regisss/math_qa huggingface dataset:
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: a train 270 metres long is moving at a speed of 25 kmph . it will cross a man coming from the opposite direction at a speed of 2 km per hour in :
Options: a ) 30 sec , b ) 32 sec , c ) 36 sec , d ) 38 sec , e ) 40 sec
Rationale: "relative speed = ( 25 + 2 ) km / hr = 27 km / hr = ( 27 × 5 / 18 ) m / sec = 15 / 2 m / sec . time taken by the train to pass the man = ( 270 × 2 / 15 ) sec = 36 sec answer : c"
Answer: c
Problem: speed of a boat in standing water is 14 kmph and the speed of the stream is 1.2 kmph . a man rows to a place at a distance of 4864 km and comes back to the starting point . the total time taken by him is :
Options: a ) 700 , b ) 200 , c ) 540 , d ) 120 , e ) 635
Rationale: "explanation : speed downstream = ( 14 + 1.2 ) = 15.2 kmph speed upstream = ( 14 - 1.2 ) = 12.8 kmph total time taken = 4864 / 15.2 + 4864 / 12.8 = 320 + 380 = 700 hours . answer : a"
Answer: a
Problem: you enter a weight loss challenge game and manage to lose 13 % of your body weight . for the final weigh in you are forced to wear clothes that add 2 % to your weight . what percentage of weight loss is measured at the final weigh in ?
Options: a ) 13 % , b ) 9.22 % , c ) 11.26 % , d ) 14 % , e ) 12 %
Rationale: ( 100 % - 13 % ) * ( 100 % + 2 % ) = 0.87 * 1.02 = 11.26 % the weigh in records your weight loss at 11.26 % ! the answer is c
Answer: c
Problem: i bought two books ; for rs . 500 . i sold one at a loss of 15 % and other at a gain of 19 % and then i found each book was sold at the same price . find the cost of the book sold at a loss ?
Options: a ) 337 , b ) 280 , c ) 299.67 , d ) 266.67 , e ) 291.67
Rationale: "x * ( 85 / 100 ) = ( 500 - x ) 119 / 100 x = 291.67 answer : e"
Answer: e
Problem: 252 ã · ? ã — 15 + 270 = 405
Options: a ) 24 , b ) 25 , c ) 28 , d ) 39 , e ) 43
Rationale: "explanation : 252 ã · ? ã — 15 = 405 - 270 = 135 ( 252 ã — 15 ) / ? = 135 ? = ( 252 ã — 15 ) / 135 = 28 answer : option c"
Answer: c
Problem: a and b put in rs . 300 and rs . 400 respectively into a business . a reinvests into the business his share of the first year ' s profit of rs . 196 where as b does not . in what ratio should they divide the second year ' s profit ?
Options: a ) 39 : 40 , b ) 39 : 49 , c ) 24 : 25 , d ) 39 : 47 , e ) 39 : 41
Rationale: "explanation : 3 : 4 a = 3 / 7 * 196 = 84 384 : 400 24 : 25 answer : c"
Answer: c
Problem: in a group of ducks and cows , the total number of legs are 40 more than twice the number of heads . find the total number of cows .
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "let the number of ducks be d and number of cows be c then , total number of legs = 2 d + 4 c = 2 ( d + 2 c ) total number of heads = c + d given that total number of legs are 40 more than twice the number of heads = > 2 ( d + 2 c ) = 40 + 2 ( c + d ) = > d + 2 c = 20 + c + d = > 2 c = 20 + c = > c = 20 i . e . , total number of cows = 20 answer is e ."
Answer: e
Problem: a student chose a number , multiplied it by 2 , then subtracted 138 from the result and got 102 . what was the number he chose ?
Options: a ) 90 , b ) 100 , c ) 120 , d ) 160 , e ) 200
Rationale: "solution : let x be the number he chose , then 2 * x * 138 = 102 2 x = 240 x = 120 correct answer c"
Answer: c
Problem: the product of two successive numbers is 4160 . which is the smaller of the two numbers ?
Options: a ) 78 , b ) 64 , c ) 88 , d ) 67 , e ) 37
Rationale: "b 4160 from the given alternatives , 64 × 65 = 4160 ∴ smaller number = 64"
Answer: b
Problem: soymilk are sold in packages of two or 3 only . if hannah bought 17 soymilk exactly , what could be the number of large packs hannah bought ?
Options: a ) 1 , b ) 4 , c ) 3 , d ) 5 , e ) 8
Rationale: let number of packs of three = t let number of packs of two = w 3 t + 2 w = 17 now , we need to test for values of w . since sum 17 is odd and 2 w will always be even , therefore w ca n ' t be even . now , we can test for values w = 1 , 3 and 5 2 * 4 + 3 * 3 = 8 + 9 = 17 answer c
Answer: c
Problem: what ratio must a shopkeeper mix peas and soybean of rs . 16 and rs . 25 / kg , as to obtain a mixture of rs . 21.50 ?
Options: a ) 10 : 7 , b ) 9 : 8 , c ) 7 : 11 , d ) 13 : 11 , e ) 14 : 8
Rationale: "correct option : ( c ) use rule of alligation , to determine the ratio the required ratio of soybean and peas = 3.50 : 5.50 = 7 : 11"
Answer: c
Problem: a 300 meter long train crosses a platform in 33 seconds while it crosses a signal pole in 18 seconds . what is the length of the platform ?
Options: a ) 250 , b ) 266 , c ) 230 , d ) 288 , e ) 271
Rationale: "speed = [ 300 / 18 ] m / sec = 50 / 3 m / sec . let the length of the platform be x meters . then , x + 300 / 33 = 50 / 3 3 ( x + 300 ) = 1650 è x = 250 m . answer : a"
Answer: a
Problem: bucket p has thrice the capacity as bucket q . it takes 60 turns for bucket p to fill the empty drum . how many turns it will take for both the buckets p and q , having each turn together to fill the empty drum ?
Options: a ) 30 , b ) 45 , c ) 50 , d ) 25 , e ) 60
Rationale: "let capacity of p be x liters then capacity of q = x / 3 liters capacity of the drum = 60 x required number of turns = 60 x / ( x + x / 3 ) = 60 x * 3 / 4 x = 45 answer is b"
Answer: b
Problem: mr . loyd wants to fence his square shaped land of 120 sqft each side . if a pole is laid every 10 ft how many poles do he need ?
Options: a ) 20 , b ) 30 , c ) 48 , d ) 50 , e ) 60
Rationale: "if each side is 120 feet . . then total perimeter is 120 * 4 = 480 poles every 10 feet hence no of poles = 480 / 10 = 48 answer : c"
Answer: c
Problem: if 4 / ( 1 + 3 / x ) = 1 , then x =
Options: a ) 3 , b ) 1 , c ) 1 / 3 , d ) - 1 / 3 , e ) - 3
Rationale: "the expression 4 / ( 1 + 3 / x ) = 1 should have been equal to something . if 4 / ( 1 + 3 / x ) = 1 = > 4 x / ( x + 3 ) = 1 = > 4 x = x + 3 = > 3 x = 3 = > x = 1 correct option : b"
Answer: b
Problem: a 16 % stock yielding 10 % is quoted at :
Options: a ) 83.33 , b ) 110 , c ) 112 , d ) 120 , e ) 160
Rationale: "solution to earn rs . 10 , money invested = rs . 100 . to earn rs . 16 , money invested = rs . ( 100 / 10 x 16 ) = rs . 160 . â ˆ ´ market value of rs . 100 stock = rs . 160 answer e"
Answer: e
Problem: there are , in a certain league , 20 teams , and each team face another team for a total of 10 times . how many games are played in the season ?
Options: a ) 1900 , b ) 3600 , c ) 2400 , d ) 180 , e ) 5400
Rationale: "1 st team : 190 2 nd team : 180 3 rd team : 170 similarly the last team will play 0 therefore ( 190 + 180 + 170 . . . . 10 ) 10 ( 19 + 18 + 17 + 16 . . . . 1 ) 10 ( n ( n + 1 ) / 2 ) = 10 ( 19 * 20 / 2 ) = 1900 answer : a"
Answer: a
Problem: if integer k is equal to the sum of all even multiples of 15 between 390 and 615 , what is the greatest prime factor of k ?
Options: a ) 5 , b ) 7 , c ) 8 , d ) 13 , e ) 17
Rationale: "if we break down what the stem is asking what is the sum of all mult of 30 between 390 and 600 . using arithmetic progression to find n : 600 = 390 + ( n - 1 ) 30 210 + 30 = 30 n 240 = 3 n = > n = 8 the sum would be : 8 * mean mean = [ 600 + 390 ] / 2 = 495 8 * 495 c"
Answer: c
Problem: if x and y are positive integers and 3 + x + y + xy = 17 , what is the value of x + y ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: "try each answer choice . for a : 3 + 3 + xy = 17 ; xy = 11 ( impossible , 11 prime number . 1 + 11 does n ' t equal 3 ) for b : 3 + 5 + xy = 17 ; xy = 9 ( no combination of xy = 9 and x + y = 5 ) for c : 3 + 6 + xy = 17 ; xy = 8 ( x + y = 6 ; x = 2 , y = 4 or x = 4 , y = 2 ) for d : 3 + 8 + xy = 17 ; xy = 6 ( no combination of xy = 6 and x + y = 8 ) for e : 3 + 9 + xy = 17 ; xy = 5 ( impossible , 5 prime number . 1 + 5 does n ' t equal 9 ) therefore , answer c ."
Answer: c
Problem: a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 30 paisa . if the share of y is rs . 54 , what is the total amount ?
Options: a ) 166 , b ) 105 , c ) 178 , d ) 177 , e ) 210
Rationale: "x : y : z = 100 : 45 : 30 20 : 9 : 6 9 - - - 54 35 - - - ? = > 210 answer : e"
Answer: e
Problem: the expenditure of a businessman increase consistently by 10 % per year . if his present expenditure is rs . 20000 then what will his expenditure be after 2 years ?
Options: a ) 24500 , b ) 24400 , c ) 24300 , d ) 24200 , e ) 24100
Rationale: explanation : expenditure = 20000 x 1.1 x 1.1 = 24200 answer : option d
Answer: d
Problem: farm tax is levied on the 25 % of the cultivated land . the tax department collected total $ 3840 through the farm tax from the village of mr . william . mr . william paid only $ 480 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is :
Options: a ) 15 % , b ) 25 % , c ) 50 % , d ) 0.2083 % , e ) none
Rationale: "this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 480 / 3840 ) x 100 = 12.5 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 12.5 % x ( 100 / 25 ) = 50 % the correct answer is ( c ) ."
Answer: c
Problem: a textile manufacturing firm employees 100 looms . it makes fabrics for a branded company . the aggregate sales value of the output of the 100 looms is rs 5 , 00,000 and the monthly manufacturing expenses is rs 1 , 50,000 . assume that each loom contributes equally to the sales and manufacturing expenses are evenly spread over the number of looms . monthly establishment charges are rs 75000 . if one loom breaks down and remains idle for one month , the decrease in profit is :
Options: a ) 13000 , b ) 7000 , c ) 10000 , d ) 3500 , e ) none of these
Rationale: "explanation : profit = 5 , 00,000 â ˆ ’ ( 1 , 50,000 + 75,000 ) = rs . 2 , 75,000 . since , such loom contributes equally to sales and manufacturing expenses . but the monthly charges are fixed at rs 75,000 . if one loan breaks down sales and expenses will decrease . new profit : - = > 500000 ã — ( 99 / 100 ) â ˆ ’ 150000 ã — ( 99 / 100 ) â ˆ ’ 75000 . = > rs 2 , 68,000 . decrease in profit = > 2 , 75,000 â ˆ ’ 2 , 71,500 = > rs . 3,500 . answer : d"
Answer: d
Problem: it is the new year and mandy has made a resolution to lose weight this year . she plans to exercise and do yoga . for exercise she plans to workout at the gym and ride her bicycle in the ratio of 2 : 3 everyday . she will also do yoga in the ratio , yoga : exercise = 2 : 3 . if she rides her bike for 18 minutes , how much time will she spend doing yoga ? ( rounded to minutes )
Options: a ) 30 min . , b ) 41 min . , c ) 17 min . , d ) 23 min . , e ) 25 min .
Rationale: "the ratio is 2 : 3 = gym : ride , so ( 18 ) ( 3 / 2 ) = 27 minutes at the gym , and 27 + 18 = 45 minutes exercise , so ( 2 / 3 ) ( 45 ) = 30 minutes yoga . answer : a"
Answer: a
Problem: when positive integer x is divided by 11 , the quotient is y and the remainder is 4 . when 2 x is divided by 8 , the quotient is 3 y and the remainder is 1 . what is the value of 13 y – x ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: ( 1 ) x = 11 y + 4 ( 2 ) 2 x = 24 y + 1 let ' s subtract equation ( 1 ) from equation ( 2 ) . 13 y - 3 = x 13 y - x = 3 the answer is b .
Answer: b
Problem: what is the least number of squares tiles required to pave the floor of a room 15.17 m long and 9.02 m broad ?
Options: a ) 814
b ) 266
c ) 287
d ) 999
e ) 661
Rationale: explanation : length of largest tile = h . c . f . of 1517 cm and 902 cm = 41 cm . area of each tile = required number of tiles = = 814 answer : a ) 814
Answer: a
Problem: a bottle contains a certain solution . in the bottled solution , the ratio of water to soap is 3 : 2 , and the ratio of soap to salt is seven times this ratio . the solution is poured into an open container , and after some time , the ratio of water to soap in the open container is halved by water evaporation . at that time , what is the ratio of water to salt in the solution ?
Options: a ) 1 : 1 , b ) 2 : 3 , c ) 3 : 2 , d ) 9 : 4 , e ) 63 : 8
Rationale: "water : soap = 3 : 2 soap : salt = 21 : 2 = > for 21 soap , salt = 2 = > for 2 soap , salt = ( 2 / 21 ) * 2 = 4 / 21 so , water : soap : salt = 3 : 2 : 4 / 21 = 63 : 42 : 4 after open container , water : soap : salt = 31.5 : 42 : 4 so , water : salt = 31.5 : 4 = 63 : 8 e"
Answer: e
Problem: if a drawing has an outer circle of diameter 30 and an inner circle of diameter 24 , then what fraction of outer circle ' s surface is not covered by the inner circle ?
Options: a ) 3 / 6
b ) 8 / 24
c ) 14 / 16
d ) 9 / 25
e ) 2 / 3
Rationale: the questions asks us to find the surface which is not covered by the inner circle i . e . , area of the surface not covered . where as circumference is the length along the edge of the circle , 2 * pi * r implies the length of the curve pi * r ^ 2 implies area enclosed by that curve . . hence area of the circle is considered for this problem area of the inner circle = pi * r ^ 2 , where r = 12 = > pi * 144 area of the outer circle = pi * 225 surface not covered by the inner circle = pi * 225 - pi * 144 = pi * 81 fraction of outer circle ' s surface is not covered by the inner circle = pi * 81 / total area of the outer circle = > pi * 81 / pi * 225 = 9 / 25 answer is d
Answer: d
Problem: the sum of three consecutive even numbers is 366 . find the middle number of the three ?
Options: a ) 111 , b ) 123 , c ) 122 , d ) 152 , e ) 142
Rationale: "middle number = 366 / 3 = 122 ans c"
Answer: c
Problem: x can finish a work in 24 days . y can finish the same work in 16 days . yworked for 10 days and left the job . how many days does x alone need to finish the remaining work ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: "work done by x in 1 day = 1 / 24 work done by y in 1 day = 1 / 16 work done by y in 10 days = 10 / 16 = 5 / 8 remaining work = 1 – 5 / 8 = 3 / 8 number of days in which x can finish the remaining work = ( 3 / 8 ) / ( 1 / 24 ) = 9 e"
Answer: e
Problem: some of 45 % - intensity red paint is replaced with 25 % solution of red paint such that the new paint intensity is 40 % . what fraction of the original paint was replaced ?
Options: a ) 2 / 5 , b ) 1 / 4 , c ) 1 / 5 , d ) 1 / 7 , e ) 2 / 3
Rationale: "let total paint = 1 let amount replaced = x 45 ( 1 - x ) + 25 x = 40 x = 1 / 4 answer : b"
Answer: b
Problem: what is the greatest positive integer e such that 3 ^ e is a factor of 9 ^ 10 ?
Options: a ) e = 5 , b ) e = 9 , c ) e = 10 , d ) e = 20 , e ) 30
Rationale: "what is the greatest positive integer e such that 3 ^ e is a factor of 9 ^ 10 ? 9 ^ 10 = ( 3 ^ 2 ) ^ 10 = 3 ^ 20 d . 20"
Answer: d
Problem: what will be the cost of building a fence around a square plot with area equal to 289 sq ft , if the price per foot of building the fence is rs . 59 ?
Options: a ) 3944 , b ) 920 , c ) 7290 , d ) 6928 , e ) 4012
Rationale: "explanation : let the side of the square plot be a ft . a 2 = 289 = > a = 17 length of the fence = perimeter of the plot = 4 a = 68 ft . cost of building the fence = 68 * 59 = rs . 4012 . answer : option e"
Answer: e
Problem: if the sum of two numbers is 45 and the h . c . f and l . c . m of these numbers are 4 and 5 respectively , then the product of the reciprocals is equal to :
Options: a ) 20 / 20 , b ) 1 / 1 , c ) 2 / 30 , d ) 11 / 20 , e ) 1 / 20
Rationale: "let the numbers be a and b . then , a + b = 45 and ab = 5 * 4 = 20 . required product = 1 / a * 1 / b = 1 / ab = 1 / 20 = 1 / 20 . answer : e"
Answer: e
Problem: at jerri ’ s pet shop , 60 cups of bird seed are used every 5 days to feed 20 parakeets . how many cups of bird seed would be required to feed 10 parakeets for 5 days ?
Options: a ) 45.6 , b ) 20 , c ) 9 , d ) 30 , e ) 65
Rationale: let ' s go step - by - step . 60 cups are used over a 5 day period , which means 12 cups a day . this feeds 20 parakeets , which means each parakeet needs . 60 of a cup every day . for 10 parakeets , we need 10 * . 60 cups = 6 cups a day . over 5 days , we need 30 cups . choice d .
Answer: d
Problem: find the value of x : 2 x ² − 4 .
Options: a ) 0,2 , b ) - 2,2 , c ) - 2,1 , d ) 0,4 , e ) - 1,4
Rationale: that quadratic is factored as follows : 2 x ² − 4 = ( 2 x − 2 ) ( x + 2 ) . now , it is easy to see that the second factor will be 0 when x = − 2 . as for the value of x that will make 2 x − 4 = 0 , we must solve that equation we have : 2 x = 4 x = 2 the solutions are : x = - 2 and 2 b
Answer: b
Problem: a jar of 180 marbles is divided equally among a group of marble - players today . if 2 people joined the group in the future , each person would receive 1 marble less . how many people are there in the group today ?
Options: a ) 16 , b ) 18 , c ) 20 , d ) 22 , e ) 24
Rationale: "180 = 18 * 10 = 20 * 9 there are 18 people in the group today . the answer is b ."
Answer: b
Problem: a cricketer whose bowling average is 12.4 runs per wicket takes 5 wickets for 26 runs and there by decreases his average by 0.4 . the number age of the family now is :
Options: a ) 18 , b ) 17 , c ) 76 , d ) 85 , e ) 86
Rationale: "let the number of wickets taken till the last match be x . then , ( 12.4 x + 26 ) / ( x + 5 ) = 12 = 12.4 x + 26 = 12 x + 60 = 0.4 x = 34 = x = 340 / 4 = 85 . answer : d"
Answer: d
Problem: the average of first 5 multiples of 5 is
Options: a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: solution average = 5 ( 1 + 2 + 3 + 4 + 5 ) / 5 = 75 / 5 . = 15 answer e
Answer: e
Problem: a technician makes a round - trip to and from a certain service center by the same route . if the technician completes the drive to the center and then completes 50 percent of the drive from the center , what percent of the round - trip has the technician completed ?
Options: a ) 70 , b ) 65 , c ) 60 , d ) 75 , e ) 80
Rationale: "round trip means 2 trips i . e . to and fro . he has completed one i . e 50 % completed . then he traveled another 50 % of 50 % i . e 25 % . so he completed 50 + 25 = 75 % of total trip . d"
Answer: d
Problem: the difference of two numbers is 1415 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder . what is the smaller number ?
Options: a ) a ) 270 , b ) b ) 280 , c ) c ) 290 , d ) d ) 300 , e ) e ) 310
Rationale: let the smaller number be x . then larger number = ( x + 1415 ) . x + 1415 = 6 x + 15 5 x = 1400 x = 280 smaller number = 280 . b )
Answer: b
Problem: the price of a jacket is reduced by 25 % . during a special sale the price of the jacket is reduced another 25 % . by approximately what percent must the price of the jacket now be increased in order to restore it to its original amount ?
Options: a ) 32.5 , b ) 77.78 , c ) 48 , d ) 65 , e ) 67.5
Rationale: "1 ) let the price of jacket initially be $ 100 . 2 ) then it is decreased by 25 % , therefore bringing down the price to $ 75 . 3 ) again it is further discounted by 10 % , therefore bringing down the price to $ 56.25 4 ) now 56.25 has to be added byx % in order to equal the original price . 56.25 + ( x % ) 56.25 = 100 . solving this eq for x , we get x = 77.78 ans is b ."
Answer: b
Problem: there is a 50 cm line marked at each centimeter and an insect is placed at every centimeter . 9 frogs are trained to jump a constant distance . the first one jumps 2 cm in every leap , the second one jumps 3 cm and so on until the 9 th one jumps 10 cm in every leap and they eat any insect that is available at that spot . if all of them start from start line and finish the entire 50 cm , how many insects were still left after the race was over ?
Options: a ) 0 , b ) 4 , c ) 6 , d ) 8 , e ) 11
Rationale: "only the prime numbers greater than 10 and less than 50 were left . that is 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43 , and 47 . the total is 11 . the answer is e ."
Answer: e
Problem: of the 180 people at a party , 70 were women , and 30 women tried the appetizer . if 50 people did not try the appetizer , what is the total number of men who tried the appetizer ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 100
Rationale: "total people at party = 180 women = 70 so men 180 - 70 = 110 no . of pple who tried appetizer = 180 - 50 ( given info ) = 130 no of women who tried appetizer = 30 so remaining ppl ( men ) who tried the appetizer = 130 - 30 = 100 correct option e"
Answer: e
Problem: danny and steve are running towards each other , each one from his own house . danny can reach steve ' s house in 25 minutes of running , which is half the time it takes steve to reach danny ' s house . if the two started to run at the same time , how much time longer will it take steve to reach the halfway point between their houses than danny to reach the halfway point between their houses ?
Options: a ) 12.5 minutes . , b ) 25 minutes , c ) 35 minutes . , d ) 35 minutes , e ) 75 minutes
Rationale: "if the distance between the two houses is d . then speed of danny = ( d / 25 ) speed of steve = ( d / 50 ) [ steve takes 50 minutes to reach danny ' s house . double the time taken by danny ) obviously speed of danny is twice that of steve . now in order to cover distance ( d / 2 ) [ they meet in middle ] , steve will take : ( d / 2 ) / ( d / 50 ) = 25 minutes . distance is same and danny ' s speed is twice of steve . thus he will take 12.5 minutes to cover this same distance . steve take 25 - 12.5 = 12.5 minutes longer . a is the answer ."
Answer: a
Problem: we run a business that rents out canoes and kayaks . a canoe rental costs $ 15 per day , and a kayak rental costs $ 18 dollars per day . one day , our business rents out 3 canoes for every 2 kayaks and receives a total of $ 405 in revenue . how many more canoes than kayaks were rented out ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "let x be the number of canoes . then 2 x / 3 is the number of kayaks . 15 x + ( 2 x / 3 ) * 18 = 405 15 x + 12 x = 405 27 x = 405 x = 15 ( canoes ) 2 x / 3 = 10 ( kayaks ) there were 15 - 10 = 5 more canoes rented out . the answer is a ."
Answer: a
Problem: how many positive integers between 1 and 200 are there such that they are multiples of 17 ?
Options: a ) 9 , b ) 11 , c ) 13 , d ) 10 , e ) 8
Rationale: "multiples of 17 = 17 , 34,51 , - - - - - 187 number of multiples of 17 = > 17 * 11 = 187 answer is b"
Answer: b
Problem: in a company the manager wants to give some gifts to all of the workers . in each block there are about 100 workers are there . the total amount for giving the gifts for all the workers is $ 4000 . the worth of the gift is $ 4 . how many blocks are there in the company ?
Options: a ) 12 , b ) 10 , c ) 15 , d ) 17 , e ) 20
Rationale: each employee will get a gift worth of = $ 4 total employees = 4000 / 4 = 1000 total blocks = 1000 / 100 = 10 correct option is b
Answer: b
Problem: in what time will a railway train 60 m long moving at the rate of 36 kmph pass a telegraph post on its way ?
Options: a ) 2 , b ) 7 , c ) 8 , d ) 6 , e ) 9
Rationale: "t = 60 / 36 * 18 / 5 = 6 sec answer : d"
Answer: d
Problem: three pipes a , b and c can fill a tank from empty to full in 30 minutes , 20 minutes and 10 minutes respectively . when the tank is empty , all the three pipes are opened . a , b and c discharge chemical solutions p , q and r respectively . what is the proportion of solution p in the liquid in the tank after 3 minutes ?
Options: a ) 3 / 11 , b ) 2 / 11 , c ) 1 / 11 , d ) 4 / 11 , e ) 1 / 11
Rationale: "part filled by ( a + b + c ) in 3 minutes = 3 ( 1 / 30 + 1 / 20 + 1 / 10 ) = 11 / 20 part filled by a in 3 minutes = 3 / 30 required ratio = 3 / 30 * 20 / 11 = 2 / 11 answer : b"
Answer: b
Problem: a man buys 54 pens at marked price of 46 pens from a whole seller . if he sells these pens giving a discount of 1 % , what is the profit percent ?
Options: a ) 7.6 % , b ) 7.7 % , c ) 16.21 % , d ) 13.6 % , e ) 7.8 %
Rationale: "explanation : let marked price be re . 1 each c . p . of 54 pens = rs . 46 s . p . of 54 pens = 99 % of rs . 54 = rs . 53.46 profit % = ( profit / c . p . ) x 100 profit % = ( 7.46 / 46 ) x 100 = 16.21 % answer : c"
Answer: c
Problem: find the area of a cuboid of length 15 cm , breadth 10 cm . and height 16 cm .
Options: a ) 2400 cm cube , b ) 2410 cm cube , c ) 2420 cm cube , d ) 2430 cm cube , e ) 2480 cm cube
Rationale: "area of a cuboid = lxbxh = 15 cm x 10 cm x 16 cm = 2400 cm cube answer : a"
Answer: a
Problem: a can do a piece of work in 15 days . a does the work for 5 days only and leaves the job . b does the remaining work in 6 days . in how many days b alone can do the work ?
Options: a ) 5 days , b ) 7 days , c ) 12 days , d ) 9 days , e ) 10 days
Rationale: "explanation : a ’ s 5 day work = 5 * 1 / 15 = 1 / 3 remaining work = 1 - 1 / 3 = 2 / 3 b completes 2 / 3 work in 6 days b alone can do in x days 2 / 3 * x = 6 x = 9 days answer : option d"
Answer: d
Problem: the sum of first n consecutive odd integers is n ^ 2 . what is the sum of all odd integers between 15 and 41 inclusive .
Options: a ) 351 , b ) 392 , c ) 410 , d ) 424 , e ) 450
Rationale: "we ' re dealing with a sequence of consecutive odd integers : 15 to 41 , inclusive . we ' re asked for the sum of this group . 1 ) start with the sum of the smallest and the biggest : 15 + 41 = 56 2 ) now look at the ' next smallest ' and the ' next biggest ' : 17 + 39 = 56 now we have proof that there is no middle term . we have 7 bunches of 56 . 7 ( 56 ) = 392 b"
Answer: b
Problem: the cost price of a radio is rs . 1800 and it was sold for rs . 1430 , find the loss % ?
Options: a ) 18 % , b ) 20.5 % , c ) 30 % , d ) 45 % , e ) 12 %
Rationale: "1800 - - - - 370 100 - - - - ? = > 20.5 % answer : b"
Answer: b
Problem: when working alone , painter w can paint a room in 2 hours , and working alone , painter x can paint the same room in z hours . when the two painters work together and independently , they can paint the room in 3 / 4 of an hour . what is the value of z ?
Options: a ) 3 / 4 , b ) 1 [ 1 / 5 ] , c ) 1 [ 2 / 5 ] , d ) 1 [ 3 / 4 ] , e ) 2
Rationale: "rate * time = work let painter w ' s rate be w and painter x ' s rate be x r * t = work w * 2 = 1 ( if the work done is same throughout the question then the work done can be taken as 1 ) = > w = 1 / 2 x * z = 1 = > x = 1 / z when they both work together then their rates get added up combined rate = ( w + x ) r * t = work ( w + x ) * 3 / 4 = 1 = > w + x = 4 / 3 = > 1 / 2 + 1 / z = 4 / 3 = > 1 / z = ( 8 - 3 ) / 6 = 5 / 6 = > z = 6 / 5 = 1 [ 1 / 5 ] answer b"
Answer: b