 19 , inclusive , what is the value of a + b ?
Options: a ) 110 , b ) 100 , c ) 190 , d ) 200 , e ) 210
Rationale: "answer is 10 yes ! there is really a faster way to solve it . sum of consecutive odd or even integers = ( no . of odd or even ints ) * ( first int + last int ) / 2 here a = sum of even ints from 2 to 20 , inclusive number of even ints = 10 , first int + last int = 2 + 20 = 22 a = 10 * 22 / 2 = 110 b = sum of odd ints from 1 to 19 , inclusive number of odd ints = 10 , first int + last int = 1 + 19 = 20 a = 10 * 20 / 2 = 100 a + b = 110 + 100 = 210 ans : e"
Answer: e
Question (physics): a car takes 6 hours to cover a distance of 540 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 35 kmph , b ) 48 kmph , c ) 52 kmph , d ) 54 kmph , e ) 60 kmph
Rationale: "time = 6 distance = 540 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 540 / 9 = 60 kmph e )"
Answer: e
Question (gain): how long will a boy take to run round a square field of side 50 meters , if he runs at the rate of 12 km / hr ?
Options: a ) 52 sec , b ) 45 sec , c ) 60 sec , d ) 25 sec , e ) 39 sec
Rationale: "speed = 12 km / hr = 12 * 5 / 18 = 10 / 3 m / sec distance = 50 * 4 = 200 m time taken = 200 * 3 / 10 = 60 sec answer is c"
Answer: c
Question (general): a batsman in his 17 th innings makes a score of 85 and their by increasing his average by 3 . what is his average after the 17 th innings ?
Options: a ) 28 , b ) 27 , c ) 12 , d ) 37 , e ) 01
Rationale: "explanation : 16 x + 85 = 17 ( x + 3 ) x = 34 + 3 = 37 answer : d"
Answer: d
Question (gain): running at the same constant rate , 6 identical machines can produce a total of 270 bottles per minute . at this rate , how many bottles could 5 such machines produce in 4 minutes ?
Options: a ) 900 , b ) 1,800 , c ) 2,700 , d ) 10,800 , e ) 64,800
Rationale: "6 machines produce 270 bottles per minute ; 1 machine produces 270 / 6 = 45 bottles per minute ; 5 machines produce 45 * 5 = 225 bottles per minute ; in 4 minutes 10 machines produce 225 * 4 = 900 bottles . answer : a ."
Answer: a
Question (physics): when a train travels at a speed of 70 kmph , it reaches the destination on time . when the same train travels at a speed of 50 kmph , it reaches its destination 15 min late . what is the length of journey ?
Options: a ) 37.5 km , b ) 50.5 km , c ) 60 km , d ) 85.5 km , e ) 95 km
Rationale: "let x be the time reached with the speed 70 km / h 50 km / h - - - - > x + 15 distance is equal so 70 ( km / h ) × xhr = 50 ( km / h ) × ( x + 15 ) hr so 70 x = 50 x + 750 so the would be in km and x = 37.5 answer : a"
Answer: a
Question (general): p , q and r have $ 9000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?
Options: a ) 2400 , b ) 3600 , c ) 3998 , d ) 2539 , e ) 1930
Rationale: "b 3600 let the amount with r be $ r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 9000 - r ) = > 3 r = 18000 - 2 r = > 5 r = 18000 = > r = 3600 ."
Answer: b
Question (probability): if two dice are thrown together , the probability of getting an even number on one die and an odd number on the other is - .
Options: a ) 1 / 3 , b ) 1 / 2 , c ) 7 / 8 , d ) 3 / 4 , e ) 7 / 3
Rationale: "answer : option b the number of exhaustive outcomes is 36 . let e be the event of getting an even number on one die and an odd number on the other . let the event of getting either both even or both odd then = 18 / 36 = 1 / 2 p ( e ) = 1 - 1 / 2 = 1 / 2 ."
Answer: b
Question (general): the sum of the present ages of two persons a and b is 60 . if the age of a is twice that of b , find the sum of their ages 2 years hence ?
Options: a ) 58 , b ) 59 , c ) 64 , d ) 70 , e ) 74
Rationale: "explanation : a + b = 60 , a = 2 b 2 b + b = 60 = > b = 20 then a = 40 . 2 years , their ages will be 42 and 22 . sum of their ages = 42 + 22 = 64 . c )"
Answer: c
Question (general): what is the units digit of the expression 13 ^ 27 + 1 ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 8 , e ) 9
Rationale: "power of 3 follows repetition pattern of = 3 , 9 , 7 , 1 , 3 , 9 , 7 , 1 . . . . repetition after 4 powers = ( 3 , 9 , 7 , 1 ) 13 ^ 27 = 27 th power = 24 + 3 24 / 4 = 6 ( 6 repetitions ) + 3 = ` ` 7 ' ' 7 + 1 = 8 answer d"
Answer: d
Question (physics): how long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 340 m in length ?
Options: a ) 18.9 sec , b ) 88.9 sec , c ) 22.9 sec , d ) 27.00 sec , e ) 72.0 sec
Rationale: "d = 110 + 340 = 450 m s = 60 * 5 / 18 = 50 / 3 t = 450 * 3 / 50 = 27.00 sec answer : d"
Answer: d
Question (gain): the cost price of 30 articles is the same as the selling price of x articles . if the profit is 25 % , what is x ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 24 , e ) 26
Rationale: let the cost price = y the cost price of 30 articles = 30 y the selling price of x articles = 1.25 y * x 1.25 y * x = 30 y x = 30 / 1.25 = 24 the answer is d .
Answer: d
Question (general): a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 42 , the how old is b ?
Options: a ) 16 , b ) 9 , c ) 8 , d ) 11 , e ) 10
Rationale: "explanation : let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 42 ⇒ 5 x = 40 ⇒ x = 8 . hence , b ' s age = 2 x = 16 years . answer : a"
Answer: a
Question (general): calculate the ratio between x and y if 15 % of x equal to 50 % of y ?
Options: a ) 3 : 5 , b ) 3 : 7 , c ) 3 : 8 , d ) 3 : 10 , e ) 3 : 9
Rationale: "explanation : 15 x = 50 y x : y = 15 : 50 = 3 : 10 answer : d"
Answer: d
Question (other): if 0.8 of a number is equal to 0.09 of another number , the ratio of the numbers i
Options: a ) 2 : 3 , b ) 3 : 4 , c ) 9 : 80 , d ) 20 : 3 , e ) none
Rationale: "sol . 0.8 a = 0.09 b â ‡ ” a / b = 0.09 / 0.8 = 9 / 80 = . â ˆ ´ a : b = 9 : 80 . answer c"
Answer: c
Question (general): the product of 3 consecutive numbers is 210 . then the sum of the smallest two numbers is ?
Options: a ) 11 , b ) 15 , c ) 20 , d ) 38 , e ) 56
Rationale: product of three numbers = 210 210 = 2 * 3 * 5 * 7 = 5 * 6 * 7 . so , the three numbers are 5 , 6 and 7 . and sum of smallest of these two = 5 + 6 = 11 . answer : option a
Answer: a
Question (general): how many integers between 263,205 and 658,805 have tens digit 1 and units digit 3 ?
Options: a ) 3,955 , b ) 3,925 , c ) 3,956 , d ) 3,926 , e ) 3,915
Rationale: "there is one number in hundred with 1 in the tens digit and 3 in the units digit : 13 , 113 , 213 , 313 , . . . the difference between 263,205 and is 658,805 - 263205 = 395,600 - one number per each hundred gives 133,900 / 100 = 3,956 answer : c ."
Answer: c
Question (geometry): the diagonals of a rhombus are 11 cm and 20 cm . find its area ?
Options: a ) 329 , b ) 288 , c ) 150 , d ) 238 , e ) 110
Rationale: "1 / 2 * 11 * 20 = 110 answer : e"
Answer: e
Question (gain): a man can row his boat with the stream at 36 km / h and against the stream in 8 km / h . the man ' s rate is ?
Options: a ) 1 kmph , b ) 6 kmph , c ) 7 kmph , d ) 14 kmph , e ) 9 kmph
Rationale: "explanation : ds = 36 us = 8 s = ? s = ( 36 - 8 ) / 2 = 14 kmph answer : d"
Answer: d
Question (general): ashok secured average of 75 marks in 6 subjects . if the average of marks in 5 subjects is 74 , how many marks did he secure in the 6 th subject ?
Options: a ) 38 , b ) 27 , c ) 99 , d ) 17 , e ) 80
Rationale: "explanation : number of subjects = 6 average of marks in 6 subjects = 75 therefore total marks in 6 subjects = 75 * 6 = 450 now , no . of subjects = 5 total marks in 5 subjects = 74 * 5 = 370 therefore marks in 6 th subject = 450 – 370 = 80 answer : e"
Answer: e
Question (geometry): a metallic sheet is of rectangular shape with dimensions 48 m x 36 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 5 m , the volume of the box ( in m 3 ) is :
Options: a ) 4940 , b ) 5120 , c ) 6420 , d ) 8960 , e ) 7960
Rationale: "clearly , l = ( 48 - 10 ) m = 38 m , b = ( 36 - 10 ) m = 26 m , h = 8 m . volume of the box = ( 38 x 26 x 5 ) m 3 = 4940 m 3 . answer : option a"
Answer: a
Question (geometry): a rectangular lawn of dimensions 80 m * 60 m has two roads each 15 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 . 3 per sq m ?
Options: a ) a ) 3820 , b ) b ) 930 , c ) c ) 9309 , d ) d ) 3900 , e ) e ) 5625
Rationale: "explanation : area = ( l + b – d ) d ( 80 + 60 – 15 ) 15 = > 1875 m 2 1875 * 3 = rs . 5625 answer : option e"
Answer: e
Question (physics): a rectangular plot measuring 90 metres by 50 metres is to be enclosed by wire fencing . if the poles of the fence are kept 4 metres apart , how many poles will be needed ?
Options: a ) 55
b ) 70
c ) 57
d ) 58
e ) none of these
Rationale: solution perimeter of the plot = 2 ( 90 + 50 ) = 280 m . ∴ number of poles = [ 280 / 4 ] = 70 m answer b
Answer: b
Question (physics): if the capacity of a cylindrical tank is 1848 m 3 and the diameter of its base is 14 m , then find the depth of the tank .
Options: a ) 10
b ) 11
c ) 12
d ) 13
e ) none of them
Rationale: let the depth of the tank be h meters . then , ∏ x 72 x h = 1848  h = ( 1848 x ( 7 / 22 ) x ( 1 / 49 ) = 12 m answer is c
Answer: c
Question (physics): if a train , travelling at a speed of 160 kmph , crosses a pole in 18 sec , then the length of train is ?
Options: a ) 800 , b ) 125 , c ) 288 , d ) 266 , e ) 121
Rationale: "d = 160 * 5 / 18 * 18 = 800 m answer : a"
Answer: a
Question (physics): a tank is 25 m long 12 m wide and 6 m deep . the cost of plastering its walls and bottom at 45 paise per sq m is
Options: a ) rs . 234.80 , b ) rs . 334.80 , c ) rs . 434.80 , d ) rs . 534.80 , e ) none of these
Rationale: "explanation : area to be plastered = [ 2 ( l + b ) ã — h ] + ( l ã — b ) = [ 2 ( 25 + 12 ) ã — 6 ] + ( 25 ã — 12 ) = 744 sq m cost of plastering = 744 ã — ( 45 / 100 ) = rs . 334.80 answer : b"
Answer: b
Question (physics): a man rows his boat 120 km downstream and 60 km upstream , taking 2 hours each time . find the speed of the stream ?
Options: a ) 6 , b ) 15 , c ) 17 , d ) 18 , e ) 2
Rationale: "speed downstream = d / t = 120 / ( 2 ) = 60 kmph speed upstream = d / t = 60 / ( 2 ) = 30 kmph the speed of the stream = ( 60 - 30 ) / 2 = 15 kmph answer : b"
Answer: b
Question (other): there are 14 slate rocks , 20 pumice rocks , and 10 granite rocks randomly distributed in a certain field . if 2 rocks are chosen at random and without replacement , what is the probability that both rocks will be slate rocks ?
Options: a ) 1 / 5 , b ) 11 / 22 , c ) 81 / 724 , d ) 91 / 946 , e ) 101 / 987
Rationale: "14 / 44 * 13 / 43 = 91 / 946 the answer is d ."
Answer: d
Question (physics): my grandson is about as many days as my son in weeks , and my grandson is as many months as i am in years . my grandson , my son and i together are 150 years . can you tell my son age in years ?
Options: a ) 63 years , b ) 60 years , c ) 50 years , d ) 53 years , e ) 46 years
Rationale: let m be my age in years . if s is my son ' s age in years , then my son is 52 s weeks old . if g is my grandson ' s age in years , then my grandson is 365 g days old . thus , 365 g = 52 s . since my grandson is 12 g months old , 12 g = m . since my grandson , my son and i together are 150 years , g + s + m = 100 . the above system of 3 equations in 3 unknowns ( g , s and m ) can be solved as follows : 52 s / 365 + s + 12 x ( 52 s / 365 ) = 150 or 52 s + 365 s + 365 x ( 624 s / 365 ) = 365 x 150 or s = 54,750 / 1,041 = 53 years answer = d
Answer: d