Cheukting/mathqa huggingface dataset:
Question (general): the population of a bacteria culture doubles every 2 minutes . approximately how many minutes will it take for the population to grow from 1,000 to 300,000 bacteria
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "the question basically asks how many minutes it takes for a population to increase by factor 300 ( 300,000 / 1,000 = 300 ) . now you know that every two minutes the population doubles , i . e . is multiplied by 2 . so the equation becomes : 2 ^ x > = 300 , where x represents the number of times the population doubles . a lot of people remember that 2 ^ 10 = 1,024 . hence , 2 ^ 8 = 256 , i . e . the population has to double 8 times . since it takes the population 2 minutes to double once it takes 8 * 2 minutes = 16 minutes to double 8 times . thus , solution d = 16 is correct ."
Answer: d
Question (other): in what ratio must tea at rs . 60 per kg be mixed with tea at rs . 70 per kg so that the mixture must be worth rs . 67.5 per kg ?
Options: a ) 3 : 1 , b ) 3 : 2 , c ) 4 : 3 , d ) 1 : 3 , e ) none
Rationale: "required ratio = 250 : 750 = 1 : 3 answer d"
Answer: d
Question (physics): in what time will a train 50 m long cross an electric pole , it its speed be 360 km / hr ?
Options: a ) 0.25 , b ) 0.5 , c ) 1.5 , d ) 2.5 , e ) 3.5
Rationale: "speed = 360 * 5 / 18 = 100 m / sec time taken = 50 / 100 = 0.5 sec . answer : b"
Answer: b
Question (general): each of the products produced yesterday was checked by worker x or worker y . 0.5 % of the products checked by worker x are defective and 0.8 % of the products checked by worker y are defective . if the total defective rate of all the products checked by worker x and worker y is 0.74 % , what fraction of the products was checked by worker y ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 5 , d ) 3 / 4 , e ) 4 / 5
Rationale: "x : 0.5 % is 0.24 % - points from 0.74 % . y : 0.8 % is 0.06 % - points from 0.74 % . therefore the ratio of products checked by y : x is 4 : 1 . thus , worker y checked 4 / 5 of the products . the answer is e ."
Answer: e
Question (gain): a sum of 11,500 amounts to 13,500 in 5 years at the rate of simple interest . what is the rate of interest ?
Options: a ) 2 % , b ) 3 % , c ) 6 % , d ) 5 % , e ) 8 %
Rationale: "b 3 % s . i . = ( 13500 - 11500 ) = 2000 . rate = ( 100 x 2000 ) / ( 11500 x 5 ) % = 3 %"
Answer: b
Question (physics): workers at a campaign office have 2000 fliers to send out . if they send out 1 / 4 of them in the morning and 1 / 5 of the remaining ones out during the afternoon , how many are left for the next day ?
Options: a ) 300 , b ) 800 , c ) 1100 , d ) 1200 , e ) 1180
Rationale: "( 1 / 4 ) * 2000 = 500 remaining = 2000 - 500 = 1500 ( 1 / 5 ) of remaining = ( 1 / 5 ) * 1600 = 320 remaining now = 1500 - 320 = 1180 answer : option e"
Answer: e
Question (geometry): abcd is a square where ab = â ˆ š 4032 . let x be a point on ab and y be a point on cd such that ax = cy . compute the area of trapezoid axyd .
Options: a ) 3008
b ) 2002
c ) 1008
d ) 2016
e ) 3000
Rationale: note that trapezoids axy d and bxy c are congruent , so the area of axy d is always 4032 / 2 = 2016 . correct answer d
Answer: d
Question (general): if n = ( 33 ) ^ 40 + ( 43 ) ^ 33 what is the units digit of n ?
Options: a ) 1 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "first of all , the units digit of ( 33 ) ^ 40 is the same as that of 3 ^ 43 and the units digit of ( 40 ) ^ 33 is the same as that of 3 ^ 33 . so , we need to find the units digit of 3 ^ 40 + 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 ^ 40 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 ^ 30 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 ( 33 ) ^ 40 + ( 40 ) ^ 33 is 7 + 4 = 1 . answer : a ."
Answer: a
Question (geometry): a circular ground whose diameter is 35 metres , has a 1.4 metre - broad garden around it . what is the area of the garden in square metres ?
Options: a ) 160.16 , b ) 6.16 , c ) 122.66 , d ) data inadequate , e ) none of these
Rationale: "req . area = π [ ( 17.5 + 1.4 ) 2 – ( 17.5 ) 2 ] = 22 ⁄ 7 × ( 36.4 × 1.4 ) [ since a 2 - b 2 = ( a + b ) ( a - b ) ] = 22 × 36.4 × 0.2 = 160.16 sq m answer a"
Answer: a
Question (general): a sports equipment store sold ping pong rackets for a total of $ 637 . if the average ( arithmetic mean ) price of a pair of rackets is $ 9.8 , how many pairs were sold ?
Options: a ) 50 , b ) 100 , c ) 65 , d ) 500 , e ) 980
Rationale: "average price for a pair of rackets = $ 9.8 total cost = $ 9.8 * x = $ 637 x = 65 pairs were sold . answer : c"
Answer: c
Question (physics): a farmer has enough food to feed her 1000 cows for 50 days . after 10 days some of the cows run away and the food was now enough for the same period of 50 days as before . how many cows ran away ?
Options: a ) 300 , b ) 200 , c ) 500 , d ) 400 , e ) 250
Rationale: 1000 - - - - 50 1000 - - - - 40 x - - - - 50 x * 50 = 1000 * 40 x = 800 1000 - - - - - - - 200 answer = b
Answer: b
Question (physics): a certain number of men can do a work in 60 days . if there were 8 men less it could be finished in 10 days more . how many men are there ?
Options: a ) 56 , b ) 42 , c ) 60 , d ) 45 , e ) 36
Rationale: "the original number of men = 8 ( 60 + 10 ) / 10 = 56 men answer is a"
Answer: a
Question (general): if - 3 x + 4 y = 28 and 3 x - 2 y = 8 , what is the product of x and y ?
Options: a ) 264 . , b ) 428 , c ) 464 . , d ) 622 , e ) 642
Rationale: given - 3 x + 4 y = 28 - - - eq 1 3 x - 2 y = 8 - - eq 2 sum both eqns we get 2 y = 36 = > y = 18 sub 2 y in eq 2 = > 3 x - 36 = 8 . = > x = 44 / 3 now xy = 44 / 3 * 18 = 264 . option a is correct answer .
Answer: a
Question (geometry): a rectangle having length 89 cm and width 34 cm . if the length of the rectangle is increased by eighty percent then how much percent the breadth should be decreased so as to maintain the same area .
Options: a ) 25 % , b ) 33.33 % , c ) 47.33 % , d ) 75 % , e ) none of these
Rationale: "explanation : solution : ( 80 / ( 89 + 80 ) * 100 ) % = 47.33 % answer : c"
Answer: c
Question (physics): two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 25 hours and 81 hours respectively . the ratio of their speeds is :
Options: a ) 2 : 3 , b ) 4 : 3 , c ) 9 : 5 , d ) 9 : 16 , e ) none of these
Rationale: "let us name the trains as a and b . then , ( a ' s speed ) : ( b ' s speed ) = â ˆ š b : â ˆ š a = â ˆ š 81 : â ˆ š 25 = 9 : 5 . answer c"
Answer: c
Question (physics): a train 100 m long takes 6 sec to cross a man walking at 5 kmph in a direction opposite to that of the train . find the speed of the train ?
Options: a ) 45 kmph , b ) 55 kmph , c ) 32 kmph , d ) 61 kmph , e ) 70 kmph
Rationale: "let the speed of the train be x kmph speed of the train relative to man = x + 5 = ( x + 5 ) * 5 / 18 m / sec 100 / [ ( x + 5 ) * 5 / 18 ] = 6 30 ( x + 5 ) = 1800 x = 55 kmph answer is b"
Answer: b
Question (general): evaluate : 96385 + 12 * 3 * 25 = ?
Options: a ) 96385 , b ) 96358 , c ) 96785 , d ) 96485 , e ) 96855
Rationale: "according to order of operations , 12 ? 3 ? 25 ( division and multiplication ) is done first from left to right 12 / 2 = 4 * 25 = 100 hence 96385 + 12 * 3 * 2 = 96385 + 100 = 96485 correct answer d"
Answer: d
Question (general): how many positive integers less than 100 have a remainder of 3 when divided by 13 ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 3
Rationale: "we have to include 3 also . as 13 * 0 + 3 = 3 if somebody says to divide 3 by 13 , we will be telling we have 0 quotient and remainder as 3 . answer is e"
Answer: e
Question (general): if y > 0 , ( 9 y ) / 20 + ( 3 y ) / 10 is what percent of y ?
Options: a ) 40 % , b ) 50 % , c ) 60 % , d ) 70 % , e ) 75 %
Rationale: "can be reduced to 9 y / 20 + 6 y / 20 = 15 y / 20 = 75 % answer e"
Answer: e
Question (general): all the students of class are told to sit in circle shape . here the boy at the 5 th position is exactly opposite to 20 th boy . total number of boys in the class ?
Options: a ) 30 , b ) 40 , c ) 45 , d ) 25 , e ) 20
Rationale: "as half the circle shape consist of 20 - 5 = 15 boys , so total number of boys in full circle = 2 * 15 = 30 answer : a"
Answer: a
Question (physics): a boy swims downstream 56 km and upstream 42 km taking 7 hours each time ; what is the speed of the current ?
Options: a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1
Rationale: "56 - - - 7 ds = 8 ? - - - - 1 42 - - - - 7 us = 6 ? - - - - 1 s = ? s = ( 8 - 6 ) / 2 = 1 answer : e"
Answer: e
Question (general): an equal number of desks and bookcases are to be placed along a library wall that is 15 meters long . each desk is 2 meters long , and each bookshelf is 1.5 meters long . if the maximum possible number of desks and bookcases are to be placed along the wall , then the space along the wall that is left over will be how many meters f long ?
Options: a ) 0.5 , b ) 1 , c ) 1.5 , d ) 2 , e ) 3
Rationale: "let x be the number of desks and bookcases that are placed along the library wall . 2 x + 1.5 x < 15 3.5 x < 15 since x is a non negative integer , the largest number x can be is 4 . when x is 4 , the desks and bookcases take up 3.5 * 4 = 14 m , leaving 1 m of empty space . thus , i believe the answer is b ) 1"
Answer: b
Question (probability): a meeting has to be conducted with 5 managers . find the number of ways in which the managers may be selected from among 9 managers , if 3 managers will not attend the meeting together .
Options: a ) 1.24 , b ) 2.91 , c ) 3.12 , d ) 4.126 , e ) 5.15
Rationale: "9 managers , but 3 of them can not attend the meeting together . we can split it into two cases . 1 . meeting without these 3 managers in it . that would mean selecting 5 , from the remaining 6 which is 6 c 5 = 6 2 . meeting with one of the 3 managers . select 1 manager from 3 , and then select 4 from the remaining 6 , which is 3 c 1 + 6 c 4 = 18 + 6 = 24 . answer : a"
Answer: a
Question (general): for every even positive integer m , f ( m ) represents the product of all even integers from 2 to m , inclusive . for example , f ( 12 ) = 2 x 4 x 6 x 8 x 10 x 12 . what is the greatest prime factor of f ( 24 ) ?
Options: a ) 23 , b ) 19 , c ) 17 , d ) 13 , e ) 11
Rationale: f ( 24 ) = 2 * 4 * 6 * 8 * 10 * 12 * 14 * 16 * 18 * 20 * 22 * 24 = 2 ^ 12 * ( 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10 * 11 ) - - > the greatest prime factor is 11 . answer : e .
Answer: e
Question (general): an employee ’ s annual salary was increased $ 5,000 . if her new annual salary now equals $ 70,000 , what was the percent increase ?
Options: a ) 15 % , b ) 0.77 % , c ) 20 % , d ) 22 % , e ) 24 %
Rationale: "new annual salary = $ 70,000 salary increase = $ 5,000 . original salary = $ 70,000 - $ 5,000 . = $ 65,000 % increase = ( $ 5,000 / $ 65,000 ) * 100 = 0.77 % hence b ."
Answer: b
Question (general): how many two - digit whole numbers yield a remainder of 1 when divided by 20 and also yield a remainder of 1 when divided by 5 ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: "the possible number n can be written as follow : n = multiple of lcm ( 20,5 ) + 1 st such number n = 20 x + 1 possible values = 1 , 21 , 41 , 61,81 answer : 4 such 2 digit number . e ."
Answer: e
Question (physics): j is faster than p . j and p each walk 24 km . sum ofthe speeds of j and p is 7 kmph . sum of time taken by them is 14 hours . then j speed is equal to ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "let j ' s speed is x then p ' s speed would be 7 - x . and given , sum of time taken by them is 14 hours = > ( 24 / x ) + ( 24 / ( 7 - x ) = 14 = > x = 4,3 therefore j ' s speed will be 4 as j walks faster than p . answer : a"
Answer: a
Question (gain): a particular library has 75 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 80 percent of books that were loaned out are returned and there are 66 books in the special collection at that time , how many books of the special collection were loaned out during that month ?
Options: a ) 20 , b ) 30 , c ) 35 , d ) 45 , e ) 55
Rationale: "there are 9 books less ( 75 - 66 ) which represents 20 % of the loaned books ( 100 - 80 ) so total loaned out books = 45 answer d"
Answer: d
Question (physics): 50 men took a dip in a water tank 30 m long and 20 m broad on a religious day . if the average displacement of water by a man is 4 m 3 , then the rise in the water level in the tank will be :
Options: a ) 20 cm , b ) 25 cm , c ) 33.3 cm , d ) 50 cm , e ) none of these
Rationale: "explanation : total volume of water displaced = ( 4 x 50 ) m 3 = 200 m 3 rise in water level = 200 / 30 ã — 20 = 0.333 m = 33.3 cm answer : c"
Answer: c
Question (gain): find the simple interest on rs . 70,000 at 16 2 / 3 % per year for 9 months .
Options: a ) 7500 , b ) 6500 , c ) 8750 , d ) 9500 , e ) none of them
Rationale: "p = rs . 70000 , r = 50 / 3 % p . a and t = 9 / 12 years = 3 / 4 years . simple interest = ( p * r * t ) / 100 = rs . ( 70,000 * ( 50 / 3 ) * ( 3 / 4 ) * ( 1 / 100 ) ) = rs . 8750 answer is c ."
Answer: c
Question (physics): a is twice as good a workman as b and they took 6 days together to do the work b alone can do it in .
Options: a ) 18 days , b ) 12 days , c ) 29 days , d ) 25 days , e ) 27 days
Rationale: "wc = 2 : 1 2 x + x = 1 / 6 x = 1 / 18 = > 18 days answer : a"
Answer: a
Question (physics): donovan and michael are racing around a circular 400 - meter track . if donovan runs each lap in 45 seconds and michael runs each lap in 36 seconds , how many laps will michael have to complete in order to pass donovan , assuming they start at the same time ?
Options: a ) 8 , b ) 7 , c ) 6 , d ) 5 , e ) 9
Rationale: "one way of approaching this question is by relative speed method 1 . speed / rate of donovan = distance / time = > 400 / 45 = > 80 / 9 2 . speed / rate of michael = distance / time = > 400 / 36 = > 100 / 9 relative speed between them = 100 / 9 - 80 / 9 = > 20 / 9 ( we subtract the rates if moving in the same direction and add the rates if moving in the opposite direction ) in order to pass donovan - distance to be covered = 400 , relative rate = 20 / 9 total time taken by micheal to surpass donovan = distance / rate = > 400 * 9 / 20 = > 3600 / 10 = > 180 no . of laps taken by michael = total time / michael ' s rate = > 180 / 36 = > 5 hence correct answer is 5 laps . d"
Answer: d
Question (physics): if 3 people can do 3 times of a particular work in 3 days , then how many days would it take 9 people to do 9 times of that particular work ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 9 , e ) 12
Rationale: "3 people can do the work one time in one day . 1 person can do 1 / 3 of the work in one day . 9 people can do 9 / 3 of the work in one day . 9 people can do 9 times the work in 3 days . the answer is c ."
Answer: c
Question (physics): a and b can do a work in 5 days and 10 days respectively . a starts the work and b joins him after 2 days . in how many days can they complete the remaining work ?
Options: a ) 6 , b ) 2 , c ) 8 , d ) 9 , e ) 3
Rationale: "work done by a in 2 days = 2 / 5 remaining work = 3 / 5 work done by both a and b in one day = 1 / 5 + 1 / 10 = 3 / 10 remaining work = 3 / 5 * 10 / 3 = 2 days . answer : b"
Answer: b
Question (general): the average age of students of a class is 15.8 years . the average age of boys in the class is 16.5 years and that of the girls is 15.4 years . the ration of the number of boys to the number of girls in the class is :
Options: a ) 2 : 5 , b ) 2 : 3 , c ) 2 : 4 , d ) 2 : 1 , e ) 4 : 7
Rationale: "let the ratio be k : 1 . then , k * 16.5 + 1 * 15.4 = ( k + 1 ) * 15.8 = ( 16.5 - 15.8 ) k = ( 15.8 - 15.4 ) = k = 0.4 / 0.7 = 4 / 7 required ratio = 4 / 7 : 1 = 4 : 7 . answer : e"
Answer: e
Question (general): before 6 years , dog a ’ s age was 4 times of dog b ’ s age and after 4 years , dog a ’ s age will be 3 times of dog b ’ s age . what is the difference of dog a ’ s age and dog b ’ s now ?
Options: a ) 36 , b ) 42 , c ) 54 , d ) 60 , e ) 64
Rationale: "a - 6 = 4 ( b - 6 ) - - > a - 4 b = - 18 . . . . . . . . . . . . . 1 a + 4 = 3 ( b + 4 ) - - > a - 3 b = 8 . . . . . . . . . . . . . 2 ( 2 ) - ( 1 ) - - > b = 26 - - > a = 3 ( 30 ) = 90 a - b = 90 - 26 = 64 answer : e"
Answer: e
Question (general): 4 wolves , wolverine , man - hunter , blue - wolf , and jasmine , caught rabbits for their evening meal . if man - hunter caught 3 more rabbits than blue - wolf did , jasmine caught 3 less than wolverine did , and wolverine caught 1 more than man - hunter did , how many more fewer rabbits did blue - wolf catch than jasmine ?
Options: a ) - 3 , b ) - 2 , c ) - 5 , d ) - 12 , e ) - 1
Rationale: in this word problem , the first key is to turn the story into equations : man - hunter caught 3 more than blue - wolf did : m = 3 + b jasmine caught 3 less than wolverine did : j = w - 3 wolverine caught 3 more than man - hunter did : w = 1 + m then , in classic gmat style , the problem does n ' t ask you to solve for a single variable , but instead to solve for the difference between b and j ( how many more rabbits did blue - wolf catch than jasmine did ? ) . this means that your goal is to get the equations in terms of b and j so that you can solve for the expression b - j . taking the first equation and solving for b , you have b = m - 3 . taking the second equation and solving for j you have j = w - 3 , and then with the third equation you can replace w with 1 + m so that both b and j are in terms of m : j = ( 1 + m ) - 3 . so if b = m - 3 and j = m - 2 , then : b - j = ( m - 3 ) - ( m - 2 ) b - j = m - 3 - m + 2 ( remove the parentheses by distributing the multiplication ) b - j = - 1 , so the answer is e .
Answer: e
Question (physics): a bullet train 160 m long is running with a speed of 70 kmph . in what time will it pass a man who is running at 8 kmph in the direction opposite to that in which the bullet train is going ?
Options: a ) 23 sec , b ) 15 sec , c ) 7.38 sec , d ) 6.92 sec , e ) 16 sec
Rationale: "c 7.38 sec speed of the bullet train relative to man = ( 70 + 8 ) kmph = 78 * 5 / 18 m / sec = 65 / 3 m / sec . time taken by the bullet train to cross the man = time taken by it to cover 160 m at ( 65 / 3 ) m / sec = ( 160 * 3 / 65 ) sec = 7.38 sec"
Answer: c
Question (general): what is the remainder when 103 * 505 * 607 is divided by 9
Options: a ) 6 , b ) 18 , c ) 2 , d ) 4 , e ) 7
Rationale: "103 / 9 = = > remainder = 4 505 / 9 = = > remainder = 1 607 / 9 = = > remainder = 4 = 4 * 4 * 1 = 16 / 9 = = > remainder = 7 answer : e"
Answer: e
Question (physics): a man can do a job in 5 days . his father takes 20 days and his son finishes it in 25 days . how long will they take to complete the job if they all work together ?
Options: a ) 6.3 , b ) 6.9 , c ) 3.5 , d ) 6.1 , e ) 6.2
Rationale: "1 day work of the three persons = ( 1 / 5 + 1 / 20 + 1 / 25 ) = 29 / 100 so , all three together will complete the work in 100 / 29 = 3.5 days . answer : c"
Answer: c
Question (general): what is the value of 3 x ^ 2 − 1.8 x + 0.3 for x = 0.9 ?
Options: a ) − 0.3 , b ) 0 , c ) 0.3 , d ) 1.11 , e ) 2.46
Rationale: "3 x ^ 2 - 1.8 x + 0.3 for x = 0.5 = 3 ( 0.9 * 0.9 ) - 2 * 0.9 * ( 0.9 ) + 0.3 = 0.9 * 0.9 + 0.3 = 0.81 + 0.3 = 1.11 correct option : d"
Answer: d
Question (other): bag a contains red , white and blue marbles such that the red to white marble ratio is 1 : 3 and the white to blue marble ratio is 2 : 3 . bag b contains red and white marbles in the ratio of 1 : 4 . together , the two bags contain 26 white marbles . how many red marbles could be in bag a ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 2 , e ) 8
Rationale: "# of red marbles in bag a can be either 2 or 6 . no 2 in the choices , so 6 . d . bag a : r : w : b = 2 : 6 : 9 bag b r : w = 1 : 4 6 x + 4 y = 26 i . e 3 x + 2 y = 13 x has to be odd to make an odd sum from the eq . x = 1 , y = 5 or x = 3 , y = 2 so r can be 2 x i . e 2 or 6 . answer d"
Answer: d
Question (gain): a restaurant spends one quarter of its monthly budget for rent and two thrid of the rest for food and beverages . what percentage of the budget does the restaurant spend for food and beverages ?
Options: a ) 23.5 % , b ) 50 % , c ) 35 % , d ) 37.5 % , e ) 75 %
Rationale: "spend on rent = 1 / 4 spend on food and beverage = 2 / 4 of remaining = 2 / 3 * 3 / 4 = 1 / 2 so 1 / 2 = 50.0 % b is the answer"
Answer: b
Question (physics): in a kilometer race , a beats b by 52 meters or 18 seconds . what time does a take to complete the race ?
Options: a ) 277 sec , b ) 190 sec , c ) 328 sec , d ) 367 sec , e ) 376 sec
Rationale: "time taken by b run 1000 meters = ( 1000 * 18 ) / 52 = 346 sec . time taken by a = 346 - 18 = 328 sec . answer : c"
Answer: c
Question (probability): what is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular octagon ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 5 , e ) 7 / 8
Rationale: "from any vertex , there are two vertices on sides , which do not make a diagonal but a side . so the remaining n - 3 vertices make diagonals . there are 2 of these diagonals which are the shortest . the probability of choosing one of the shortest diagonals is 2 / 5 . the answer is d ."
Answer: d
Question (gain): a towel , when bleached , lost 30 % of its length and 25 % of its breadth . what is the percentage decrease in area ?
Options: a ) 24 % , b ) 30 % , c ) 44 % , d ) 54 % , e ) 47.5 %
Rationale: "percentage change in area = ( − 30 − 25 + ( 30 × 25 ) / 100 ) % = − 47.5 % i . e . , area is decreased by 47.5 % answer : e"
Answer: e
Question (physics): two women can do a work in 4 days . six men can complete the same work in 3 days . what is the ratio between the capacity of a man and a woman ?
Options: a ) 1 : 2 , b ) 2 : 1 , c ) 4 : 9 , d ) 3 : 2 , e ) none of these
Rationale: "explanation : ( 2 ã — 4 ) women can complete the work in 1 day . â ˆ ´ 1 woman ' s 1 day ' s work = 1 / 8 ( 6 ã — 3 ) men can complete the work in 1 day . â ˆ ´ 1 man ' s 1 day ' s work = 1 / 18 so , required ratio = 1 / 8 : 1 / 18 = 4 : 9 answer : c"
Answer: c
Question (general): 10 x 0.5 = ?
Options: a ) 0.0001 , b ) 0.001 , c ) 0.01 , d ) 0.1 , e ) 5
Rationale: "explanation : 10 x 5 = 50 . sum of decimal places = 1 10 x 0.5 = 5 answer - e"
Answer: e
Question (general): what is the remainder when 54617 ^ ( 42788234 ) is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "we need to find the units digit of the number . the units digit of powers of seven repeats 7 , 9 , 3 , and 1 cyclically . since 42788234 has the form 4 a + 2 , the units digit is 9 . then the remainder when dividing by 5 is 4 . the answer is e ."
Answer: e
Question (physics): a cube of side two meter length is cut into small cubes of side 10 cm each . how many such small cubes can be obtained ?
Options: a ) 2878 , b ) 2778 , c ) 1000 , d ) 8000 , e ) 8900
Rationale: "along one edge , the number of small cubes that can be cut = 200 / 10 = 20 along each edge 10 cubes can be cut . ( along length , breadth and height ) . total number of small cubes that can be cut = 20 * 20 * 20 = 8000 answer : d"
Answer: d
Question (general): how many numbers between 200 and 600 are divisible by 4 , 5 and 6 ?
Options: a ) 5 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: "sol . every such numbers must be divisible by l . c . m . of 4 , 5 , 6 , i . e . 60 . such numbers are 240 , 300 , 360 , 420 , 480 , 540 . clearly , there are 6 such numbers . answer b"
Answer: b