Cheukting/mathqa huggingface dataset:
Question (geometry): danny is sitting on a rectangular box . the area of the front face of the box is half the area of the top face , and the area of the top face is 1.5 times the area of the side face . if the volume of the box is 1536 , what is the area of the side face of the box ?
Options: a ) 34 , b ) 65 , c ) 88 , d ) 90 , e ) 128
Rationale: "lets suppose length = l , breadth = b , depth = d front face area = l * w = 1 / 2 w * d ( l = 1 / 2 d or d = 2 l ) top face area = w * d side face area = w * d = 1.5 d * l ( w = 1.5 l ) volume = l * w * d = 1536 l * 1.5 l * 2 l = 1536 l = 8 side face area = l * d = l * 2 l = 8 * 2 * 8 = 128 e is the answer"
Answer: e
Question (general): sum of the squares of 3 no . is 276 and the sum of their products taken two at a time is 150 . find the sum ?
Options: a ) 22 , b ) 18 , c ) 26 , d ) 24 , e ) 32
Rationale: "( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 276 + 2 * 150 a + b + c = â ˆ š 576 = 24 answer d"
Answer: d
Question (general): zachary is helping his younger brother , sterling , learn his multiplication tables . for every question that sterling answers correctly , zachary gives him 3 pieces of candy . for every question that sterling answers incorrectly , zachary takes away two pieces of candy . after 14 questions , if sterling had answered 2 more questions correctly , he would have earned 31 pieces of candy . how many of the 14 questions did zachary answer correctly ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: i got two equations : 3 x - 2 y = 25 x + y = 14 3 x - 2 ( 14 - x ) = 25 3 x - 28 + 2 x = 25 5 x = 53 x = 10.6 or between 10 and 11 . ( ans e )
Answer: e
Question (physics): bhaman travelled for 15 hours . he covered the first half of the distance at 40 kmph and remaining half of the distance at 10 kmph . find the distance travelled by bhaman ?
Options: a ) 240 , b ) 230 , c ) 260 , d ) 220 , e ) 340
Rationale: let the distance travelled be x km . total time = ( x / 2 ) / 40 + ( x / 2 ) / 10 = 15 = > x / 80 + x / 20 = 15 = > ( x + 4 x ) / 80 = 15 = > x = 240 km answer : a
Answer: a
Question (general): in a survey of parents , exactly 7 / 8 of the mothers and 3 / 4 of the fathers held full - time jobs . if 40 percent of the parents surveyed were women , what percent of the parents did not hold full - time jobs ?
Options: a ) 20 % , b ) 23 % , c ) 15 % , d ) 18 % , e ) 16 %
Rationale: fathers without full - time jobs are 1 / 4 * 3 / 5 = 3 / 20 of all the parents surveyed . mothers without full - time jobs are 1 / 8 * 2 / 5 = 1 / 20 of all the parents surveyed . the percent of parents without full - time jobs is 3 / 20 + 1 / 20 = 1 / 5 = 20 % the answer is a .
Answer: a
Question (physics): three pipes of same capacity can fill a tank in 8 hours . if there are only two pipes of same capacity , the tank can be filled in .
Options: a ) 11 hours , b ) 12 hours , c ) 15 hours , d ) 16 hours , e ) 17 hours
Rationale: the part of the tank filled by three pipes in one hour = 1 / 8 = > the part of the tank filled by two pipes in 1 hour = 2 / 3 * 1 / 8 = 1 / 12 . the tank can be filled in 12 hours . answer : b
Answer: b
Question (other): each factor of 220 is inscribed on its own plastic ball , and all of the balls are placed in a jar . if a ball is randomly selected from the jar , what is the probability that the ball is inscribed with a multiple of 55 ?
Options: a ) 1 / 16 , b ) 5 / 42 , c ) 1 / 8 , d ) 3 / 16 , e ) 1 / 4
Rationale: "the # of factors 220 has is 12 ; so out of 12 factors only three are multiples of 55 : 55 , 110 and 220 , itself ; so , the probability is 3 / 12 = 1 / 4 . answer : e ."
Answer: e
Question (gain): john makes $ 40 a week from his job . he earns a raise andnow makes $ 70 a week . what is the % increase ?
Options: a ) 16 % , b ) 16.66 % , c ) 76.69 % , d ) 76.98 % , e ) 75 %
Rationale: "increase = ( 30 / 40 ) * 100 = ( 3 / 4 ) * 100 = 75 % . e"
Answer: e
Question (gain): an association of mathematics teachers has 1,260 members . only 525 of these members cast votes in the election for president of the association . what percent of the total membership voted for the winning candidate if the winning candidate received 72 percent of the votes cast ?
Options: a ) 75 % , b ) 58 % , c ) 30 % , d ) 34 % , e ) 25 %
Rationale: "total number of members = 1260 number of members that cast votes = 525 since , winning candidate received 72 percent of the votes cast number of votes for winning candidate = ( 72 / 100 ) * 525 = 378 percent of total membership that voted for winning candidate = ( 378 / 1260 ) * 100 = 30 % answer c"
Answer: c
Question (general): a grocer has a sale of rs . 6435 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6500 ?
Options: a ) 4551 , b ) 4771 , c ) 4991 , d ) 4881 , e ) 4661
Rationale: "let the sale in the sixth month = x then ( 6435 + 6927 + 6855 + 7230 + 6562 + x ) / 6 = 6500 = > 6435 + 6927 + 6855 + 7230 + 6562 + x = 6 × 6500 = > 34009 + x = 39000 = > x = 39000 − 34009 = 4991 answer is c ."
Answer: c
Question (general): one half of a two digit number exceeds its one third by 4 . what is the sum of the digits of the number ?
Options: a ) 6 , b ) 9 , c ) 11 , d ) 12 , e ) 15
Rationale: "explanation : x / 2 – x / 3 = 4 = > x = 24 2 + 4 = 6 a"
Answer: a
Question (physics): calculate the number of bricks , each measuring 25 cm x 15 cm x 8 cm required to construct a wall of dimensions 10 m x 4 cm x 6 m when 10 % of its volume is occupied by mortar ?
Options: a ) 720 , b ) 600 , c ) 660 , d ) 6000 , e ) none of these
Rationale: explanation : let the number of bricks be ' n ' 10 x 4 / 100 x 6 x 90 / 100 = 25 / 100 x 15 / 100 x 8 / 100 x n 10 x 4 x 6 x 90 = 15 x 2 x n = > n = 720 . answer is a
Answer: a
Question (geometry): if the side length of square b is three times that of square a , the area of square b is how many times the area of square a ?
Options: a ) 9 , b ) 8 , c ) 6 , d ) 3 , e ) 2
Rationale: "let x be the side length of square a . then the area of square a is x ^ 2 . the area of square b is ( 3 x ) ^ 2 = 9 x ^ 2 . the answer is a ."
Answer: a
Question (physics): the lcm and hcf of two numbers are 8 and 48 respectively . if one of them is 24 , find the other ?
Options: a ) 12 , b ) 14 , c ) 15 , d ) 16 , e ) 20
Rationale: hcf x lcm = product of numbers 8 x 48 = 24 x the other number other number = ( 8 x 48 ) / 24 other number = 16 answer : d
Answer: d
Question (gain): one night a certain hotel rented 3 / 5 of its rooms , including 2 / 3 of their air conditioned rooms . if 3 / 5 of its rooms were air conditioned , what percent of the rooms that were not rented were air conditioned ?
Options: a ) 50 % , b ) 55 % , c ) 60 % , d ) 65 % , e ) 70 %
Rationale: the rooms which were not rented is 2 / 5 the ac rooms which were not rented is ( 1 / 3 ) * ( 3 / 5 ) = 1 / 5 the percentage of unrented rooms which were ac rooms is ( 1 / 5 ) / ( 2 / 5 ) = 1 / 2 = 50 % the answer is a .
Answer: a
Question (physics): in what time will a train 180 m long cross an electric pole , it its speed be 144 km / hr ?
Options: a ) 2.5 sec , b ) 1.9 sec , c ) 8.9 sec , d ) 4.5 sec , e ) 2.9 sec
Rationale: "speed = 144 * 5 / 18 = 40 m / sec time taken = 180 / 40 = 4.5 sec . answer : d"
Answer: d
Question (general): how many 7 - digits number are palindromic numbers ? a palindromic number reads the same forward and backward , example 1234321 .
Options: a ) 100 , b ) 610 , c ) 729 , d ) 9000 , e ) 1000
Rationale: "take the task of building palindromes and break it intostages . stage 1 : select the 7 th digit we can choose 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , or 9 so , we can complete stage 1 in 9 ways stage 2 : select the 6 th digit we can choose 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , or 9 so , we can complete stage 2 in 10 ways stage 3 : select the 5 th digit we can choose 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , or 9 so , we can complete stage 3 in 10 ways stage 4 : select the 5 th digit we can choose 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , or 9 so , we can complete stage 4 in 10 ways important : at this point , the remaining digits are alreadylocked in . stage 5 : select the hundreds digit this digit must be the same as the thousands digit ( which we already chose in stage 2 ) so , we can complete this stage in 1 way . stage 6 : select the tens digit this digit must be the same as the thousands digit ( which we already chose in stage 2 ) so , we can complete this stage in 1 way . stage 7 : select the units digit this digit must be the same as the ten - thousands digit ( which we already chose in stage 1 ) so , we can complete this stage in 1 way . by thefundamental counting principle ( fcp ) , we can complete all 5 stages ( and thus build a 7 - digit palindrome ) in ( 9 ) ( 10 ) ( 10 ) ( 10 ) ( 1 ) ( 1 ) ( 1 ) ways ( = 9000 ways ) answer : d"
Answer: d
Question (general): the average monthly salary of 25 employees in an organisation is rs . 2500 . if the manager ' s salary is added , then the average salary increases by rs . 200 . what is the manager ' s monthly salary ?
Options: a ) rs . 7700 , b ) rs . 3618 , c ) rs . 3600 , d ) rs . 3619 , e ) rs . 3610
Rationale: "manager ' s monthly salary = rs . ( 2700 * 26 - 2500 * 25 ) = rs . 7700 answer : a"
Answer: a
Question (physics): the sum of two consecutive number is 49 . which is the larger number ?
Options: a ) 42 , b ) 43 , c ) 25 , d ) 45 , e ) 46
Rationale: "let consecutive number be x , x + 1 therefore sum of the consecutive number is x + x + 1 = 49 2 x + 1 = 49 2 x = 48 x = 24 therefore larger number is x + 1 = 25 answer : c"
Answer: c
Question (gain): we had $ 1400 left after spending 30 % of the money that we took for shopping . how much money did we start with ?
Options: a ) $ 2000 , b ) $ 2100 , c ) $ 2200 , d ) $ 2300 , e ) $ 2400
Rationale: "let x be the amount of money we started with . 0.7 x = 1400 x = 2000 the answer is a ."
Answer: a
Question (gain): each of the cucumbers in 100 pounds of cucumbers is composed of 99 % water , by weight . after some of the water evaporates , the cucumbers are now 94 % water by weight . what is the new weight of the cucumbers , in pounds ?
Options: a ) 2 , b ) 16 , c ) 92 , d ) 96 , e ) 98
Rationale: "out of 100 pounds 99 % or 99 pounds is water and 1 pound is non - water . after somewaterevaporates the cucumbers become 94 % water and 6 % of non - water , so now 1 pound of non - water composes 6 % of cucucmbers , which means that the new weight of cucumbers is 1 / 0.06 = 16 pounds . answer : b ."
Answer: b
Question (general): the average of 5 numbers is 6.8 . if one of the numbers is multiplied by a factor of 4 , the average of the numbers increases to 9.2 . what number is multiplied by 4 ?
Options: a ) 1.5 , b ) 3.0 , c ) 3.9 , d ) 4.0 , e ) 6.0
Rationale: "the average of 5 numbers is 6.8 the sum of 5 numbers will be 6.8 x 5 = 34 the average of 5 number after one of the number is multiplied by 4 is 9.2 the sum of the numbers will now be 9.2 x 5 = 46 so the sum has increased by 46 - 34 = 12 let the number multiplied by 4 be n then , 4 n = n + 12 or 3 n = 12 or n = 4 answer : - d"
Answer: d
Question (general): in a party every person shakes hands with every other person . if there are 105 hands shakes , find the number of person in the party .
Options: a ) 14 , b ) 12 , c ) 13 , d ) 15 , e ) 16
Rationale: "let n be the number of persons in the party . number of hands shake = 105 ; total number of hands shake is given by nc 2 . now , according to the question , nc 2 = 105 ; or , n ! / [ 2 ! * ( n - 2 ) ! ] = 105 ; or , n * ( n - 1 ) / 2 = 105 ; or , n 2 - n = 210 ; or , n 2 - n - 210 = 0 ; or , n = 15 , - 14 ; but , we can not take negative value of n . so , n = 15 i . e . number of persons in the party = 15 . option d"
Answer: d
Question (physics): the angle between the minute hand and the hour hand of a clock when the time is 10.30 , is
Options: a ) 35 ° , b ) 65 ° , c ) 45 ° , d ) 135 ° , e ) 95 °
Rationale: "angle between hands of a clock when the minute hand is behind the hour hand , the angle between the two hands at m minutes past h ' o clock = 30 ( h − m / 5 ) + m / 2 degree when the minute hand is ahead of the hour hand , the angle between the two hands at m minutes past h ' o clock = 30 ( m / 5 − h ) − m / 2 degree here h = 10 , m = 30 and minute hand is behind the hour hand . hence the angle = 30 ( h − m / 5 ) + m / 2 = 30 ( 10 − 30 / 5 ) + 30 / 2 = 30 ( 10 − 6 ) + 15 = 30 × 4 + 15 = 135 ° answer is d ."
Answer: d
Question (physics): darcy lives 1.5 miles from work . she can walk to work at a constant rate of 3 miles per hour , or she can ride the train to work at a constant rate of 20 miles per hour . if she rides the train , there is an additional x minutes spent walking to the nearest train station , waiting for the train , and walking from the final train station to her work . if it takes darcy a total of 5 more minutes to commute to work by walking than it takes her to commute to work by riding the train , what is the value of x ?
Options: a ) 20.5 , b ) 15 , c ) 25.5 , d ) 30 , e ) 60
Rationale: "the time it takes darcy to walk to work is ( 1.5 / 3 ) * 60 = 30 minutes the time it takes darcy to take the train is ( 1.5 / 20 ) * 60 + x = 4.5 + x minutes it takes 15 minutes longer to walk , so 30 = 4.5 + x + 5 x = 20.5 minutes answer : a"
Answer: a
Question (general): what is the last digit of 13 ^ 35 ?
Options: a ) 5 , b ) 7 , c ) 6 , d ) 8 , e ) 9
Rationale: "explanation : let ’ s begin by looking for a pattern as we increase the exponent . 13 ^ 1 = 13 ( units digit is 3 ) 13 ^ 2 = 169 ( units digit is 9 ) 13 ^ 3 = 2197 ( units digit is 7 ) notice that a nice pattern emerges . we get : 3 - 9 - 7 - 1 - 3 - 9 - 7 - 1 - 3 - 9 - 7 - 1 - … whenever n is a multiple of 4 , the units digit of 13 ^ n is 1 the units digit of 13 ^ 35 is 7 answer is b"
Answer: b
Question (general): x is the product of each integer from 1 to 25 , inclusive and y = 100 ^ k , where k is an integer . what is the greatest value of k for which y is a factor of x ?
Options: a ) 5 , b ) 4 , c ) 3 , d ) 6 , e ) 7
Rationale: "the number of trailing zeros in the decimal representation of n ! , the factorial of a non - negative integer n , can be determined with this formula : n 5 + n 52 + n 53 + . . . + n 5 k , where k must be chosen such that 5 k ≤ n x = 1 * 2 * 3 . . . . * 25 = 25 ! no . of trailing zeros in 25 ! = 25 / 5 + 25 / 5 ^ 2 = 6 100 ^ k = 10 ^ 2 k → k = 6 / 2 = 3 c"
Answer: c
Question (geometry): a lawn is in the form of a rectangle having its sides in the ratio 2 : 3 . the area of the lawn is ( 1 / 6 ) hectares . find the length and breadth of the lawn .
Options: a ) 50
b ) 30
c ) 20
d ) 40
e ) 10
Rationale: let length = 2 x meters and breadth = 3 x meter . now , area = ( 1 / 6 ) x 1000 m 2 = 5000 / 3 m 2 so , 2 x * 3 x = 5000 / 3 < = > x 2 = 2500 / 9 < = > x = 50 / 3 therefore length = 2 x = ( 100 / 3 ) m = 33 ( 1 / 3 ) m and breadth = 3 x = 3 ( 50 / 3 ) m = 50 m . answer is a
Answer: a
Question (physics): 12 men work 8 hours per day to complete the work in 10 days . to complete the same work in 8 days , working 10 hours a day , the number of men required ?
Options: a ) 10 days , b ) 12 days , c ) 13 days , d ) 11 days , e ) 9 days
Rationale: "that is , 1 work done = 12 × 8 × 10 then , 12 8 × 10 = ? × 10 × 8 ? ( i . e . no . of men required ) = 12 × 8 × 10 / 10 × 8 = 12 days b )"
Answer: b
Question (other): there are 240 doctors and nurses at a hospital . if the ratio of doctors to nurses is 3 to 7 , how many nurses are at the hospital ?
Options: a ) 168 , b ) 172 , c ) 176 , d ) 180 , e ) 184
Rationale: "the number of nurses at the hospital is ( 7 / 10 ) * 240 = 168 . the answer is a ."
Answer: a
Question (gain): what annual payment will discharge a debt of rs . 1125 due in 2 years at the rate of 5 % compound interest ?
Options: a ) 993.2 , b ) 551.25 , c ) 534.33 , d ) 605.03 , e ) 646.33
Rationale: "explanation : let each installment be rs . x . then , x / ( 1 + 5 / 100 ) + x / ( 1 + 5 / 100 ) 2 = 1125 820 x + 1125 * 441 x = 605.03 so , value of each installment = rs . 605.03 answer : option d"
Answer: d
Question (physics): abel can complete a work in 8 days , ben in 12 days and carla in 15 days . all of them began the work together , but abel had to leave after 2 days and ben 3 days before the completion of the work . how long did the work last ?
Options: a ) 4 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "abel in the 2 days that he worked completed 1 / 4 of the job = 3 / 4 remains then if ben had to leave 3 days before the completion , this means that carla had to work alone for these 3 days in which she completed 1 / 5 of the job . now together , ben and carla completed the job in ( 1 / 12 + 1 / 15 ) ( t ) = 3 / 20 3 / 20 ( t ) = 3 / 20 - - - > t = 1 therefore , these 1 day worked plus the 3 days that carla had to work by herself add to 4 days answer : a"
Answer: a
Question (general): if x ¤ y = ( x + y ) ^ 2 - ( x - y ) ^ 2 . then √ 2 ¤ √ 2 =
Options: a ) 0 , b ) 8 , c ) 10 , d ) 15 , e ) 20
Rationale: "x = √ 2 and y also = √ 2 applying the function ( √ 2 + √ 2 ) ^ 2 - ( √ 2 - √ 2 ) ^ 2 = ( 2 √ 2 ) ^ 2 - 0 = 4 x 2 = 8 . note : alternative approach is the entire function is represented as x ^ 2 - y ^ 2 = ( x + y ) ( x - y ) which can be simplified as ( x + y + x - y ) ( x + y - ( x - y ) ) = ( 2 x ) ( 2 y ) = 4 xy . substituting x = √ 2 and y = √ 2 you get the answer 8 . answer b"
Answer: b
Question (physics): jamshid can paint a fence in 50 percent less time than taimour can when each works alone . when they work together , they can paint the fence in 4 hours . how long would it take taimour to paint the fence alone ?
Options: a ) 6 hours , b ) 8 hours , c ) 12 hours , d ) 24 hours , e ) 32 hours
Rationale: i believe the answer is c . please see below for explanation . if jamshid can paint a dence in 50 percent less time then taimour we can infer the following rate j = 2 t if working together they can do the job in 8 hours we can infer 1 = 2 t + t * 4 = > 1 / 12 working alone taimour can do the job in 1 = 1 / 12 * hours = > 12 answer c
Answer: c
Question (general): in the faculty of reverse - engineering , 100 second year students study numeric methods , 300 second year students study automatic control of airborne vehicles and 200 second year students study them both . how many students are there in the faculty if the second year students are approximately 40 % of the total ?
Options: a ) 550 , b ) 500 , c ) 600 , d ) 650 , e ) 700
Rationale: "total number of students studying both are 100 + 300 - 200 = 200 ( subtracting the 200 since they were included in the both the other numbers already ) . so 40 % of total is 200 , so 100 % is 500 answer is b"
Answer: b
Question (general): if the probability of rain on any given day in chicago during the summer is 50 % , independent of what happens on any other day , what is the probability of having exactly 3 rainy days from july 4 through july 9 inclusive ?
Options: a ) 3 / 16 , b ) 5 / 16 , c ) 7 / 32 , d ) 11 / 32 , e ) 17 / 64
Rationale: "one possible case is : rainy - rainy - rainy - not rainy - not rainy - not rainy . the probability of this case is ( 1 / 2 ) ^ 6 = 1 / 64 the number of possible cases is 6 c 3 = 20 . p ( exactly 3 rainy days ) = 20 * 1 / 64 = 5 / 16 the answer is b ."
Answer: b
Question (general): find √ ? / 20 = 4 ?
Options: a ) 76 , b ) 6400 , c ) 304 , d ) 1296 , e ) none
Rationale: "answer let √ n / 20 = 4 then √ n = 20 x 4 = 80 ∴ n = 80 x 80 = 6400 . correct option : b"
Answer: b
Question (physics): the time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 45 kmph , find the speed of the stream ?
Options: a ) 12 kmph , b ) 13 kmph , c ) 14 kmph , d ) 15 kmph , e ) 16 kmph
Rationale: "the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 45 / 3 = 15 kmph answer : d"
Answer: d
Question (general): a box contains 14 pairs of shoes ( 28 shoes in total ) . if two shoes are selected at random , what it is the probability that they are matching shoes ?
Options: a ) 1 / 190 , b ) 1 / 20 , c ) 1 / 19 , d ) 1 / 27 , e ) 1 / 9
Rationale: "the problem with your solution is that we do n ' t choose 1 shoe from 28 but rather choose the needed one after we just took one and need the second to be the pair of it . so , the probability would simply be : 1 / 1 * 1 / 27 ( as after taking one at random there are 27 shoes left and only one is the pair of the first one ) = 1 / 27 answer : d"
Answer: d
Question (general): find the value of x from the below equation ? : x ^ 2 + 5 x + 4 = 0
Options: a ) 1 , b ) - 3 , c ) 3 , d ) 2 , e ) 0
Rationale: a = 1 , b = 5 , c = 4 x 1,2 = ( - 5 â ± â ˆ š ( 5 ^ 2 - 4 ã — 1 ã — 4 ) ) / ( 2 ã — 1 ) = ( - 5 â ± â ˆ š ( 25 - 16 ) ) / 2 = ( - 5 â ± 3 ) / 2 x 1 = ( - 5 + 3 ) / 2 = - 2 / 2 = - 1 x 2 = ( - 5 - 1 ) / 2 = - 6 / 2 = - 3 b
Answer: b
Question (gain): there are 1000 students in a school and among them 10 % of them attends chess class . 10 % of the students who are in the chess class are also enrolled for swimming . no other students are interested in swimming so how many will attend the swimming class if all enrolled attends ?
Options: a ) 1 , b ) 10 , c ) 100 , d ) 50 , e ) 20
Rationale: "10 % of 1000 gives 100 . so 100 attends chess and 10 % of 100 gives 10 . so 10 enrolled for swimming answer : b"
Answer: b
Question (gain): a furniture dealer purchased a desk for $ 150 and then set the selling price equal to the purchase price plus a markup that was 20 % of the selling price . if the dealer sold the desk at the selling price , what was the amount of the dealer ' s gross profit from the purchase and the sale of the desk ?
Options: a ) 45 % , b ) 40 % , c ) 35 % , d ) 30 % , e ) 25 %
Rationale: anyway , in this question , there is no discount but the mark up is given as 40 % of the selling price . so it is not 20 % of $ 150 but instead , 20 % of selling price which is obtained by adding mark up to $ 150 . so if selling price is s , 150 + 20 % of s = s s = 150 / 0.8 profit = 150 / 0.8 - 150 = which is calculated on cost price in % terms . so 37.5 / 150 * 100 = 25 % is profit . e
Answer: e
Question (physics): a and b start walking towards each other at 4 pm at speed of 2 kmph and 3 kmph . they were initially 15 km apart . at what time do they meet ?
Options: a ) 8 pm , b ) 6 pm , c ) 7 pm , d ) 10 pm , e ) 5 pm
Rationale: time of meeting = distance / relative speed = 15 / 3 + 2 = 15 / 5 = 3 hrs after 4 pm = 7 pm answer is c
Answer: c
Question (general): each digit 1 through 5 is used exactly once to create a 5 - digit integer . if the 3 and the 24 can not be adjacent digits in the integer , how many 5 - digit integers are possible ?
Options: a ) 48 , b ) 72 , c ) 76 , d ) 78 , e ) 90
Rationale: "number of arrangements using 5 distinct digits = 5 ! number of arrangements in which 3 and 4 are adjacent - consider 3 and 2 together as one group . now you have 4 numbers / groups to arrange which can be done in 4 ! ways . in each of these arrangements , 3 and 2 can be arranged as 32 or 23 . number of arrangements in which 3 and 4 are not adjacent = 5 ! - 2 * 4 ! = 72 answer : b"
Answer: b
Question (geometry): in a certain parallelogram the degree measure of one angle exceeds that of the other by 20 what is the degree measure of the smaller angle ?
Options: a ) 75 , b ) 80 , c ) 85 , d ) 90 , e ) 95
Rationale: "in a parallelogram opposite angles are equal and the angles at each side are supplementary to each other ( supplementary angles are two angles that add up to 180 ° ) . given : x + ( x + 20 ) = 180 - - > x = 80 . answer : b ."
Answer: b
Question (general): 3 years ago , the average age of a , b and c was 27 years and that of b and c 5 years ago was 20 years . a ’ s present age is :
Options: a ) 22 , b ) 88 , c ) 40 , d ) 87 , e ) 17
Rationale: explanation : sum of the present ages of a , b and c = ( 27 × 3 + 3 × 3 ) years = 90 years . sum of the present ages of b and c = ( 20 × 2 + 5 × 2 ) years = 50 years . a ' s present age = 90 – 50 = 40 years . answer : c
Answer: c