Cheukting/mathqa huggingface dataset:
Question (general): if the remainder is 11 when positive integer n is divided by 18 , what is the remainder when n is divided by 9 ?
Options: a ) 0 , b ) 2 , c ) 1 , d ) 3 , e ) 4
Rationale: "assume x is quotient here , n = 18 x + 11 - - - - - - - - - - ( 1 ) and n = 9 x + ? we can also write equation ( 1 ) as : n = ( 18 x + 9 ) + 2 . ie 9 ( 2 x + 1 ) + 2 ie the first term is perfectly divisible by 6 . so , the remainder left is 2 . so , answer ( b ) is right choice ."
Answer: b
Question (general): in a certain game , a large bag is filled with blue , green , purple and red chips worth 1 , 5 , x and 11 points each , respectively . the purple chips are worth more than the green chips , but less than the red chips . a certain number of chips are then selected from the bag . if the product of the point values of the selected chips is 88,000 , how many purple chips were selected ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "b - > 1 g - > 5 p - > x ; 5 < x < 11 r - > 11 now , 88000 = 11 * 8 ^ 2 * 5 ^ 4 * 1 ^ n hence no of balls drawn , b = cant be determined g = 4 p = 2 ( only possible value is 8 ) r = 1 hence b"
Answer: b
Question (general): if n = 16 × 10 ^ ( - p ) and − 4 < p < 4 , how many different integer values of p will make n a perfect square ?
Options: a ) 0 , b ) 2 , c ) 3 , d ) 5 , e ) 7
Rationale: i think the answer should be c . thoose are p - values that satisfy given restriction : - 2 , 0 , 2 ( note , a fraction can be also a perfect square ) - - > 16 * 100 , 16 * 1 , 16 / 100
Answer: c
Question (general): in 10 years , a will be twice as old as b was 10 years ago . if a is now 9 years older than b the present age of b is
Options: a ) 37 , b ) 38 , c ) 39 , d ) 40 , e ) 41
Rationale: "let present age of a be a and b be b a + 10 = 2 * ( b - 10 ) = > 2 b - a = 30 . . . . . . ( i ) a = b + 9 = > 2 b - b - 9 = 30 b = 39 so the present age of b is 39 years answer : c"
Answer: c
Question (gain): a reduction of 15 % in the price of salt enables a lady to obtain 10 kgs more for rs . 100 , find the original price per kg ?
Options: a ) 2.8 , b ) 2.3 , c ) 1.8 , d ) 2.1 , e ) 2.9
Rationale: "100 * ( 15 / 100 ) = 15 - - - 10 ? - - - 1 = > rs . 1.5 100 - - - 85 ? - - - 1.5 = > rs . 1.8 answer : c"
Answer: c
Question (gain): on the first of the year , james invested x dollars at proudstar bank in an account that yields 2.5 % in interest every quarter year . at the end of the year , during which he made no additional deposits or withdrawals , he had y dollars in the account . if james had invested the same amount in an account which pays interest on a yearly basis , what must the interest rate be for james to have y dollars at the end of the year ?
Options: a ) 22.04 % , b ) 16.12 % , c ) 8 % , d ) 18.25 % , e ) 10.5 %
Rationale: per quarter , interest = 2.5 % so for a year , interest = 10 % due to quarter cumulation , effective yield ( ytm ) would be slight higher than 10 % answer = 10.5 % = answer : e
Answer: e
Question (physics): a train which has 250 m long , is running 40 kmph . in what time will it cross a person moving at 4 kmph in same direction ?
Options: a ) 30 sec , b ) 28 sec , c ) 29 sec , d ) 35 sec , e ) 25 sec
Rationale: "time taken to cross a moving person = length of train / relative speed time taken = 250 / ( ( 40 - 4 ) ( 5 / 18 ) = 250 / 36 * ( 5 / 18 ) = 250 / 10 = 25 sec answer : e"
Answer: e
Question (physics): two tains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post . if the length of each train be 120 metres , in what time ( in seconds ) will they cross each other travelling in opposite direction ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 20 , e ) 18
Rationale: "sol . speed of the first train = [ 120 / 10 ] m / sec = 12 m / sec . speed of the second train = [ 120 / 15 ] m / sec = 8 m / sec . relative speed = ( 12 + 8 ) = m / sec = 20 m / sec . ∴ required time = ( 120 + 120 ) / 20 secc = 12 sec . answer a"
Answer: a
Question (general): if x is a positive number and 2 the square root of x is equal to x / 2 , then x =
Options: a ) 1 / 16 , b ) 4 , c ) 1 , d ) 2 , e ) 8
Rationale: "2 of sqrt ( x ) = x / 2 , which means that sqrt ( x ) = x or x = x ^ 2 - > divide by x 1 = x x = 1 c ."
Answer: c
Question (physics): two trains of length 100 m and 200 m are 100.00001 m apart . they start moving towards each other on parallel tracks , at speeds 108 kmph and 72 kmph . in how much time will the trains cross each other ?
Options: a ) 8 , b ) 7 , c ) 9 , d ) 2 , e ) 1
Rationale: "relative speed = ( 108 + 72 ) * 5 / 18 = 50 mps . the time required = d / s = ( 100 + 100 + 200 ) / 50 = 400 / 50 = 8 sec . answer : a"
Answer: a
Question (other): in what ratio mental a at rs . 68 per kg be mixed with another metal at rs . 96 per kg so that cost of alloy ( mixture ) is rs . 82 per kg ?
Options: a ) 5 : 8 , b ) 4 : 7 , c ) 3 : 7 , d ) 1 : 1 , e ) 9 : 8
Rationale: "( 96 - 82 ) / ( 82 - 68 ) = 14 / 14 = 1 / 1 answer : d"
Answer: d
Question (general): if a ( a + 2 ) = 48 and b ( b + 2 ) = 48 , where a ≠ b , then a + b =
Options: a ) - 10 , b ) - 9 , c ) - 5 , d ) - 4 , e ) - 2
Rationale: "i . e . if a = 6 then b = - 8 or if a = - 8 then b = 6 but in each case a + b = - 8 + 6 = - 2 answer : b"
Answer: b
Question (gain): an article with cost price of 240 is sold at 20 % profit . what is the selling price ?
Options: a ) 288 , b ) 200 , c ) 204 , d ) 207 , e ) 210
Rationale: "sp = 1.20 * 240 = 288 answer : a"
Answer: a
Question (physics): how many seconds will it take for a car that is traveling at a constant rate of 120 miles per hour to travel a distance of 77 yards ? ( 1 mile = 1,160 yards )
Options: a ) 1.25 , b ) 1.31 , c ) 1.58 , d ) 1.87 , e ) 2.3
Rationale: "speed = 120 miles / hr = 58.67 yard / s distance = 77 yards time = distance / speed = 77 / 58.67 = 1.31 sec ans - b"
Answer: b
Question (probability): a box contains 100 balls , numbered from 1 to 100 . if 3 balls are selected at random and with replacement from the box . if the 3 numbers on the balls selected contain two odd and one even . what is the probability r that the first ball picked up is odd numbered ?
Options: a ) 0 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 1
Rationale: "answer - d selecting the balls either even or odd is having probability 50 / 100 = 1 / 2 we have already selected 3 balls with 2 odd numbers and 1 even number . so we have 3 combinations ooe , oeo , eoo . we have 3 outcomes and 2 are favourable as in 2 cases 1 st number is odd . so probability r is 2 / 3 . d"
Answer: d
Question (general): a store reported total sales of $ 460 million for february of this year . if the total sales for the same month last year was $ 320 million , approximately what was the percent increase in sales ?
Options: a ) 2 % , b ) 17 % , c ) 44 % , d ) 65 % , e ) 83 %
Rationale: "new value – old value ) / old value x 100 we are given : february sales this year = 460 million february sales last year = 320 million we need to determine the percent increase between sales from last year to sales this year . thus , the new value = 460 million and the old value = 320 million . let ’ s plug them into our percent change formula . ( new value – old value ) / old value x 100 [ ( 460 – 320 ) / 320 ] x 100 ≈ 44 % . the answer is c ."
Answer: c
Question (physics): water boils at 212 ° f or 100 ° c and ice melts at 32 ° f or 0 ° c . if the temperature of a pot of water is 55 ° c , what is the temperature of the pot of water in ° f ?
Options: a ) 116 ° f , b ) 125 ° f , c ) 131 ° f , d ) 138 ° f , e ) 145 ° f
Rationale: "let f and c denote the temperature in fahrenheit and celsius respectively . ( f - 32 ) / ( 212 - 32 ) = ( c - 0 ) / ( 100 - 0 ) f = 9 c / 5 + 32 f = 9 ( 55 ) / 5 + 32 = 131 ° f the answer is c ."
Answer: c
Question (physics): what distance will be covered by a bus moving at 126 kmph in 10 seconds ?
Options: a ) 287 , b ) 600 , c ) 350 , d ) 276 , e ) 207
Rationale: "126 kmph = 126 * 5 / 18 = 35 mps d = speed * time = 35 * 10 = 350 m . answer : c"
Answer: c
Question (physics): the dimensions of a room are 10 m x 7 m x 5 m . there are 2 doors and 3 windows in the room . the dimensions of the doors are 1 m x 3 m . one window is of size 2 m x 1.5 m and the other 2 windows are of size 1 m x 1.5 m . the cost of painting the walls at rs . 3 per sq m is
Options: a ) 2488 , b ) 378 , c ) 739 , d ) 474 , e ) 291
Rationale: explanation : area of 4 walls = 2 ( l + b ) h = 2 ( 10 + 7 ) x 5 = 170 sq m area of 2 doors and 3 windows = 2 ( 1 x 3 ) + ( 2 x 1.5 ) + 2 ( 1 x 1.5 ) = 12 sq m area to be planted = 170 - 12 = 158 sq m cost of painting = rs . 158 x 3 = rs . 474 answer : d
Answer: d
Question (general): o ( x ) represents the least odd integer greater than x , whereas o ( x ) represents the greatest odd integer less than x . likewise , e ( x ) represents the least even integer greater than x , whereas e ( x ) represents the greatest even integer less than x . according to these definitions , the value of o ( 5.3 ) + e ( – 6.7 ) + o ( – 7.3 ) + e ( 6.6 ) is :
Options: a ) - 4 , b ) - 2 , c ) 0 , d ) 2 , e ) 4
Rationale: o ( 5.3 ) + e ( – 6.7 ) + o ( – 7.3 ) + e ( 6.6 ) = 7 + ( - 6 ) + ( - 9 ) + 6 = - 2 the answer is b .
Answer: b
Question (general): a quadratic function f ( x ) attains a maximum of 3 at x = 1 . the value of the function at x = 0 is 1 . what is the value of f ( x ) at x = 10 ?
Options: a ) - 119 , b ) - 159 , c ) - 110 , d ) - 180 , e ) - 105
Rationale: explanation : let , the quadratic equation be ax 2 + bx + c . so , f ( x ) = ax 2 + bx + c at x = 0 , the value of function is 1 . x = 0 , f ( x ) = 1 ax 2 + bx + c = a * 0 + b * 0 + c = c c = 1 . at x = 1 , f ( x ) = 3 x = 1 , f ( x ) = 3 a * 1 + b * 1 + c = 3 since c = 1 , a + b = 2 . also , we know that f ( x ) is maximum when x = 1 . if f ( x ) is maximum , ( dx / dt ) ( f ( x ) ) = 0 differentiating f ( x ) , we have d / dt ( ax 2 + bx + c ) = 2 ax + b at x = 1 , 2 ax + b = 0 . 2 a + b = 0 . b = - 2 a . substituting we have a + b = 2 , or a + - 2 a = 2 . a = - 2 . so , b = 4 . so the equation is - 2 x 2 + 4 x + 1 . at x = 10 , the value is - 2 * 100 + 4 * 10 + 1 i . e - 159 . answer : b
Answer: b
Question (gain): in a certain company , a third of the workers do not have a retirement plan . 40 % of the workers who do not have a retirement plan are women , and 40 % of the workers who do have a retirement plan are men . if 120 of the workers of that company are men , how many of the workers are women ?
Options: a ) 80 , b ) 95 , c ) 105 , d ) 120 , e ) 137
Rationale: "set up equation : x = total number of workers 120 = 0,4 * 2 / 3 * x + 0,6 * 1 / 3 * x 120 = 14 / 30 x x = 257 257 - 120 = 137 answer e"
Answer: e
Question (gain): the credit card and a global payment processing companies have been suffering losses for some time now . a well known company recently announced its quarterly results . according to the results , the revenue fell to $ 48.0 billion from $ 72.0 billion , a year ago . by what percent did the revenue fall ?
Options: a ) 20.8 , b ) 30.4 , c ) 31.8 , d ) 32.5 , e ) 33.3
Rationale: "$ 72 - $ 48 = 24 $ ( 24 / 72 ) * 100 = 33.33 % answer : e"
Answer: e
Question (gain): a trader bought a car at 10 % discount on its original price . he sold it at a 80 % increase on the price he bought it . what percent of profit did he make on the original price ?
Options: a ) 17 % , b ) 62 % , c ) 12 % , d ) 19 % , e ) 22 %
Rationale: "original price = 100 cp = 90 s = 90 * ( 180 / 100 ) = 162 100 - 162 = 62 % answer : b"
Answer: b
Question (gain): sue ' s trail mix is 30 % nuts and 70 % dried fruit . jane ' s trail mix is 60 % nuts and 40 % chocolate chips . if the combined mixture of sue and jane ' s trails mix contains 40 % nuts , what percent of the combined mixture is dried fruit ?
Options: a ) 16.7 % , b ) 23.33 % , c ) 25 % , d ) 33.3 % , e ) 46.7 %
Rationale: "40 % is 10 % - points above 30 % and 20 % - points below 60 % . so the ratio of sue ' s mix to jane ' s mix is 2 : 1 . 2 / 3 * 70 % = 140 % / 3 = 46.7 % the answer is e ."
Answer: e
Question (gain): a man buys a cycle for rs . 2800 and sells it at a loss of 25 % . what is the selling price of the cycle ?
Options: a ) s . 2090 , b ) s . 2160 , c ) s . 2100 , d ) s . 2202 , e ) s . 2092
Rationale: "s . p . = 75 % of rs . 2800 = rs . 75 x 2800 / 100 = rs . 1190 answer : option c"
Answer: c
Question (general): if 42.12 = k ( 14 + m / 50 ) , where k and m are positive integers and m < 50 , then what is the value of k + m ?
Options: a ) 5 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "42.12 = 14 k + km / 50 . . . we can rewrite the number as follows : 42 + 0.12 = 14 k + km / 50 . . . . . . . . since k is integer , then 42 = 14 k . . . . . . . . . . k = 3 0.12 = km / 50 . . . . . . 12 / 100 = 3 m / 50 . . . . . . m = 2 k + m = 3 + 2 = 5 answer : a"
Answer: a
Question (general): the ratio of a to b is 4 to 5 , where a and b are positive . if x equals a increased by 25 percent of a , and m equals b decreased by 40 percent of b , what is the value of m / x ?
Options: a ) 2 / 5 , b ) 3 / 4 , c ) 4 / 5 , d ) 5 / 4 , e ) 3 / 5
Rationale: a / b = 4 / 5 m / x = ( 3 / 5 ) * 5 / ( 5 / 4 ) * 4 = 3 / 5 the answer is e .
Answer: e
Question (general): a , b and c rents a pasture for rs . 730 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should c pay ?
Options: a ) 270 , b ) 199 , c ) 676 , d ) 156 , e ) 227
Rationale: "12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 9 / 29 * 730 = 227 answer : e"
Answer: e
Question (geometry): the area of a triangle is with base 10 m and height 5 m ?
Options: a ) 11 , b ) 25 , c ) 787 , d ) 122 , e ) 12
Rationale: "1 / 2 * 10 * 5 = 25 m 2 answer : b"
Answer: b
Question (general): a certain fraction is equivalent to 2 / 5 . if the numerator of the fraction is increased by 4 and the denominator is doubled , the new fraction is equivalent to 1 / 4 . what is the sum of the numerator and denominator of the original fraction ?
Options: a ) 49 , b ) 35 , c ) 56 , d ) 26 , e ) 21
Rationale: "x / y = 2 / 5 - > 1 ( x + 4 ) / 2 y = 1 / 4 - > 2 divide 1 by 2 : = > 2 x / ( x + 4 ) = 8 / 5 = > 5 x = 4 x + 16 = > x = 16 = > y = 5 / 2 * 16 = 40 so x + y = 56 the answer is c"
Answer: c
Question (geometry): how many diagonals does a polygon with 13 sides have , if one of its vertices does not connect to any diagonal ?
Options: a ) 65 , b ) 62 , c ) 58 , d ) 54 , e ) 60
Rationale: "if i calculate it using the formulae , # diagonals = n ( n - 3 ) / 2 each vertex sends of n - 3 diagonals n = 13 - 1 then 12 * ( 12 - 3 ) / 2 = 54 correct option : d"
Answer: d
Question (physics): a car averages 30 miles per hour for the first 5 hours of a trip and averages 42 miles per hour for each additional hour of travel time . if the average speed for the entire trip is 38 miles per hour , how many hours long is the trip ?
Options: a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17
Rationale: "let t be the total time of the trip . 30 * 5 + 42 ( t - 5 ) = 38 t 4 t = 210 - 150 t = 15 the answer is c ."
Answer: c
Question (general): in a certain country 1 / 5 of 8 = 4 . assuming the same proportion , what would be the value of 1 / 4 of 16 ?
Options: a ) 13 , b ) 12 , c ) 10 , d ) 16 , e ) 14
Rationale: c 10
Answer: c
Question (other): in what ratio must a grocer mix two varieties of pulses costing rs . 15 and rs . 20 per kg respectively so as to get a mixture worth rs . 16.50 per kg ?
Options: a ) 3 : 7 , b ) 5 : 7 , c ) 7 : 3 , d ) 7 : 5 , e ) none
Rationale: solution required ratio = 3.50 : 1.50 = 35 : 15 = 7 : 3 . answer c
Answer: c
Question (physics): a can do a piece of work in 4 days . b can do it in 10 days . with the assistance of c they completed the work in 2 days . find in how many days can c alone do it ?
Options: a ) 22 days , b ) 20 / 3 days , c ) 67 days , d ) 17 / 6 days , e ) 18 days
Rationale: "c = 1 / 2 - 1 / 4 - 1 / 10 = 3 / 20 = > 20 / 3 days answer : b"
Answer: b
Question (gain): a and b invests rs . 1500 and rs . 4000 respectively in a business . if a doubles his capital after 6 months . in what ratio should a and b divide that year ' s profit ?
Options: a ) 9 : 5 , b ) 9 : 8 , c ) 9 : 2 , d ) 9 : 9 , e ) 9 : 16
Rationale: "( 1.5 * 6 + 3 * 6 ) : ( 4 * 12 ) 27 : 48 = > 9 : 16 answer : e"
Answer: e
Question (geometry): the length of a rectangular garden is 2 feet longer than 3 times its width . if the perimeter of the garden is 100 feet , find the length of the garden .
Options: a ) 42
b ) 38
c ) 28
d ) 57
e ) 49
Rationale: let l and w be the length and width of the garden . the statement ` ` the length of a rectangular garden is 2 feet longer than 3 times its width ' ' may be formulated by l = 2 + 3 w the formula for the perimeter is given by p = 2 l + 2 w substitute p and l in the above equation by 100 and 2 + 3 w respectively to obtain 100 = 2 ( 2 + 3 w ) + 2 w solve for w and l w = 12 and l = 2 + 3 w = 38 . check that the perimeter of the rectangular garden is 100 p = 2 l + 2 w = 76 + 24 = 100 correct answer b
Answer: b
Question (general): calculate 24 x 99
Options: a ) 2673 , b ) 2763 , c ) 2637 , d ) 2736 , e ) 2376
Rationale: "= 24 - 1 = 23 = ( decrement each digit of the number obtained from 9 ) here we got 23 . now = 9 - 2 = 7 and 9 - 3 = 6 . so we have 76 just write these numbers together . that is we have 23 and 76 . hence answer is 2376 answer is e ."
Answer: e
Question (physics): a fill pipe can fill 1 / 4 of cistern in 16 minutes . in how many minutes , it can fill 3 / 4 of the cistern ?
Options: a ) 24 min , b ) 30 min , c ) 48 min , d ) 26 min , e ) 16 min
Rationale: "required time = 16 * 4 * 3 / 4 = 48 minutes answer is c"
Answer: c
Question (gain): a reduction of 40 % in the price of oil enables a house wife to obtain 8 kgs more for rs . 2400 , what is the reduced price for kg ?
Options: a ) rs . 120 , b ) rs . 125 , c ) rs . 130 , d ) rs . 135 , e ) rs . 140
Rationale: "explanation : 2400 * ( 40 / 100 ) = 960 - - - - 8 ? - - - - 1 = > rs . 120 answer : a"
Answer: a
Question (general): a trail mix company keeps costs down by employing the peanuts : cashews : almonds ratio of 10 : 4 : 1 in each bag of up to 75 total nuts . what is the maximum percentage by which the company could decrease its number of peanuts per bag and still have peanuts constitute more than half the total amount of nuts ?
Options: a ) 40 % , b ) 48 % , c ) 49 % , d ) 50 % , e ) 58 %
Rationale: peanuts = 50 cashews = 20 almonds = 5 we want to remove as many peanuts as possible while still having peanuts represent more than half of the mixture . . . the number of cashews and almonds will stay the same though , so we have 20 + 5 = 25 of those non - peanuts in total . if we had 25 peanuts and 25 non - peanuts , then that would be 50 % exactly . we want more than 50 % though , so we need to add in 1 more peanut . this gives us . . . peanuts = 26 cashews = 20 almonds = 5 the question asked for the decrease in the number of peanuts as a percentage . we started with 50 peanuts and removed 24 = 24 / 50 = 48 % ; answer : b
Answer: b
Question (probability): there is a 30 % chance that tigers will not win at all during the whole season . there is a 30 % chance that portugeese will not play at all in the whole season . what is the greatest possible probability that the tigers will win and portugeese will play during the season ?
Options: a ) 55 % , b ) 60 % , c ) 70 % , d ) 72 % , e ) 80 %
Rationale: "there is a 30 % chance that tigers will not win at all during the whole season we can infer that there is 70 % chance tigers will win . similarly there is a 30 % chance that portugeese will not play at all in the whole season we can also infer that there is 70 % chance that portugeese will play . answer c"
Answer: c
Question (general): we bought a total of 90 books at the store . math books cost $ 4 and history books cost $ 5 . the total price was $ 390 . how many math books did we buy ?
Options: a ) 57 , b ) 60 , c ) 63 , d ) 66 , e ) 69
Rationale: "m + h = 90 h = 90 - m 4 m + 5 h = 390 4 m + 5 * ( 90 - m ) = 390 m = 60 the answer is b ."
Answer: b
Question (physics): the sum of three consecutive even numbers is 60 . find the middle number of the three ?
Options: a ) 14 , b ) 60 , c ) 18 , d ) 70 , e ) 45
Rationale: "three consecutive even numbers ( 2 p - 2 ) , 2 p , ( 2 p + 2 ) . ( 2 p - 2 ) + 2 p + ( 2 p + 2 ) = 60 6 p = 60 = > p = 10 . the middle number is : 10 p = 60 . answer : b"
Answer: b
Question (general): a number when divided by 133 leaves 16 as a remainder . what will be the remainder if the number is divided by 50 ?
Options: a ) 51 , b ) 56 , c ) 49 , d ) 17 , e ) 7
Rationale: "133 + 16 = 149 dividing 149 evenly into whole numbers is 2 and leaves 49 remaining . the correct answer is c ."
Answer: c
Question (gain): the length of a rectangular floor is more than its breadth by 200 % . if rs . 240 is required to paint the floor at the rate of rs . 3 per sq m , then what would be the length of the floor ?
Options: a ) 65 , b ) 44 , c ) 18 , d ) 15.49 , e ) 14
Rationale: "let the length and the breadth of the floor be l m and b m respectively . l = b + 200 % of b = l + 2 b = 3 b area of the floor = 240 / 3 = 80 sq m l b = 80 i . e . , l * l / 3 = 240 l 2 = 240 = > l = 15.49 answer : d"
Answer: d
Question (physics): a train 100 m long crosses a platform 125 m long in 15 sec ; find the speed of the train ?
Options: a ) 91.2 kmph , b ) 61.9 kmph , c ) 45.9 kmph , d ) 61.2 kmph , e ) 71.2 kmph
Rationale: "d = 100 + 155 = 255 t = 15 s = 255 / 15 * 18 / 5 = 61.2 kmph answer : d"
Answer: d
Question (general): john has 10 pairs of matched socks . if he loses 3 individual socks , what is the greatest number of pairs of matched socks he can have left ?
Options: a ) 7 , b ) 8 , c ) 5 , d ) 4 , e ) 3
Rationale: "because we have to maximize the pair of matched socks , we will remove 1 pairs ( 2 socks ) out of 10 pairs 1 sock from the 2 th pair . thus the no of matching socks pair remaining = 10 - 2 = 8 answer b"
Answer: b
Question (physics): a train 250 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 ) 15 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 250 m at ( 50 / 3 ) m / sec = ( 250 x 3 / 50 ) sec = 15 sec . answer d"
Answer: d
Question (other): a garrison of 400 men had a provision for 31 days . after 26 days 275 persons re - enforcement leave the garrison . find the number of days for which the remaining ration will be sufficient ?
Options: a ) 16 days , b ) 45 days , c ) 10 days , d ) 17 days , e ) 18 days
Rationale: "400 - - - 31 400 - - - 5 125 - - - ? 400 * 5 = 125 * x = > x = 16 days . answer : a"
Answer: a
Question (gain): if the cost price of 50 articles is equal to the selling price of 40 articles , then the gain or loss percent is ?
Options: a ) 33 % , b ) 29 % , c ) 25 % , d ) 55 % , e ) 39 %
Rationale: "c 25 % given that , cost price of 50 article is equal to selling price of 40 articles . let cost price of one article = rs . 1 selling price of 40 articles = rs . 50 but cost price of 40 articles = rs . 40 therefore , the trader made profit . \ percentage of profit = 10 / 40 * 100 = 25 %"
Answer: c
Question (other): if two dice are thrown together , the probability of getting an even number on both dice is
Options: a ) 1 / 4 , b ) 1 / 5 , c ) 1 / 6 , d ) 1 / 3 , e ) 1 / 2
Rationale: "the number of exhaustive outcomes is 36 . let e be the event of getting an even number on both dies is 9 / 36 = 1 / 4 p ( e ) = 1 / 4 . a )"
Answer: a