Cheukting/mathqa huggingface dataset:
Question (physics): if in a race of 80 m , a covers the distance in 20 seconds and b in 25 seconds , then a beats b by :
Options: a ) 16 m , b ) 18 m , c ) 15 m , d ) 14 m , e ) 11 m
Rationale: "explanation : the difference in the timing of a and b is 5 seconds . hence , a beats b by 5 seconds . the distance covered by b in 5 seconds = ( 80 * 5 ) / 25 = 16 m hence , a beats b by 16 m . answer : a"
Answer: a
Question (probability): when two dice are rolled , what is the probability that the sum of the two numbers is 6 ?
Options: a ) 1 / 9 , b ) 5 / 36 , c ) 1 / 3 , d ) 2 / 36 , e ) none of the above
Rationale: we have 5 outcomes that satisfy the question : 1 - 5 2 - 4 3 - 3 4 - 2 5 - 1 the probability is ( 1 / 6 * 1 / 6 ) * 5 = 5 / 36 . i think the answer is b
Answer: b
Question (physics): two trains start from a & b and travel towards each other at speed of 50 kmph and 60 kmph resp . at the time of the meeting the second train has traveled 100 km more than the first . the distance between them .
Options: a ) 800 km , b ) 900 km , c ) 1000 km , d ) 1100 km , e ) 1200 km
Rationale: let the distance traveled by the first train be x km then distance covered by the second train is x + 100 km x / 50 = x + 100 / 60 x = 500 so the distance between a & b is x + x + 100 = 1100 km answer is d .
Answer: d
Question (other): a dog takes 5 leaps for every 7 leaps of a hare . if one leap of the dog is equal to 3 leaps of the hare , the ratio of the speed of the dog to that of the hare is :
Options: a ) 16 : 7 , b ) 15 : 7 , c ) 20 : 7 , d ) 7 : 15 , e ) 14 : 7
Rationale: explanation : dog : hare = ( 5 * 3 ) leaps of hare : 7 leaps of hare = 15 : 7 answer : b
Answer: b
Question (general): if x < y < z and y - x > 5 , where x is an even integer and y and z are odd integers , what is the least possible value a of z - x ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "x < y < z to find the least possible value for z - x ; we need to find the values for z and x that can be closest to each other . if x is some even number , then what could be minimum possible odd z . if x is some even number y - x > 5 ; y > x + 5 ; minimum value for y = x + 5 + 2 = x + 7 [ note : x + 5 is as even + odd = odd and nearest odd greater than x + 5 is x + 5 + 2 ] minimum value for z = y + 2 = x + 7 + 2 = x + 9 [ note : z = y + 2 because both z and y are odd . difference between two odd numbers is 2 ] a = z - x = x + 9 - x = 9 ans : d"
Answer: d
Question (general): 0.1 + ( 0.1 ) ^ 2 + ( 0.1 ) ^ 3 =
Options: a ) 0.1 , b ) 0.111 , c ) 0.1211 , d ) 0.2341 , e ) 0.3
Rationale: "explanation : 0.1 + ( 0.1 ) ^ 2 + ( 0.1 ) ^ 3 = 0.1 + 0.01 + 0.001 = 0.111 answer : option b"
Answer: b
Question (physics): a train 360 m long runs with a speed of 45 km / hr . what time will it take to pass a platform of 140 m long ?
Options: a ) 38 sec , b ) 35 sec , c ) 44 sec , d ) 40 sec , e ) 48 sec
Rationale: "train length = 360 m platform length = 140 m time = ? length = speed * time total length = 360 + 140 = 500 m speed = 45 km / hr = 45 * ( 5 / 18 ) ( m / sec ) = 12.5 m / sec time = length / speed = 500 / 12.5 = 40 sec answer : d"
Answer: d
Question (physics): convert the 17 / 36 m / s into kilometers per hour ?
Options: a ) 1.7 , b ) 1.5 , c ) 1.3 , d ) 1.1 , e ) 1.2
Rationale: "17 / 36 m / s = 17 / 36 * 18 / 5 = 17 / 10 = 1.7 kmph . answer : a"
Answer: a
Question (physics): two guys a and b leave point a and point b simultaneously and travel towards point b and point a on the same route at their respective constant speeds . they meet along the route and immediately proceed to their respective destinations in 32 minutes and 50 minutes respectively . how long will b take to cover the entire journey between point b and point a ?
Options: a ) 65 , b ) 90 , c ) 70 , d ) 75 , e ) 80
Rationale: let x per minute be the speed of a and y per minute be the speed of b . after meeting at a point , a travels for 32 mins and b travels for 50 mins . so distance covered by each of them post point of crossing a = 32 x and b = 50 y the distance covered by a and b before they cross each would be distance covered by b and a post crossing respectively . therefore distance covered by b before he meets a = 32 x time taken by b cover 32 x distance = 32 x / y mins therefore total time taken by b = 32 x / y + 50 mins . . . . . . . . . . . . . . . . . i we need to find value of x in terms of y to arrive at final answer . total distance = 32 x + 50 y combined speed of a and b = x + y therefore time taken before a and b meet en - route = ( 32 x + 50 y ) / ( x + y ) time taken by b reach destination after meeting a = 50 mins total travel time for b = [ ( 32 x + 50 y ) / ( x + y ) ] + 50 mins . . . . . . . . . . . . . . . . . . . ii equate i and ii 32 x / y + 50 = [ ( 32 x + 50 y ) / ( x + y ) ] + 50 ( 32 x + 50 y ) / y = ( 82 x + 100 y ) / ( x + y ) 32 x ^ 2 + 50 xy + 32 xy + 50 y ^ 2 = 82 xy + 100 y ^ 2 32 x ^ 2 + 82 xy - 82 xy + 50 y ^ 2 - 100 y ^ 2 = 0 32 x ^ 2 - 50 y ^ 2 = 0 32 x ^ 2 = 50 y ^ 2 16 x ^ 2 = 25 y ^ 2 taking square root . . ( since x and y denote speed , square root ca n ' t be negative ) 4 x = 5 y y = 4 x / 5 . . . . . . . . . . . . iii substitute in i = 32 x / ( 4 x / 5 ) + 50 = 32 x * 5 / 4 x + 50 = 40 + 50 = 90 mins b
Answer: b
Question (physics): in what time will a train 140 m long cross an electric pole , it its speed be 190 km / hr ?
Options: a ) 2.6 sec , b ) 2.9 sec , c ) 2.7 sec , d ) 8.7 sec , e ) 8.5 sec
Rationale: "speed = 190 * 5 / 18 = 53 m / sec time taken = 140 / 53 = 2.6 sec . answer : a"
Answer: a
Question (other): if 63 percent of a class answered the first question on a certain test correctly , 50 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ?
Options: a ) 24 % , b ) 27 % , c ) 30 % , d ) 33 % , e ) 36 %
Rationale: "63 % answered the first question correctly and 20 % answered neither correctly . then 17 % missed the first question but answered the second question correctly . then the percent who answered both correctly is 50 % - 17 % = 33 % . the answer is d ."
Answer: d
Question (geometry): the area of a square garden is a square feet and the perimeter is p feet . if a = 2 p + 26.25 , what is the perimeter of the garden , in feet ?
Options: a ) 28 , b ) 36 , c ) 40 , d ) 42 , e ) 64
Rationale: "perimeter of square = p side of square = p / 4 area of square = ( p ^ 2 ) / 16 = a given that a = 2 p + 26.25 ( p ^ 2 ) / 16 = 2 p + 26.25 p ^ 2 = 32 p + 420 p ^ 2 - 32 p - 420 = 0 p ^ 2 - 42 p + 10 p - 420 = 0 p ( p - 42 ) + 10 ( p + 42 ) = 0 ( p - 42 ) ( p + 10 ) = 0 p = 42 or - 10 discarding negative value , p = 42 answer is d"
Answer: d
Question (general): for the past n days , the average ( arithmetic mean ) daily production at a company was 50 units . if today ' s production of 95 units raises the average to 55 units per day , what is the value of n ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "the average daily production was raised by 5 units for n days , which has a weighting of 5 n . 5 n = 95 - 55 = 40 n = 8 the answer is c ."
Answer: c
Question (physics): how many seconds will a 300 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 ) 12 sec , b ) 30 sec , c ) 86 sec , d ) 15 sec , e ) 18 sec
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 = 300 * 3 / 50 = 18 sec . answer : e"
Answer: e
Question (gain): by investing in 1623 % stock at 64 , one earns rs . 1600 . the investment made is
Options: a ) s . 9600 , b ) s . 7500 , c ) s . 5640 , d ) s . 6144 , e ) s . 6760
Rationale: "explanation : market value = rs . 64 face value is not given and hence take it as rs . 100 16 2 / 3 % of the face value = 50 / 3 ie , to earn 50 / 3 , investment = rs . 64 hence , to earn rs . 1600 , investment needed = 64 × 3 × 1600 / 50 = 6144 answer : option d"
Answer: d
Question (geometry): abcd is a parallelogram . bd = 2 . the angles of triangle bcd are all equal . what is the perimeter of the parallelogram ?
Options: a ) 12
b ) 9 √ 3
c ) 9
d ) 8
e ) 3 √ 3
Rationale: so , bc = bd = cd = ba = ad = 2 the parallelogram has 4 equal sides bc = cd = ba = ad = 2 so the perimeter of the parallelogram will be 2 * 4 = 8 hence answer will be ( d ) 2
Answer: d
Question (geometry): the number 42 can be written as the sum of the squares of 3 different positive integers . what is the sum of these 3 integers ?
Options: a ) 17 , b ) 10 , c ) 15 , d ) 14 , e ) 13
Rationale: "i think brute force with some common sense should be used to solve this problem . write down all perfect squares less than 42 : 1 , 4 , 9 , 16 , 25 , 36 . now , 42 should be the sum of 3 of those 8 numbers . also to simplify a little bit trial and error , we can notice that as 42 is an odd numbers then either all three numbers must be odd ( odd + odd + odd = odd ) or two must be even and one odd ( even + even + odd = odd ) . we can find that 42 equals to 1 + 16 + 25 = 1 ^ 2 + 4 ^ 2 + 5 ^ 2 = 42 - - > 1 + 5 + 4 = 10 . answer : b ."
Answer: b
Question (general): if the price of petrol increases by 40 , by how much must a user cut down his consumption so that his expenditure on petrol remains constant ?
Options: a ) 25 % , b ) 20 % , c ) 16.67 % , d ) 28.6 % , e ) none of these
Rationale: "explanation : let us assume before increase the petrol will be rs . 100 . after increase it will be rs ( 100 + 40 ) i . e 140 . now , his consumption should be reduced to : - = ( 140 − 100 ) / 140 ∗ 100 . hence , the consumption should be reduced to 28.6 % . answer : d"
Answer: d
Question (other): how many factors does 36 ^ 2 have ?
Options: a ) 2 , b ) 8 , c ) 24 , d ) 25 , e ) 26
Rationale: "36 ^ 2 = 2 ^ 4 3 ^ 4 total factors = ( 4 + 1 ) ( 4 + 1 ) = 25 . answer is d ."
Answer: d
Question (general): the average of 6 no . ' s is 3.95 . the average of 2 of them is 3.8 , while the average of theother 2 is 3.85 . what is the average of the remaining 2 no ' s ?
Options: a ) 4.2 , b ) 4.4 , c ) 4.6 , d ) 5.6 , e ) 5.7
Rationale: "sum of the remaining two numbers = ( 3.95 * 6 ) - [ ( 3.8 * 2 ) + ( 3.85 * 2 ) ] = 8.4 . required average = ( 8.4 / 2 ) = 4.2 . a"
Answer: a
Question (general): 14 times a number gives 210 . the number is
Options: a ) 11 , b ) 12 , c ) 15 , d ) none , e ) can not be determined
Rationale: "explanation : let the number be ' n ' 14 × n = 210 ⇒ n = 15 correct option : c"
Answer: c
Question (general): the average of 7 numbers is 24 . if each number be multiplied by 5 . find the average of new set of numbers ?
Options: a ) 110 , b ) 122 , c ) 120 , d ) 125 , e ) 145
Rationale: "explanation : average of new numbers = 24 * 5 = 120 answer : option c"
Answer: c
Question (gain): a cycle is bought for rs . 900 and sold for rs . 1080 , find the gain percent ?
Options: a ) 27 % , b ) 20 % , c ) 25 % , d ) 40 % , e ) 28 %
Rationale: "900 - - - - 180 100 - - - - ? = > 20 % answer : b"
Answer: b
Question (physics): excluding stoppages , the speed of a train is 45 kmph and including stoppages it is 30 kmph . of how many minutes does the train stop per hour ?
Options: a ) a ) 5 , b ) b ) 10 , c ) c ) 20 , d ) d ) 30 , e ) e ) 40
Rationale: "explanation : t = 15 / 45 * 60 = 20 answer : option c"
Answer: c
Question (general): if rs . 544 be divided among a , b , c in such a way that a gets 2 / 3 of what b gets and b gets 1 / 4 of what c gets , then their shares are respectively ?
Options: a ) s . 300 , b ) s . 360 , c ) s . 389 , d ) s . 384 , e ) s . 323
Rationale: "( a = 2 / 3 b and b = 1 / 4 c ) = a / b = 2 / 3 and b / c = 1 / 4 a : b = 2 : 3 and b : c = 1 : 4 = 3 : 12 a : b : c = 2 : 3 : 12 a ; s share = 544 * 2 / 17 = rs . 64 b ' s share = 544 * 3 / 17 = rs . 96 c ' s share = 544 * 12 / 17 = rs . 384 . answer : d"
Answer: d
Question (general): m = { - 6 , - 5 , - 4 , - 3 , - 2 } t = { - 3 , - 2 , - 1 , 0 , 1 , 2 , 3 , 4 } if an integer is to be randomly selected from set m above and an integer is to be randomly selected from set t above , what is the probability that the product of the two integers will be negative ?
Options: a ) 0 , b ) 1 / 3 , c ) 2 / 5 , d ) 1 / 2 , e ) 3 / 5
Rationale: we will have a negative product only if 1 , 2 , 3 , or 4 are selected from set t . p ( negative product ) = 4 / 8 = 1 / 2 the answer is d .
Answer: d
Question (physics): a 300 m long train crosses a platform in 48 sec while it crosses a signal pole in 18 sec . what is the length of the platform ?
Options: a ) 500 , b ) 350 , c ) 828 , d ) 277 , e ) 122
Rationale: "speed = 300 / 18 = 50 / 3 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 489 = 50 / 3 3 x + 900 = 2400 = > x = 500 m . answer : a"
Answer: a
Question (general): the average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 22 years . find the average age of the women ?
Options: a ) 87 , b ) 98 , c ) 30 , d ) 29 , e ) 37
Rationale: "20 + 22 + 8 * 2 = 58 / 2 = 29 answer : d"
Answer: d
Question (gain): a tank contains 7,000 gallons of a solution that is 5 percent sodium chloride by volume . if 2,500 gallons of water evaporate from the tank , the remaining solution will be approximately what percent sodium chloride ?
Options: a ) 4.77 % , b ) 5.77 % , c ) 6.77 % , d ) 7.77 % , e ) 8.77 %
Rationale: "we start with 7,000 gallons of a solution that is 5 % sodium chloride by volume . this means that there are 0.05 x 7,000 = 350 gallons of sodium chloride . when 2,500 gallons of water evaporate we are left with 4,500 gallons of solution . from here we can determine what percent of the 4,500 gallon solution is sodium chloride . ( sodium chloride / total solution ) x 100 = ? ( 350 / 4,500 ) x 100 = ? 0.077 x 100 = ? = 7.7 % answer is d ."
Answer: d
Question (general): if 20 % of x is 15 less than 15 % of 1500 , then x is ?
Options: a ) 872 , b ) 738 , c ) 837 , d ) 840 , e ) 1050
Rationale: "20 % of x = x / 5 ; 15 % of 1500 = 15 / 100 * 1500 = 225 given that , x / 5 = 225 - 15 = > x / 5 = 210 = > x = 1050 . answer : e"
Answer: e
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 / 3 . what is the difference of the numerator and denominator of the original fraction ?
Options: a ) 49 , b ) 9 , c ) 28 , d ) 26 , e ) 21
Rationale: "x / y = 2 / 5 - > 1 ( x + 4 ) / 2 y = 1 / 3 - > 2 divide 1 by 2 : = > 2 x / ( x + 4 ) = 6 / 5 = > 5 x = 3 x + 12 = > x = 6 = > y = 5 / 2 * 6 = 15 so x - y = 9 the answer is b"
Answer: b
Question (general): the average of numbers 0.34204 , 0.34203 , 0.34202 and 0.34201 is ?
Options: a ) 0.34202 , b ) 0.34204 , c ) 0.342022 , d ) 0.342025 , e ) none
Rationale: "answer average = ( 0.34204 + 0.34203 + 0.34202 + 0.34201 ) / 4 = 1.3681 / 4 = 0.342025 correct option : d"
Answer: d
Question (general): what is the total number of integers between 10 and 100 ( exclusive ) that are divisible by 7 ?
Options: a ) 10 , b ) 13 , c ) 15 , d ) 12 , e ) 11
Rationale: "14 , 21 , 28 , . . . , 91,98 this is an equally spaced list ; you can use the formula : n = ( largest - smallest ) / ( ' space ' ) + 1 = ( 98 - 14 ) / ( 7 ) + 1 = 12 + 1 = 13 answer is b"
Answer: b
Question (general): if the average of 5 positive integers is 70 and the difference between the largest and the smallest of these 5 numbers is 10 , what is the maximum value possible for the largest of these 5 integers ?
Options: a ) 50 , b ) 52 , c ) 69 , d ) 78 , e ) 84
Rationale: "sum of 5 integer ( a , b , c , d , e ) = 5 * 70 = 350 e - a = 10 i . e . e = a + 10 for e to be maximum remaining 4 must be as small as possible since smallest of 5 numbers is a so to minimize other numbers we can take them equal to the smallest of 5 numbers i . e . a + a + a + a + ( a + 10 ) = 350 i . e . 5 a = 340 i . e . a = 68 i . e . largest e = 68 + 10 = 78 answer : option d"
Answer: d
Question (geometry): a rectangular photograph is surrounded by a border that is 3 inch wide on each side . the total area of the photograph and the border is m square inches . if the border had been 6 inches wide on each side , the total area would have been ( m + 178 ) square inches . what is the perimeter of the photograph , in inches ?
Options: a ) 34 , b ) 36 , c ) 38 , d ) 40 , e ) 20
Rationale: "let length and breadth of photograph be l and b respectively . perimeter is given by 2 * ( l + b ) - - - - - ( 1 ) according to the question : ( l + 6 ) ( b + 6 ) = m - - - - ( 2 ) and ( l + 12 ) ( b + 12 ) = m + 178 - - - - - - - - - > ( l + 12 ) ( b + 12 ) - 178 = m - - - - - - ( 3 ) equating ( 2 ) and ( 3 ) ( l + 6 ) ( b + 6 ) = ( l + 12 ) ( b + 12 ) - 178 lb + 6 l + 6 b + 36 = lb + 12 l + 12 b + 144 - 168 simplify 6 l + 6 b = 60 - - - - - - > 2 ( l + b ) = 20 ( check eq ( 1 ) ) answer is e"
Answer: e
Question (general): the two lines y = x and x = - 4 intersect on the coordinate plane . if z represents the area of the figure formed by the intersecting lines and the x - axis , what is the side length e of a cube whose surface area is equal to 6 z ?
Options: a ) e = 16 , b ) e = 8 √ 2 , c ) e = 8 , d ) e = 2 √ 2 , e ) ( √ 2 ) / 3
Rationale: "800 score official solution : the first step to solving this problem is to actually graph the two lines . the lines intersect at the point ( - 4 , - 4 ) and form a right triangle whose base length and height are both equal to 4 . as you know , the area of a triangle is equal to one half the product of its base length and height : a = ( 1 / 2 ) bh = ( 1 / 2 ) ( 4 × 4 ) = 8 ; so z = 8 . the next step requires us to find the length of a side of a cube that has a face area equal to 8 . as you know the 6 faces of a cube are squares . so , we can reduce the problem to finding the length of the side of a square that has an area of 8 . since the area of a square is equal to s ² , where s is the length of one of its side , we can write and solve the equation s ² = 8 . clearly s = √ 8 = 2 √ 2 , oranswer choice ( d ) ."
Answer: d
Question (other): two numbers are in the ratio 3 : 5 . if 9 be subtracted from each , they are in the ratio of 1 : 2 . the first number is :
Options: a ) a ) 27 , b ) b ) 98 , c ) c ) 34 , d ) d ) 35 , e ) e ) 62
Rationale: "( 3 x - 9 ) : ( 5 x - 9 ) = 9 : 17 x = 9 = > 3 x = 27 answer : a"
Answer: a
Question (general): what number times ( 1 ⁄ 6 ) ^ 2 will give the value of 6 ^ 3 ?
Options: a ) 6 , b ) 36 , c ) 216 , d ) 1296 , e ) 7776
Rationale: "x * ( 1 / 6 ) ^ 2 = 6 ^ 3 x = 6 ^ 2 * 6 ^ 3 = 6 ^ 5 = 7776 the answer is e ."
Answer: e
Question (other): a can contains a mixture of liquids a and b is the ratio 7 : 5 . when 18 litres of mixture are drawn off and the can is filled with b , the ratio of a and b becomes 7 : 9 . how many liter of liquid a was contained by the can initially ?
Options: a ) 32 , b ) 52 , c ) 62 , d ) 42 , e ) 48
Rationale: "ci * vi = cf * vf ( 7 / 12 ) * ( v 1 - 18 ) = ( 7 / 16 ) * v 1 ( v 1 - 18 ) / v 1 = 3 / 4 18 accounts for the difference of 1 on ratio scale so initial volume = v 1 = 4 * 18 = 72 litres . 7 / 12 of the initial mixture was liquid a so liquid a was ( 7 / 12 ) * 72 = 42 litres . answer : d"
Answer: d
Question (general): angelo and isabella are both salespersons . in any given week , angelo makes $ 560 in base salary plus 8 percent of the portion of his sales above $ 1,000 for that week . isabella makes 10 percent of her total sales for any given week . for what amount of weekly sales would angelo and isabella earn the same amount of money ?
Options: a ) 23,500 , b ) 24,000 , c ) 25,500 , d ) 26,500 , e ) 27,500
Rationale: "let the weekly sales of both = x 560 + ( x − 1000 ) 8 / 100 = 10 / 100 x x = 24000 answer : b"
Answer: b
Question (physics): a can do a piece of work in 16 days . when he had worked for 2 days b joins him . if the complete work was finished in 8 days . in how many days b alone can finish the work ?
Options: a ) 18 , b ) 77 , c ) 66 , d ) 55 , e ) 12
Rationale: "8 / 16 + 6 / x = 1 x = 12 days answer : e"
Answer: e
Question (gain): what is the normal price of an article sold at $ 72 after two successive discounts of 10 % and 20 % ?
Options: a ) $ 92 , b ) $ 96 , c ) $ 100 , d ) $ 104 , e ) $ 108
Rationale: 0.8 * 0.9 * cost price = $ 72 cost price = $ 100 the answer is c .
Answer: c
Question (general): during a certain two - week period , 76 percent of the movies rented from a video store were comedies , and of the remaining movies rented , there were 5 times as many dramas as action movies . if no other movies were rented during that two - week period and there were a action movies rented , then how many comedies , in terms of a , were rented during that two - week period ?
Options: a ) 16 a , b ) 19 a , c ) 17 a , d ) 18 a , e ) 20 a
Rationale: "total movies = 100 . comedies = 76 . action + drama = 24 . since there were 5 times as many dramas as action movies , then action + 5 * action = 24 - - > action = a = 4 . comedies = 76 = 19 a . answer : b ."
Answer: b
Question (other): of the 200 stamps in a collection , 80 are foreign and 50 are more than 10 years old . if 20 stamps are both foreign and more than 10 years old , how many stamps are neither foreign nor more than 10 years old ?
Options: a ) 60 , b ) 90 , c ) 100 , d ) 130 , e ) 150
Rationale: "20 stamps are both foreign and more than 10 years old . 60 stamps are foreign only . 30 stamps are 10 years old only . the number of remaining stamps is 200 - ( 20 + 60 + 30 ) = 90 the answer is b ."
Answer: b
Question (general): running at their respective constant rates , machine x takes 2 days longer to produce w widgets than machine y . at these rates , if the two machines together produce 5 / 4 w widgets in 3 days , how many days would it take machine x alone to produce 3 w widgets ?
Options: a ) 4 , b ) 6 , c ) 18 , d ) 10 , e ) 12
Rationale: "let y produce w widgets in y days hence , in 1 day y will produce w / y widgets . also , x will produce w widgets in y + 2 days ( given , x takes two more days ) hence , in 1 day x will produce w / y + 2 widgets . hence together x and y in 1 day will produce { w / y + w / y + 2 } widgets . together x and y in 3 days will produce = 3 * [ { w / y + w / y + 2 } ] widgets . it is given that in 3 days together they produce ( 5 / 4 ) w widgets . equating , 3 * [ { w / y + w / y + 2 } ] = ( 5 / 4 ) w take out w common and move 3 to denominator of rhs w { 1 / y + 1 / ( y + 2 ) } = ( 5 / 12 ) w canceling w from both sides { 1 / y + 1 / ( y + 2 ) } = 5 / 12 2 y + 2 / y ( y + 2 ) = 5 / 12 24 y + 24 = 5 y ^ 2 + 10 y 5 y ^ 2 - 14 y - 24 = 0 5 y ^ 2 - 20 y + 6 y - 24 = 0 5 y ( y - 4 ) + 6 ( y - 4 ) = 0 ( 5 y + 6 ) + ( y - 4 ) = 0 y = - 6 / 5 or y = 4 discarding y = - 6 / 5 as no of days can not be negative y = 4 hence it takes y , 4 days to produce w widgets . therefore , it will take x ( 4 + 2 ) = 6 days to produce w widgets . hence it will take x 3 * 6 = 18 days to produce 3 w widgets . answer : c"
Answer: c
Question (physics): joe needs to paint all the airplane hangars at the airport , so he buys 360 gallons of paint to do the job . during the first week , he uses 1 / 4 of all the paint . during the second week , he uses 1 / 3 of the remaining paint . how many gallons of paint has joe used ?
Options: a ) 18 , b ) 180 , c ) 175 , d ) 216 , e ) 250
Rationale: "total paint initially = 360 gallons paint used in the first week = ( 1 / 4 ) * 360 = 90 gallons . remaning paint = 270 gallons paint used in the second week = ( 1 / 3 ) * 270 = 90 gallons total paint used = 180 gallons . option b"
Answer: b
Question (general): the cost of 2 chairs and 3 tables is rs . 1400 . the cost of 3 chairs and 2 tables is rs . 1200 . the cost of each table is more than that of each chair by ?
Options: a ) 228 , b ) 287 , c ) 277 , d ) 188 , e ) 200
Rationale: "explanation : 2 c + 3 t = 1400 - - - ( 1 ) 3 c + 2 t = 1200 - - - ( 2 ) subtracting 2 nd from 1 st , we get - c + t = 200 = > t - c = 200 answer : e"
Answer: e