Cheukting/mathqa huggingface dataset:
Question (general): the number of boxes in a warehouse can be divided evenly into 9 equal shipments by boat or 24 equal shipments by truck . what is the smallest number of boxes that could be in the warehouse ?
Options: a ) 27 , b ) 33 , c ) 72 , d ) 81 , e ) 162
Rationale: "answer is the lcm of 9 and 24 = 72 answer c"
Answer: c
Question (physics): an outlet pipe empties a tank which is full in 5 hours . if the inlet pipe is kept open , which lets water in at the rate of 8 litres / min then outlet pipe would take 3 hours longer . find the capacity of the tank .
Options: a ) 8600 litres , b ) 200 litres , c ) 12800 litres , d ) 6400 litres , e ) 13200 litres
Rationale: "let the rate of outlet pipe be x liters / hour ; rate of inlet pipe is 8 litres / min , or 8 * 60 = 480 liters / hour ; net outflow rate when both pipes operate would be x - 480 liters / hour . capacity of the tank = x * 5 hours = ( x - 480 ) * ( 5 + 3 ) hours 5 x = ( x - 480 ) * 8 - - > x = 1280 - - > capacity = 5 x = 6400 liters . answer : d"
Answer: d
Question (physics): a can do a piece of work in 3 hours ; b and c together can do it in 2 hours , which a and b together can do it in 2 hours . how long will c alone take to do it ?
Options: a ) 2 hours , b ) 5 hours , c ) 6 hours , d ) 4 hours , e ) 3 hours
Rationale: "a ' s 1 hour work = 1 / 3 ; ( b + c ) ' s 1 hour work = 1 / 2 ; ( a + b ) ' s 1 hour work = 1 / 2 ( a + b + c ) ' s 1 hour work = ( 1 / 3 + 1 / 2 ) = 5 / 6 c ' s 1 hour work = ( 5 / 6 - 1 / 2 ) = 1 / 3 c alone will take 3 hours to do the work . answer : e"
Answer: e
Question (physics): tony alone can paint a wall in 7 days and his friend roy alone can paint the same wall in 9 days . in how many days they can paint the wall working together ? round off the answer to the nearest integer .
Options: a ) 2 , b ) 4 , c ) 6 , d ) 7 , e ) 9
Rationale: sol . use formula ( xy / x + y ) so nearest value for 3.93 = 4 answer : option b
Answer: b
Question (general): when the number 9 y 30012 is exactly divisible by 11 , what is the smallest whole number that can replace y ?
Options: a ) 1 , b ) 2 , c ) 5 , d ) 6 , e ) 8
Rationale: "the given number = 9 y 30012 sum of the odd places = 2 + 0 + 3 + 9 = 14 sum of the even places = 1 + 0 + y ( sum of the odd places ) - ( sum of even places ) = number ( exactly divisible by 11 ) 14 - ( 1 + y ) = divisible by 11 13 � y = divisible by 11 . y must be 2 , to make given number divisible by 11 . b"
Answer: b
Question (physics): a worker ' s daily wage is increased by 40 % and the new wage is $ 35 per day . what was the worker ' s daily wage before the increase ?
Options: a ) $ 20 , b ) $ 21 , c ) $ 24 , d ) $ 25 , e ) $ 28
Rationale: "let x be the daily wage before the increase . 1.4 x = $ 35 x = $ 25 the answer is d ."
Answer: d
Question (general): for the past n days , the average ( arithmetic mean ) daily production at a company was 60 units . if today ' s production of 90 units raises the average to 65 units per day , what is the value of n ?
Options: a ) 30 , b ) 18 , c ) 10 , d ) 9 , e ) 5
Rationale: "( average production for n days ) * n = ( total production for n days ) - - > 60 n = ( total production for n days ) ; ( total production for n days ) + 90 = ( average production for n + 1 days ) * ( n + 1 ) - - > 60 n + 90 = 65 * ( n + 1 ) - - > n = 5 . or as 30 extra units increased the average for n + 1 days by 5 units per day then 30 / ( n + 1 ) = 5 - - > n = 5 . answer : e ."
Answer: e
Question (general): a 7 - digit combination lock on a safe has zero exactly 3 times , does not have the digit 1 at all . what is the probability that exactly 3 of its digits are odd ?
Options: a ) 9 / 16 , b ) 1 / 2 , c ) 1 / 3 , d ) 1 / 4 , e ) 1 / 6
Rationale: remaining number of digits after three ' 0 ' digits = 4 constraint - no more ' 0 ' and no more ' 1 ' well , these four digits can be odd or even 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 16 ways to choose 3 odd digits out of total 4 digits = 4 c 3 = 4 4 * 1 / 16 = 1 / 4 d is the answer hi ! since we are talking about remaining 4 digits . each digit can either be odd or even ( total ways to select = 2 . desired outcome = 1 ) so let ' s say we want to choose first 3 digits as odd digits and last digit as even . the probability will be : - 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 16 but out of remaining 4 digit , any 3 can be odd and one even as there are no constraints in the question . therefore , total ways of choosing 3 odd digits out of 4 total digits = 4 c 3 so , the probability = 4 * 1 / 16 = 1 / 4 answer is d
Answer: d
Question (geometry): area of a square is 1 / 2 hectare . the diagonal of the square is ?
Options: a ) 250 meter
b ) 100 meter
c ) 50 √ 2 meter
d ) 50 meter
e ) 35 meter
Rationale: area = 1 / 2 hectare = 10000 / 2 m 2 = 5000 m 2 again area = 1 / 2 x ( diagonal ) 2 so 1 / 2 x ( diagonal ) 2 = 5000 m 2 diagonal 2 = 10000 diagonal = 100 answer : b
Answer: b
Question (gain): the ratio of the cost price and the selling price is 4 : 5 . the profit percent is :
Options: a ) 67 % , b ) 45 % , c ) 25 % , d ) 70 % , e ) 50 %
Rationale: "c c . p . = rs . 4 x . then , s . p . = rs . 5 x gain = ( 5 x - 4 x ) = rs . x gain % = ( x * 100 ) / 4 x = 25 % ."
Answer: c
Question (physics): pipe a and pipe b fill water into a tank of capacity 5000 litres , at a rate of 200 l / min and 50 l / min . pipe c drains at a rate of 25 l / min . pipe a is open for 1 min and closed , then pipe b is open for 2 min and closed . further the pipe c is opened and drained for another 2 min . this process is repeated until the tank is filled . how long will it take to fill the tank ?
Options: a ) 120 , b ) 100 , c ) 140 , d ) 80 , e ) 90
Rationale: tank capacity : 5000 l , 1 st - 200 l / min for 1 min , volume filled : 200 l 2 nd - 100 l / min for 2 min , volume filled : 100 l 3 rd ( water draining ) : 25 l / min * 2 : 50 l total : ( 200 + 100 ) - 50 = 250 l filled for 1 cycle number of 250 in 5000 l tank : 1000 / 250 = 20 time taken to fill : 20 * total time = 20 * 5 = 100 ( option b )
Answer: b
Question (physics): a can do a piece of work in 10 days and b in 20 days . they began the work together but 5 days before the completion of the work , a leaves . the work was completed in ?
Options: a ) 15 days , b ) 10 days , c ) 12 days , d ) 19 days , e ) 13 days
Rationale: b ( x â € “ 5 ) / 10 + x / 20 = 1 x = 10 days
Answer: b
Question (physics): a car gets 20 kilometers per gallon of gasoline . how many gallons of gasoline would the car need to travel 130 kilometers ?
Options: a ) 8.5 gallons , b ) 7.5 gallons , c ) 6.5 gallons , d ) 5.5 gallons , e ) 4.5 gallons
Rationale: "each 20 kilometers , 1 gallon is needed . we need to know how many 20 kilometers are there in 130 kilometers ? 130 / 20 = 6.5 * 1 gallon = 6.5 gallons correct answer c"
Answer: c
Question (physics): the diameter of a garden roller is 1.4 m and it is 2 m long . how much area will it cover in 6 revolutions ? ( use ï € = 22 â  „ 7 )
Options: a ) 40 m 2 , b ) 44 m 2 , c ) 52.8 m 2 , d ) 36 m 2 , e ) none of these
Rationale: "required area covered in 5 revolutions = 6 ã — 2 ï € rh = 6 ã — 2 ã — 22 â  „ 7 ã — 0.7 ã — 2 = 52.8 m 2 answer c"
Answer: c
Question (gain): at what price must an article costing rs . 200 be marked in order that after deducting 10 % from the list price . it may be sold at a profit of 20 % on the cost price ?
Options: a ) 62.5 , b ) 62.0 , c ) 266.67 , d ) 62.1 , e ) 62.2
Rationale: "cp = 200 sp = 200 * ( 120 / 100 ) = 240 mp * ( 90 / 100 ) = 240 mp = 266.67 answer : c"
Answer: c
Question (general): evaluate : 11 + sqrt ( - 4 + 6 × 4 ÷ 3 ) = ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "according to order of operations , inner brackets first where 6 × 4 ÷ 3 is first calculated since it has a multiplication and a division . 6 × 4 ÷ 3 = 24 ÷ 3 = 8 hence 11 + sqrt ( - 4 + 6 × 4 ÷ 3 ) = 11 + sqrt ( - 4 + 8 ) = 11 + sqrt ( 4 ) = 11 + 2 = 13 correct answer d ) 13"
Answer: d
Question (physics): the lcm and hcf of two numbers are 1000 and 100 respectively . find the larger of the two numbers if their sum is 1100 .
Options: a ) 1000 , b ) 10 , c ) 567 , d ) 57 , e ) 678
Rationale: "there are 2 approaches in solving this . methode 1 . hcf * lcm = the actual number . 1000 * 100 = 100000 so the answer which we are looking for has to be a factor of 100000 . so among the options shortlist the answers by eliminating those numbers which is not divisible by 100000 . and then take the highest number as the answer as the question asks abt the highest number . answer is a"
Answer: a
Question (gain): ramesh purchased a refrigerator for rs . 12500 after getting a discount of 20 % on the labelled price . he spent rs . 125 on transport and rs . 250 on installation . at what price should it be sold so that the profit earned would be 15 % if no discount was offered ?
Options: a ) 17608 , b ) 17606 , c ) 17604 , d ) 18400 , e ) 117601
Rationale: "price at which the tv set is bought = rs . 12,500 discount offered = 20 % marked price = 12500 * 100 / 80 = rs . 15625 the total amount spent on transport and installation = 125 + 250 = rs . 375 \ total price of tv set = 15625 + 375 = rs . 16000 the price at which the tv should be sold to get a profit of 15 % if no discount was offered = 16000 * 115 / 100 = rs . 18400 . answer : d"
Answer: d
Question (other): in a school 10 % of the boys are same in number as 1 / 6 th of the girls . what is the ratio of boys to the girls in the school ?
Options: a ) 5 : 3 , b ) 2 : 3 , c ) 1 : 4 , d ) 3 : 7 , e ) 2 : 5
Rationale: "10 % of b = 1 / 6 g 10 b / 100 = g / 6 b = 5 g / 3 b / g = 5 / 3 b : g = 5 : 3 answer is a"
Answer: a
Question (general): the number of positive integer solutions for the equation x + y + z + t = 15 is
Options: a ) 654 , b ) 584 , c ) 384 , d ) 364 , e ) 394
Rationale: the number of positive integer solutions for the equatio fx 1 + x 2 + ⋯ + xn = k ( k - 1 ) c ( n - 1 ) - where k is the number and n is number of variable in the equation . 15 - 1 c 4 - 1 = 14 c 3 = 364 answer : d
Answer: d
Question (gain): in a certain pond , 50 fish were caught , tagged , and returned to the pond . a few days later , 50 fish were caught again , of which 2 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what ` s the approximate number of fish in the pond ?
Options: a ) 400 , b ) 625 , c ) 1250 , d ) 2500 , e ) 10 000
Rationale: "if x is total number of fish in the pond : 4 = 50 / x * 100 = > x = 1250 so answer is c"
Answer: c
Question (gain): if the cost price of 12 pencils is equal to the selling price of 8 pencils , the gain percent is :
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70
Rationale: c 50 % let c . p . of each pencil be $ 1 . then , c . p . of 8 pencils = $ 8 ; s . p . of 8 pencils = $ 12 . gain % = 4 / 8 * 100 = 50 %
Answer: c
Question (physics): a and b together can do a work in 9 days . if a alone can do it in 18 days . in how many days can b alone do it ?
Options: a ) 10 , b ) 99 , c ) 18 , d ) 55 , e ) 21
Rationale: "1 / 9 – 1 / 18 = 1 / 18 = > 18 answer : c"
Answer: c
Question (general): solve below question 6 x - 1 = - 13
Options: a ) - 8 , b ) - 2 , c ) - 5 , d ) - 4 , e ) 1
Rationale: 1 . subtract 1 from both sides : 6 x - 1 + 1 = - 13 + 1 2 . simplify both sides : 6 x = - 12 3 . divide both sides by 6 : 4 . simplify both sides : x = - 2 b
Answer: b
Question (general): if n = ( 32 ) ^ 43 + ( 43 ) ^ 33 what is the units digit of n ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "first of all , the units digit of ( 32 ) ^ 43 is the same as that of 3 ^ 43 and the units digit of ( 43 ) ^ 33 is the same as that of 3 ^ 33 . so , we need to find the units digit of 3 ^ 43 + 3 ^ 33 . next , the units digit of 3 in positive integer power repeats in blocks of four { 3 , 9 , 7 , 1 } : 3 ^ 1 = 3 ( the units digit is 3 ) 3 ^ 2 = 9 ( the units digit is 9 ) 3 ^ 3 = 27 ( the units digit is 7 ) 3 ^ 4 = 81 ( the units digit is 1 ) 3 ^ 5 = 243 ( the units digit is 3 again ! ) . . . thus : the units digit of 3 ^ 43 is the same as the units digit of 3 ^ 3 , so 7 ( 43 divided by the cyclicity of 4 gives the remainder of 3 ) . the units digit of 3 ^ 33 is the same as the units digit of 3 ^ 1 , so 3 ( 33 divided by the cyclicity of 4 gives the remainder of 1 ) . therefore the units digit of ( 23 ) ^ 43 + ( 43 ) ^ 33 is 5 + 3 = 0 . answer : e ."
Answer: e
Question (general): if 125 ( 5 ^ y ) = 1 then y =
Options: a ) – 2 , b ) – 1 , c ) 0 , d ) 1 , e ) - 3
Rationale: 5 ^ x = 1 / 125 5 ^ x = 1 / 5 ^ 3 5 ^ x = 5 ^ - 3 x = - 3 e
Answer: e
Question (general): a certain store sells all maps at one price and all books at another price . on monday the store sold 12 maps and 8 books for a total of $ 38.00 , and on tuesday the store sold 20 maps and 12 books for a total of $ 60.00 . at this store , how much less does a map sell for than a book ?
Options: a ) $ 0.25 , b ) $ 0.50 , c ) $ 0.75 , d ) $ 1.00 , e ) $ l . 25
Rationale: "12 x + 8 y = 38 20 x + 12 y = 60 multiply eq 1 by 5 and eq 2 by 3 60 x + 40 y = 38 * 5 60 x + 36 y = 60 * 3 subtracting 1 from 2 4 y = 190 - 180 y = 2.5 therefore x = 1.5 difference in price = 1 d"
Answer: d
Question (general): the salary of a , b , c , d , e is rs . 8000 , rs . 5000 , rs . 11000 , rs . 7000 , rs . 9000 per month respectively , then the average salary of a , b , c , d , and e per month is
Options: a ) rs . 7000 , b ) rs . 8000 , c ) rs . 8500 , d ) rs . 9000 , e ) none
Rationale: "answer average salary = 8000 + 5000 + 11000 + 7000 + 9000 / 5 = rs . 8000 correct option : b"
Answer: b
Question (general): a car averages 75 mph for the first 4 hours of a trip and averages 60 mph for each additional hour . the average speed for the entire trip was 70 mph . how many hours long is the trip ?
Options: a ) 6 , b ) 78 , c ) 8 , d ) 9 , e ) 10
Rationale: "let the time for which car averages 60 mph = t 70 * ( t + 4 ) = 75 * 4 + 60 t = > 10 t = 20 = > t = 2 total duration of the trip = 4 + 2 = 6 answer a"
Answer: a
Question (general): linda spent 3 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 210 , what were her original savings ?
Options: a ) $ 840 , b ) $ 800 , c ) $ 1000 , d ) $ 700 , e ) $ 1500
Rationale: "if linda spent 3 / 4 of her savings on furnitute , the rest 4 / 4 - 3 / 4 = 1 / 4 on a tv but the tv cost her $ 210 . so 1 / 4 of her savings is $ 210 . so her original savings are 4 times $ 210 = $ 840 correct answer a"
Answer: a
Question (other): the duplicate ratio of 1 : 4 is ?
Options: a ) 1 : 2 , b ) 1 : 4 , c ) 1 : 8 , d ) 1 : 18 , e ) 1 : 13
Rationale: "1 ^ 2 : 4 ^ 2 = 2 : 16 = 1 : 8 answer : c"
Answer: c
Question (physics): find the cost of fencing around a circular field of diameter 20 m at the rate of rs . 1.50 a meter ?
Options: a ) 287 , b ) 94.2 , c ) 156 , d ) 158 , e ) 267
Rationale: "2 * 22 / 7 * 10 = 62.8 62.8 * 1 1 / 2 = rs . 94.2 answer : b"
Answer: b
Question (other): a 60 kg metal bar made of alloy of tin and silver lost 6 kg of its weight in the water . 10 kg of tin loses 1.375 kg in the water ; 5 kg of silver loses 0.375 kg . what is the ratio of tin to silver in the bar ?
Options: a ) 1 / 4 , b ) 2 / 5 , c ) 1 / 2 , d ) 3 / 5 , e ) 2 / 3
Rationale: "you can simply use this formula to avoid confusion : w 1 / w 2 = ( a 2 - aavg ) / ( avg - a 1 ) here is how you will find the values of a 1 an a 2 . we have an overall loss ( average loss ) . the average loss is 6 kg when 60 kg alloy is immersed . this is a loss of ( 6 / 60 ) * 100 = 10 % . this is aavg the loss of tin is 1.375 kg for every 10 kg . this means it loses ( 1.375 / 10 ) * 100 = 13.75 % of its weight in water . this is a 1 . the loss of silver is . 375 kg for every 5 kg . this means it loses ( . 375 / 5 ) * 100 = 7.5 % of its weight in water . this is a 2 . weight of tin / weight of silver = ( silver ' s loss - avg loss ) / ( avg loss - tin ' s loss ) x / y = ( 7.5 - 10 ) / ( 10 - 13.75 ) = 2 / 3 e"
Answer: e
Question (physics): a walks at 10 kmph and 10 hours after his start , b cycles after him at 20 kmph . how far from the start does b catch up with a ?
Options: a ) 100 km , b ) 150 km , c ) 50 km , d ) 120 km , e ) 200 km
Rationale: "suppose after x km from the start b catches up with a . then , the difference in the time taken by a to cover x km and that taken by b to cover x km is 10 hours . x / 10 - x / 20 = 10 x = 200 km answer is e"
Answer: e
Question (general): the sum of the non - prime numbers between 60 and 70 , non - inclusive , is
Options: a ) 387 , b ) 429 , c ) 457 , d ) 499 , e ) 536
Rationale: "sum of consecutive integers from 61 to 69 , inclusive = = = = > ( a 1 + an ) / 2 * # of terms = ( 61 + 69 ) / 2 * 9 = 65 * 9 = 585 sum of non - prime numbers b / w 60 and 70 , non inclusive = = = > 585 - 128 ( i . e . , 61 + 67 , being the prime # s in the range ) = 457 answer : c"
Answer: c
Question (physics): how many seconds will a 500 meter long train moving with a speed of 63 km / hr , take to cross a man walking with a speed of 3 km / hr in the direction of the train ?
Options: a ) 15 s , b ) 20 s , c ) 25 s , d ) 30 s , e ) 35 s
Rationale: distance = 500 m speed = 63 - 3 km / hr = 60 km / hr = 600 / 36 m / s = 50 / 3 m / s time taken = distance / speed = 500 / ( 50 / 3 ) = 30 s answer is d .
Answer: d
Question (gain): evaluate 50 % of 450 + 45 % of 500
Options: a ) 232 , b ) 450 , c ) 252 , d ) 262 , e ) 272
Rationale: "explanation : = ( 50 / 100 ) * 450 + ( 45 / 100 ) * 500 = 450 option b"
Answer: b
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 b - a ?
Options: a ) - 10 , b ) 10 , c ) - 19 , d ) 20 , e ) 21
Rationale: "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 b - a = 100 - 110 = - 10 ans : a"
Answer: a
Question (gain): the angle of elevation of a ladder leaning against a wall is 60 º and the foot of the ladder is 4.6 m away from the wall . the length of the ladder is :
Options: a ) 2.3 m , b ) 4.6 m , c ) 7.8 m , d ) 9.2 m , e ) 10.1
Rationale: "let ab be the wall and bc be the ladder . then , acb = 60 º and ac = 4.6 m . ac / bc = cos 60 º = 1 / 2 bc = 2 x ac = ( 2 x 4.6 ) m = 9.2 m . answer : option d"
Answer: d
Question (physics): what is the cost of leveling the field in the form of parallelogram at the rate of rs . 50 / 10 sq . metre , whose base & perpendicular distance from the other side being 94 m & 54 m respectively ?
Options: a ) s . 6420 , b ) s . 3563 , c ) s . 2400 , d ) s . 5480 , e ) s . 5076
Rationale: "area of the parallelogram = length of the base * perpendicular height = 94 * 54 = 5076 m . total cost of levelling = rs . 5076 e"
Answer: e
Question (general): what is the minimum value of | x - 4 | + | x + 8 | + | x - 5 | ?
Options: a ) - 13 , b ) 13 , c ) 5 , d ) 7 , e ) 8
Rationale: "a can not be the answer as all the three terms are in modulus and hence the answer will be non negative . | x - 4 | > = 0 - - > minimum occurs at x = 4 | x + 8 | > = 0 - - > minimum occurs at x = - 8 | x - 5 | > = 0 - - > minimum occurs at x = 5 x = - 8 - - > result = 12 + 0 + 13 = 25 . also any negative value will push the combined value of | x - 4 | + | x - 5 | to a value > 9 . x = 4 - - > result = 0 + 12 + 1 = 13 x = 5 - - > result = 1 + 13 + 0 = 14 x = 8 - - > result = 4 + 16 + 3 = 23 so minimum value of the expression occurs at x = 4 and the resultant value = 13 answer : b"
Answer: b
Question (general): divide rs . 1600 among a , b and c so that a receives 1 / 4 as much as b and c together and b receives 3 / 4 as a and c together . a ' s share is ?
Options: a ) 350 , b ) 375 , c ) 320 , d ) 530 , e ) 230
Rationale: "a + b + c = 1600 a = 1 / 4 ( b + c ) ; b = 3 / 4 ( a + c ) a / ( b + c ) = 1 / 4 a = 1 / 5 * 1600 = > 320 answer : c"
Answer: c
Question (gain): the population of a town is 10000 . it increases annually at the rate of 15 % p . a . what will be its population after 2 years ?
Options: a ) 13300 , b ) 13350 , c ) 13225 , d ) 13500 , e ) 13600
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 10000 ã — 115 / 100 ã — 115 / 100 = 13225 c"
Answer: c
Question (gain): a man ' s speed with the current is 16 km / hr and the speed of the current is 3.2 km / hr . the man ' s speed against the current is
Options: a ) 9 , b ) 9.6 , c ) 11 , d ) 12 , e ) 13
Rationale: "man ' s rate in still water = ( 16 - 3.2 ) km / hr = 12.8 km / hr . man ' s rate against the current = ( 12.8 - 3.2 ) km / hr = 9.6 km / hr . answer : b"
Answer: b
Question (general): a card game called “ high - low ” divides a deck of 52 playing cards into 2 types , “ high ” cards and “ low ” cards . there are an equal number of “ high ” cards and “ low ” cards in the deck and “ high ” cards are worth 2 points , while “ low ” cards are worth 1 point . if you draw cards one at a time , how many ways can you draw “ high ” and “ low ” cards to earn 6 points if you must draw exactly 3 “ low ” cards ?
Options: a ) 1 , b ) 20 , c ) 3 , d ) 4 , e ) 5
Rationale: "great question ravih . this is a permutations problem ( order matters ) with repeating elements . given thatlowcards are worth 1 pt andhigh cards 2 pts , and you must draw 3 low cards , we know that you must also draw 1 high card . the formula for permutations problems with repeating elements isn ! / a ! b ! . . . where n represents the number of elements in the group and a , b , etc . represent the number of times that repeating elements are repeated . here there are 4 elements and thelowcard is repeated 3 times . as a result , the formula is : 5 ! / 3 ! which represents ( 5 * 4 * 3 * 2 * 1 ) / ( 3 * 2 * 1 ) which simplifies to just 20 , giving you answer b ."
Answer: b
Question (probability): a card is drawn from a pack of 52 cards . the probability of not getting a face card ?
Options: a ) 9 / 13 , b ) 5 / 12 , c ) 3 / 13 , d ) 6 / 17 , e ) 1 / 13
Rationale: clearly in the 52 cards other than face cards = 52 - 16 = 36 probability of not getting a face card = 36 / 52 = 9 / 13 correct option is a
Answer: a
Question (general): what number is 64 more than two - fourth of itself ?
Options: a ) 128 , b ) 225 , c ) 288 , d ) 324 , e ) 336
Rationale: "2 / 4 x + 64 = x that means 64 = 2 / 4 x x = 64 * 2 = 128 a is the answer"
Answer: a
Question (general): in 10 years , a will be twice as old as b was 10 years ago . if a is now 6 years older than b the present age of b is
Options: a ) 37 , b ) 36 , 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 + 6 = > 2 b - b - 6 = 30 b = 36 so the present age of b is 36 years answer : b"
Answer: b
Question (physics): a train running at the speed of 56 km / hr crosses a pole in 9 sec . what is the length of the train ?
Options: a ) 140 m , b ) 786 m , c ) 566 m , d ) 546 m , e ) 445 m
Rationale: "speed = 56 * 5 / 18 = 140 / 9 m / sec length of the train = speed * time = 140 / 9 * 9 = 140 m answer : a"
Answer: a
Question (physics): the cross - section of a cannel is a trapezium in shape . if the cannel is 11 m wide at the top and 9 m wide at the bottom and the area of cross - section is 960 sq m , the depth of cannel is ?
Options: a ) 69 , b ) 92 , c ) 94 , d ) 49 , e ) 96
Rationale: "1 / 2 * d ( 11 + 9 ) = 960 d = 96 answer : e"
Answer: e
Question (physics): suppose 6 monkeys take 6 minutes to eat 6 bananas . how many monkeys would it take to eat 18 bananas in 18 minutes ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 6 , e ) 13
Rationale: "one monkey takes 6 min to eat 1 banana , so in 18 mins 1 monkey will eat 3 bananas , so for 18 bananas in 18 min we need 18 / 3 = 6 monkeys answer : d"
Answer: d