Cheukting/mathqa huggingface dataset:
Question (general): for all real numbers v , an operation is defined by the equation v * = v - v / 3 . if ( v * ) * = 24 , then v =
Options: a ) 45 , b ) 48 , c ) 51 , d ) 54 , e ) 57
Rationale: "( v * ) * = ( v - v / 3 ) - ( v - v / 3 ) / 3 24 = 2 v / 3 - 2 v / 9 = 4 v / 9 v = 54 the answer is d ."
Answer: d
Question (geometry): the least perfect square , which is divisible by each of 21,36 and 66 is
Options: a ) 213444
b ) 214344
c ) 214434
d ) 213443
e ) none of these
Rationale: l . c . m . of 21 , 36 , 66 = 2772 . now , 2772 = 2 x 2 x 3 x 3 x 7 x 11 to make it a perfect square , it must be multiplied by 7 x 11 . so , required number = 22 x 32 x 72 x 112 = 213444 answer a
Answer: a
Question (general): what is the greatest prime factor of 2 ^ 10 - 1 ?
Options: a ) 17 , b ) 19 , c ) 23 , d ) 29 , e ) 31
Rationale: "2 ^ 10 - 1 = ( 2 ^ 5 - 1 ) ( 2 ^ 5 + 1 ) = 31 * 33 the answer is e ."
Answer: e
Question (general): a wholesaler wishes to sell 100 pounds of mixed nuts at $ 2.50 a pound . she mixes peanuts worth $ 1.50 a pound with cashews worth $ 5.00 a pound . how many pounds of cashews must she use ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60
Rationale: "from the question stem we know that we need a mixture of 100 pounds of peanuts and cashews . if we represent peanuts as x and cashews as y , we get x + y = 100 . since the wholesaler wants to sell the mixture of 100 pounds @ $ 2.50 , we can write this as : $ 2.5 * ( x + y ) = $ 1.5 x + $ 4 y from the equation x + y = 100 , we can rewrite y as y = 100 - x and substitute this into our equation to get : $ 2.5 * ( x + 100 - x ) = $ 1.5 x + $ 4 ( 100 - x ) if you solve for x , you will get x = 60 , and therefore y = 40 . so the wholesaler must use 40 pounds of cashews . you can substitute into the original equation to see that : $ 250 = $ 1.5 ( 60 ) + $ 4 ( 40 ) answer is b"
Answer: b
Question (general): 4 years ago , paula was 4 times as old as karl . in 12 years , paula will be twice as old as karl . what is the sum of their ages now ?
Options: a ) 36 , b ) 40 , c ) 44 , d ) 48 , e ) 52
Rationale: "p - 4 = 4 ( k - 4 ) and so p = 4 k - 12 p + 12 = 2 ( k + 12 ) ( 4 k - 12 ) + 12 = 2 k + 24 k = 12 p = 36 p + k = 48 the answer is d ."
Answer: d
Question (general): there are 15 teams in a certain league and each team plays each of the other teams exactly twice . if each game is played by 2 teams , what is the total number of games played ?
Options: a ) 15 , b ) 16 , c ) 28 , d ) 56 , e ) 210
Rationale: "every team plays with 14 teams . . . so total no of matches = 15 x 14 = 210 . now , each match is played twice = > 210 x 2 but 2 teams play a match = > 210 x 2 / 2 = 210 . answer : e"
Answer: e
Question (general): if w / x = 2 / 3 and w / y = 6 / 15 , then ( x + y ) / y =
Options: a ) 4 / 5 , b ) 6 / 5 , c ) 7 / 5 , d ) 8 / 5 , e ) 9 / 5
Rationale: w / x = 2 / 3 = > x = 3 / 2 w and w / y = 6 / 15 = > y = 15 / 6 w ( x + y ) / y = ( 3 / 2 w + 15 / 6 w ) / 15 / 6 w = 4 w / ( 15 / 6 w ) = 8 / 5 correct option : d
Answer: d
Question (general): a “ palindromic integer ” is an integer that remains the same when its digits are reversed . so , for example , 43334 and 516615 are both examples of palindromic integers . how many 6 - digit palindromic integers are both even and greater than 500,000 ?
Options: a ) 160 , b ) 200 , c ) 240 , d ) 300 , e ) 480
Rationale: the first digit and last digit are the same so the 2 possibilities are 6 or 8 . the second and third digits can be any number from 0 to 9 . the total number of palindromic integers is 2 * 10 * 10 = 200 the answer is b .
Answer: b
Question (gain): a trader sold an article on a certain price with 40 % profit . if he sold double of previous selling price then find its profit %
Options: a ) 140 % , b ) 180 % , c ) 120 % , d ) 100 % , e ) 150 %
Rationale: "let cost price = 100 % selling price = 140 % new s . p . = 280 % p % = 280 - 100 = 180 % answer is b"
Answer: b
Question (general): the average price of an decoration piece increases over the years . if from 1990 to 1996 , the price of the decoration piece increased by 13 % and from 1996 to 2001 it increased by 20 % , what is the price of the decoration piece in 2001 if the price in 1990 was $ 11500 ?
Options: a ) $ 15594 . , b ) $ 15322 . , c ) $ 14786 . , d ) $ 14543 . , e ) $ 12988 .
Rationale: whenever you have a question in which a value is increased by x % and then increased by y % then the overall effective increase = ( x + y + xy / 100 ) % the effective increase = 13 + 20 + ( 13 × 20 / 100 ) = 35.6 % this is a little more 33 % or 1 / 3 the original value . the quickest way to solve this question is to use approximation . 11500 + 1 / 3 ( 12000 ) = 15500 therefore option a is the answer . i selected 12000 because it ' s value is a little more 11500 and it ' s easier to divide by 3 ( ie to calculate 1 / 3 or 33 % ) .
Answer: a
Question (geometry): how many 2 - inch by 3 - inch rectangular tiles are required to tile this shaded region ?
Options: a ) less than 10
b ) 10 — 100
c ) 101 — 1,000
d ) 1,001 — 1,500
e ) 1,500 +
Rationale: convert all feet into inches as we are looking into tiles which are in inches so total area of garden = 6 * 12 * 12 * 12 shaded region = 12 * 12 ( 6 * 12 - 2 * 3 ) = 12 * 12 * 2 * 3 ( 12 - 1 ) no of 2 ' ' * 3 ' ' tiles required = 12 ∗ 12 ∗ 12 ∗ 2 ∗ 3 ∗ 11 / 2 ∗ 3 = 12 ∗ 12 ∗ 11 = 1584 > 1500 so ans is 1500 + answer : e
Answer: e
Question (geometry): a cube is painted red on all faces . it is then cut into 27 equal smaller cubes . how many h 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 . h = 4 + 4 + 4 = 12 . answer a"
Answer: a
Question (geometry): the length of a rectangle is increased by 15 % and its breadth is decreased by 20 % . what is the effect on its area ?
Options: a ) 1288 , b ) 1299 , c ) 1000 , d ) 10000 , e ) 9200
Rationale: "100 * 100 = 10000 115 * 80 = 9200 answer : e"
Answer: e
Question (gain): solve the quickfire maths brain teaser â ˆ š 16 % = ?
Options: a ) 30 % , b ) 40 % , c ) 85 % , d ) 19 % , e ) 29 %
Rationale: "â ˆ š 16 % = > â ˆ š 16 / â ˆ š 100 = > 4 / 10 = > 40 / 100 = > 40 % b"
Answer: b
Question (physics): how many seconds will a train 150 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph ?
Options: a ) 28 sec , b ) 23 sec , c ) 29 sec , d ) 30 sec , e ) 36 sec
Rationale: "d d = 150 + 150 = 300 s = 36 * 5 / 18 = 10 mps t = 300 / 10 = 30 sec"
Answer: d
Question (general): the price of a bushel of corn is currently $ 3.20 , and the price of a peck of wheat is $ 8.80 . the price of corn is increasing at a constant rate of 5 x cents per day while the price of wheat is decreasing at a constant rate of x ( 2 ^ 1 / 2 ) - x cents per day . what is the approximate price when a bushel of corn costs the same amount as a peck of wheat ?
Options: a ) $ 8.40 , b ) $ 5.10 , c ) $ 5.30 , d ) $ 5.50 , e ) $ 5.60
Rationale: "i tried using time / rate approach : - initial price difference = 8.80 - 3.20 = 5.60 price of corn increasing by 5 x price of wheat decreasing by x ( 1.4 ) - x = . 4 x since both the quantities are moving towards reducing the price gap hence : - relative increase = 5 x + . 4 x let t be the time by which gap is filled so , 5.6 = t ( 5.4 x ) - > t = ( 5.6 ) / 5.4 x final price = 3.20 + 5 x * t - > 3.20 + 5 * 5.6 / 5.4 = 8.4 answer a ."
Answer: a
Question (geometry): find the area of the quadrilateral of one of its diagonals is 28 cm and its off sets 9 cm and 6 cm ?
Options: a ) 210 cm 2 , b ) 150 cm 2 , c ) 168 cm 2 , d ) 198 cm 2 , e ) 987 cm 2
Rationale: "1 / 2 * 28 ( 9 + 6 ) = 210 cm 2 answer : a"
Answer: a
Question (geometry): the largest one digit number which is a perfect cube , is :
Options: a ) 7 , b ) 8 , c ) 9 , d ) 1 , e ) 0
Rationale: "explanation : 2 * 2 * 2 = 8 answer : b"
Answer: b
Question (general): when the price of a product was decreased by 20 % , the number sold increased by 60 % . what was the effect on the total revenue ?
Options: a ) 28 % , b ) 32 % , c ) 35 % , d ) 45 % , e ) 52 %
Rationale: let the price of the product be $ 100 and let original sale be 100 pieces then , total revenue = 100 * 100 = $ 10000 new revenue = 80 * 160 = $ 12800 increase in revenue = 2800 * 100 / 10000 = 28 % answer is a
Answer: a
Question (general): in a rare coin collection , all coins are either pure gold or pure silver , and there is initially one gold coin for every 3 silver coins . with the addition of 15 more gold coins to the collection , the ratio of gold coins to silver coins is 1 to 2 . based on this information , how many total coins are there now in this collection ( after the acquisition ) ?
Options: a ) 124 , b ) 135 , c ) 146 , d ) 157 , e ) 168
Rationale: initially the number of gold coins and silver coins is 2 k and 6 k . after adding gold coins , the number of coins is 3 k and 6 k . thus k = 15 and the total number of coins is 9 k = 135 . the answer is b .
Answer: b
Question (general): positive integer y is 50 percent of 50 percent of positive integer x , and y percent of x equals 100 . what is the value of y ?
Options: a ) 50 , b ) 100 , c ) 200 , d ) 1,000 , e ) 2,000
Rationale: "y = 50 % of 50 % 0 f x = x / 4 and y / 100 of x = 100 y / 100 * 4 y = 100 y = 50 answer - a"
Answer: a
Question (gain): after giving a discount of rs . 45 the shopkeeper gets a loss of 10 % , if the cost price is rs . 180 . find the markup % ?
Options: a ) 0.21 , b ) 0.2 , c ) 0.17 , d ) 0.21 , e ) 0.15
Rationale: "cost price = 180 s . p = 180 * 90 / 100 = 162 disc = 45 so . . . mark price = 162 + 45 = 207 . . . . . . mark up % = 207 - 180 / 180 = 81 / 180 = . 15 or 15 % answer : e"
Answer: e
Question (general): a student has to obtain 35 % of the total marks to pass . he got 100 marks and failed by 40 marks . the maximum marks are ?
Options: a ) 280 , b ) 400 , c ) 420 , d ) 480 , e ) 520
Rationale: "let the maximum marks be x then , 35 % of x = 100 + 40 35 x / 100 = 140 35 x = 140 * 100 = 14000 x = 400 answer is b"
Answer: b
Question (general): if a : b = 3 : 4 , b : c = 7 : 9 , c : d = 5 : 7 , find a : d ?
Options: a ) 5 / 12 , b ) 5 / 15 , c ) 5 / 10 , d ) 5 / 11 , e ) 5 / 13
Rationale: "a / d = ( 3 / 4 ) * ( 7 / 9 ) * ( 5 / 7 ) = > 5 / 12 answer : a"
Answer: a
Question (general): the average age of an adult class is 40 years . 12 new students with an avg age of 32 years join the class . therefore decreasing the average by 4 year . find what was theoriginal strength of class ?
Options: a ) 8 , b ) 12 , c ) 15 , d ) 17 , e ) 18
Rationale: "let original strength = y then , 40 y + 12 x 32 = ( y + 12 ) x 36 ⇒ 40 y + 384 = 36 y + 432 ⇒ 4 y = 48 ∴ y = 12 b"
Answer: b
Question (physics): a , b and c can do a piece of work in 24 days , 30 days and 40 days respectively . they began the work together but c left 12 days before the completion of the work . in how many days was the work completed ?
Options: a ) 13 days , b ) 16 days , c ) 18 days , d ) 11 days , e ) 38 days
Rationale: "one day work of a , b and c = 1 / 24 + 1 / 30 + 1 / 40 = 1 / 10 work done by a and b together in the last 12 days = 12 * ( 1 / 24 + 1 / 30 ) = 9 / 10 remaining work = 1 / 10 the number of days required for this initial work = 1 days . the total number of days required = 12 + 1 = 13 days . answer : a"
Answer: a
Question (general): a parking garage rents parking spaces for $ 10 per week or $ 25 per month . how much does a person save in a year by renting by the month rather than by the week ?
Options: a ) $ 120 , b ) $ 160 , c ) $ 220 , d ) $ 240 , e ) $ 260
Rationale: "10 $ per week ! an year has 52 weeks . annual charges per year = 52 * 10 = 520 $ 30 $ per month ! an year has 12 months . annual charges per year = 12 * 25 = 300 $ 520 - 300 = 120 ans a"
Answer: a
Question (general): if n is a positive integer and the product of all integers from 1 to n , inclusive , is a multiple of 630 , what is the least possible value of n ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "630 = 2 * 3 * 3 * 5 * 7 , so n must be at least 7 . the answer is c ."
Answer: c
Question (general): the total marks obtained by a student in mathematics and physics is 30 and his score in chemistry is 20 marks more than that in physics . find the average marks scored in mathamatics and chemistry together .
Options: a ) 40 , b ) 30 , c ) 25 , d ) data inadequate , e ) none of these .
Rationale: "let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 30 and c - p = 20 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 30 + 20 ) / 2 = 25 . answer : c"
Answer: c
Question (gain): a lent rs . 5000 to b for 2 years and rs . 3000 to c for 4 years on simple interest at the same rate of interest and received rs . 1540 in all from both of them as interest . the rate of interest per annum is ?
Options: a ) 7 % , b ) 12 % , c ) 74 % , d ) 10 % , e ) 45 %
Rationale: "let the rate be r % p . a . then , ( 5000 * r * 2 ) / 100 + ( 3000 * r * 4 ) / 100 = 1540 100 r + 120 r = 1540 r = 7 % answer : a"
Answer: a
Question (general): solve for x and check : 25 x = 675
Options: a ) 675 , b ) 725 , c ) 895 , d ) 1025 , e ) none of these
Rationale: "solution : dividing each side by 25 , we obtain ( 25 x / 675 ) = ( 675 / 25 ) therefore : x = 27 check : 25 x = 675 ( 25 * 27 ) = 675 675 = 675 answer : a"
Answer: a
Question (general): given that x and y are events such that z ( x ) = 0.02 z ( y ) = 0.10 z ( xny ) = 0.10 z ( x | y ) = find z ( x | y ) and z ( x | y )
Options: a ) 1 / 5 , b ) 1 / 6 , c ) 1 / 6 , d ) 1 / 4 , e ) 1 / 2
Rationale: here , x and y are events z ( x | y ) = z ( xny ) / z ( y ) = 0.10 / 0.10 = 1 q ( g | h ) = z ( xny ) / z ( x ) = 0.4 / 0.02 = 1 / 5 answer is a
Answer: a
Question (other): a jar contains a mixture of ab in the ratio 4 : 1 . when 40 l of mixture is replaced with liquid b , ratio becomes 2 : 3 . how many liters of liquid a was present in mixture initially .
Options: a ) 12 , b ) 15 , c ) 16 , d ) 64 , e ) 25
Rationale: 40 litres of mixture that is replaced will contain 32 litres of a and 8 litres of b ( as a : b = 4 : 1 ) let the initial volume of the mixture be 4 k + 1 k = 5 k so by condition , [ 4 k - 32 ] / [ k - 8 + 40 ] = 2 / 3 = > 12 k - 96 = 2 k - 16 + 80 = > 10 k = 160 solve for k which is k = 16 so initial volume of liquid a = 4 k = 64 litres answer : d
Answer: d
Question (geometry): the length of a rectangle is 3 times its width . if the width of the rectangle is 6 inches , what is the rectangle ' s area , in square inches ?
Options: a ) 30 square inches , b ) 108 square inches , c ) 68 square inches , d ) 89 square inches , e ) 92 square inches
Rationale: "if the width is 6 in and the length is 3 times the width , then the length is 3 * 6 = 18 in the area is given by 6 * 18 = 108 square inches correct answer b"
Answer: b
Question (gain): a , b and c started a business with capitals of rs . 8000 , rs . 10000 and rs . 12000 respectively . at the end of the year , the profit share of b is rs . 2500 . the difference between the profit shares of a and c is ?
Options: a ) 621 , b ) 276 , c ) 236 , d ) 1000 , e ) 211
Rationale: "explanation : ratio of investments of a , b and c is 8000 : 10000 : 12000 = 4 : 5 : 6 and also given that , profit share of b is rs . 2500 = > 5 parts out of 15 parts is rs . 2500 now , required difference is 6 - 4 = 2 parts required difference = 2 / 5 ( 2500 ) = rs . 1000 answer : d"
Answer: d
Question (physics): a truck drives 80 miles on local roads at 30 mph , and 50 miles on the highway at 60 mph , the truck also take a hour lunch break . what is the average speed of the entire trip ?
Options: a ) 30 mph , b ) 29 mph , c ) 28 mph , d ) 31 mph , e ) 23 mph
Rationale: so the answer is plainly a . . . . we have a general relation for speed , time and distance : v ( velocity ) * t ( time ) = d ( distance ) for first part we have d = 80 miles , and v = 30 mph so we can obtain time : 30 * t = 80 or t = 80 / 30 = 2.6 hours the needed time to cover 80 miles in the same way we should divide 50 to 60 to find the needed time to cover 50 miles , so t = 0.8 hours so the total time for covering total distance would be 2.6 + 0.8 + 1 ( lunch time ) = 4.4 hours and total distance is 80 + 50 = 130 miles final stage : average speed is total distance divide to total time : 130 / 4.4 = 29.5 miles per hour rounding up to 30 . . . .
Answer: a
Question (general): carrey rented a car for rs . 20 plus rs . 0.25 per kilometer driven . samuel rented a car for rs . 24 plus rs . 0.16 per kilometer driven . if each drove d km . and each was charged exactly the same amount for the rental , then d equals ?
Options: a ) 44.4 , b ) 44.8 , c ) 1 , d ) 19 , e ) 44.11
Rationale: explanation : 20 + 0.25 × d = 24 + 0.16 d solving we get d = 44.4 answer : a
Answer: a
Question (general): the first doughnut is priced at $ 1 and then if you purchase additional doughnuts as dozens then the price is $ 6 / dozen . what is the total number of doughnuts purchased if you paid $ 24 ?
Options: a ) 44 , b ) 46 , c ) 48 , d ) 50 , e ) 52
Rationale: $ 24 = 4 * $ 6 the number of doughnuts is 4 * 12 = 48 the answer is c .
Answer: c
Question (physics): the speed of the boat in still water in 12 kmph . it can travel downstream through 48 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 = 48 / 3 = 16 km / hr upstream = > > still water = ( u + v / 2 ) = > > 12 = u + 16 / 2 = 8 km / hr so time taken in upstream = 48 / 8 = 6 hrs answer : e"
Answer: e
Question (gain): on a sum of money , the simple interest for 2 years is rs . 326 , while the compound interest is rs . 340 , the rate of interest being the same in both the cases . the rate of interest is
Options: a ) 15 % , b ) 14.25 % , c ) 8.58 % , d ) 10.5 % , e ) 11.5 %
Rationale: "explanation : the difference between compound interest and simple interest on rs . p for 2 years at r % per annum = ( r ã — si ) / ( 2 ã — 100 ) difference between the compound interest and simple interest = 340 - 326 = 14 ( r ã — si ) / ( 2 ã — 100 ) = 14 ( r ã — 326 ) / ( 2 ã — 100 ) = 14 r = 8.58 % answer : option c"
Answer: c
Question (general): in a certain supermarket , a triangular display of cans is arranged in 9 rows , numbered 1 through 9 from top to bottom . each successively numbered row contains 3 more cans than the row immediately above it . if there are fewer than 120 cans in the entire display , how many cans are in the seventh row ?
Options: a ) 13 , b ) 15 , c ) 17 , d ) 19 , e ) 21
Rationale: "let x be the number of cans in row 1 . the total number of cans is x + ( x + 3 ) + . . . + ( x + 24 ) = 9 x + 3 ( 1 + 2 + . . . + 8 ) = 9 x + 3 ( 8 ) ( 9 ) / 2 = 9 x + 108 since the total is less than 120 , x must equal 1 . the number of cans in the 7 th row is 1 + 3 ( 6 ) = 19 the answer is d ."
Answer: d
Question (geometry): the length of a rectangle is 3 times its width . if the width of the rectangle is 4 inches , what is the rectangle ' s area , in square inches ?
Options: a ) 30 square inches , b ) 75 square inches , c ) 68 square inches , d ) 48 square inches , e ) 92 square inches
Rationale: "if the width is 4 in and the length is 3 times the width , then the length is 3 * 4 = 12 in the area is given by 4 * 12 = 48 square inches correct answer d"
Answer: d
Question (general): the average age of students of a class is 15.8 years . the average age of boys in the class is 16.4 years and that of the girls is 15.7 years . the ration of the number of boys to the number of girls in the class is ?
Options: a ) 1 : 6 , b ) 2 : 3 , c ) 2 : 5 , d ) 2 : 1 , e ) 2 : 4
Rationale: "let the ratio be k : 1 . then , k * 16.4 + 1 * 15.7 = ( k + 1 ) * 15.8 = ( 16.4 - 15.8 ) k = ( 15.8 - 15.7 ) = k = 0.1 / 0.6 = 1 / 6 required ratio = 1 / 6 : 1 = 1 : 6 . answer : a"
Answer: a
Question (gain): a man walking at a rate of 5 km / hr crosses a bridge in 15 minutes . the length of the bridge is ?
Options: a ) 1250 m , b ) 1310 m , c ) 1500 m , d ) 1000 m , e ) 1195 m
Rationale: "speed = 5 * 5 / 18 = 25 / 18 m / sec distance covered in 15 minutes = 25 / 18 * 15 * 60 = 1250 m answer is a"
Answer: a
Question (physics): a train traveling at 108 kmph crosses a platform in 30 seconds and a man standing on the platform in 12 seconds . what is the length of the platform in meters ?
Options: a ) 240 meters , b ) 360 meters , c ) 420 meters , d ) 600 meters , e ) can not be determined
Rationale: "answer distance covered by the train when crossing a man and when crossing a platform when a train crosses a man standing on a platform , the distance covered by the train is equal to the length of the train . however , when the same train crosses a platform , the distance covered by the train is equal to the length of the train plus the length of the platform . the extra time that the train takes when crossing the platform is on account of the extra distance that it has to cover . i . e . , length of the platform . compute length of platform length of the platform = speed of train * extra time taken to cross the platform . length of platform = 108 kmph * 12 seconds convert 108 kmph into m / sec 1 kmph = 5 / 18 m / s ( this can be easily derived . but if you can remember this conversion , it saves a good 30 seconds ) . ∴ 108 kmph = 5 / 18 ∗ 108 = 30 m / sec therefore , length of the platform = 30 m / s * 12 sec = 360 meters . choice b"
Answer: b
Question (gain): the ratio of investments of two partners p and q is 7 : 5 and the ratio of their profits is 7 : 11 . if p invested the money for 5 months , find for how much time did q invest the money ?
Options: a ) 19 , b ) 17 , c ) 13 , d ) 11 , e ) 12
Rationale: "7 * 5 : 5 * x = 7 : 11 x = 11 answer : d"
Answer: d
Question (gain): a fair price shopkeeper takes 10 % profit on his goods . he lost 30 % goods during theft . his loss percent is :
Options: a ) 23 % , b ) 42 % , c ) 32 % , d ) 12 % , e ) 22 %
Rationale: "explanation : suppose he has 100 items . let c . p . of each item be re . 1 . total cost = rs . 100 . number of items left after theft = 70 . s . p . of each item = rs . 1.10 total sale = 1.10 * 70 = rs . 77 hence , loss % = 23 / 100 * 100 = 23 % answer : a"
Answer: a
Question (geometry): some people are standing square . from them 32 are removed and then form a small square and then 8 more removed . now we can not form the square . so how many people are there at the beginning ?
Options: a ) 31 , b ) 32 , c ) 33 , d ) 34 , e ) ca n ' t be determined
Rationale: we should find the two square numbers whose difference is 32 . starting from 9,16 , 25,36 , 49,64 , 81,100 , . . . . we observe 81 - 49 = 32 & 49 - 8 = 41 which is not a square . answer : e
Answer: e
Question (physics): how many seconds will a 500 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
Options: a ) 22 , b ) 30 , c ) 88 , d ) 26 , e ) 12
Rationale: "speed of train relative to man = 63 - 3 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 500 * 3 / 50 = 30 sec . answer : b"
Answer: b
Question (general): the ages of 2 persons differ by 32 years . if 12 years ago the elder one be 6 times as old as the younger one , find the present age of elder person .
Options: a ) 30 , b ) 48.5 , c ) 50.4 , d ) 62.6 , e ) 47.9
Rationale: "age of the younger person = x age of the elder person = x + 32 6 ( x - 12 ) = x + 32 - 12 x = 18.4 age of elder person = 18.4 + 32 = 50.4 answer is c"
Answer: c