Cheukting/mathqa huggingface dataset:
Question (general): for any positive number x , the function [ x ] denotes the greatest integer less than or equal to x . for example , [ 1 ] = 1 , [ 1.367 ] = 1 and [ 1.996 ] = 1 . if k is a positive integer such that k ^ 2 is divisible by 45 and 80 , what is the units digit of k ^ 3 / 4000 ?
Options: a ) 0 , b ) 1 , c ) 0 , d ) 54 , e ) can not be determined
Rationale: "k = [ lcm of 80 and 45 ] * ( any integer ) however minimum value of k is sq . rt of 3 ^ 2 * 4 ^ 2 * 5 ^ 2 = 60 * any integer for value of k ( 60 ) * any integer unit value will be always zero . c"
Answer: c
Question (physics): a train passes a man standing on a platform in 8 seconds and also crosses the platform which is 276 metres long in 20 seconds . the length of the train ( in metres ) is :
Options: a ) 184 , b ) 176 , c ) 175 , d ) 96 , e ) none of these
Rationale: "explanation : let the length of train be l m . acc . to question ( 276 + l ) / 20 = l / 8 2208 + 8 l = 20 l l = 2208 / 12 = 184 m answer a"
Answer: a
Question (general): to be considered for “ movie of the year , ” a film must appear in at least 1 / 4 of the top - 10 - movies lists submitted by the cinematic academy ’ s 760 members . what is the smallest number of top - 10 lists a film can appear on and still be considered for “ movie of the year ” ?
Options: a ) 191 , b ) 190 , c ) 193 , d ) 212 , e ) 213
Rationale: "total movies submitted are 760 . as per question we need to take 1 / 4 of 760 to be considered for top 10 movies = 190 approximate the value we 190 . imo option b is the correct answer . . ."
Answer: b
Question (general): each child has 4 crayons and 14 apples . if there are 9 children , how many crayons are there in total ?
Options: a ) 22 , b ) 65 , c ) 12 , d ) 36 , e ) 10
Rationale: 4 * 9 = 36 . answer is d .
Answer: d
Question (physics): a man cycles round the boundary of a rectangular park at the rate of 12 kmph and completes one full round in 8 minutes . if the ratio between the length and breadth of the park be 3 : 2 , then its area is :
Options: a ) 1536 m 2
b ) 15360 m 2
c ) 153600 m 2
d ) 163600 m 2
e ) none of these
Rationale: perimeter = distance covered in 8 min = ( 12000 / 60 * 8 ) m = 1600 m let , length = 3 x meters and breadth = 2 x meters then , 2 ( 3 x + 2 x ) = 1600 or x = 160 therefore , length = 480 m and breadth = 320 m therefore , area = ( 480 * 320 ) m 2 = 153600 m 2 answer : c
Answer: c
Question (general): find the value of m 12519 x 9999 = m ?
Options: a ) 125177481 , b ) 353654655 , c ) 545463251 , d ) 725117481 , e ) 477899932
Rationale: "12519 x 9999 = 12519 x ( 10000 - 1 ) = 12519 x 10000 - 12519 x 1 = 125190000 - 12519 = 125177481 a"
Answer: a
Question (physics): a is twice as good a workman as b and they took 9 days together to do the work b alone can do it in .
Options: a ) 17 days , b ) 12 days , c ) 29 days , d ) 25 days , e ) 27 days
Rationale: "wc = 2 : 1 2 x + x = 1 / 9 x = 1 / 27 = > 27 days answer : e"
Answer: e
Question (general): find the value of ( 875 233 / 899 ) × 899
Options: a ) 786845 , b ) 786857 , c ) 786858 , d ) 786859 , e ) 786860
Rationale: "( 875 233 / 899 ) × 899 ( 786625 + 233 ) / 899 × 899 786858 / 899 × 899 786858 c"
Answer: c
Question (other): a certain store sold pens for $ 0.35 each and pencils for $ 0.25 each . if a customer purchased both pens and pencils from the store for a total of $ 2.00 , what total number of pens and pencils did the customer purchase ?
Options: a ) 6 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "answer : aalgebraically , the question looks like this : 2.5 = 0.35 x + 0.25 ythere are six possible numbers of pens that fit that requirement : 1 pen : $ 0.35 2 pens : $ 0.70 3 pens : $ 1.05 4 pens : $ 1.40 5 pens : $ 1.75 and 1 pencils for $ 0.25 each . that ' s 5 pens and 1 pencils for a total of 6 pens and pencils . choice ( a ) is correct ."
Answer: a
Question (physics): the length of the bridge , which a train 130 metres long and travelling at 108 km / hr can cross in 30 seconds , is :
Options: a ) 200 m , b ) 225 m , c ) 245 m , d ) 170 m , e ) 240 m
Rationale: "speed = [ 108 x 5 / 18 ] m / sec = 30 m / sec time = 10 sec let the length of bridge be x metres . then , ( 130 + x ) / 30 = 10 = > 130 + x = 300 = > x = 170 m . answer : d"
Answer: d
Question (general): what is the smallest number which , when increased by 9 , is divisible by 7 , 8 , and 24 ?
Options: a ) 143 , b ) 150 , c ) 159 , d ) 168 , e ) 177
Rationale: "lcm ( 7 , 8,24 ) = 24 x 7 = 168 so the least divisible number is 168 , and the number we are looking for is 168 - 9 = 159 . the answer is c ."
Answer: c
Question (general): what is the sum of all the prime numbers greater than 50 but less than 70 ?
Options: a ) 249 , b ) 248 , c ) 246 , d ) 240 , e ) 241
Rationale: "required sum = ( 53 + 59 + 61 + 67 ) = 240 note : 1 is not a prime number answer d"
Answer: d
Question (gain): the length of a rectangular floor is more than its breadth by 200 % . if rs . 150 is required to paint the floor at the rate of rs . 2 per sq m , then what would be the length of the floor ?
Options: a ) 65 , b ) 15 , c ) 18 , d ) 16 , e ) 14
Rationale: "let the length and the breadth of the floor be l m and b m respectively . l = b + 200 % of b = l + 2 b = 3 b area of the floor = 150 / 2 = 75 sq m l b = 75 i . e . , l * l / 3 = 75 l 2 = 225 = > l = 15 answer : b"
Answer: b
Question (physics): a car traveled from san diego to san francisco at an average speed of 66 miles per hour . if the journey back took twice as long , what was the average speed of the trip ?
Options: a ) 24 . , b ) 32 . , c ) 36 . , d ) 42 . , e ) 44 .
Rationale: "let the time taken be = x one way distance = 66 x total distance traveled = 2 * 66 x = 132 x total time taken = x + 2 x = 3 x average speed = 132 x / 3 x = 44 answer : e"
Answer: e
Question (physics): a cube of side 5.5 meter length is cut into small cubes of side 110 cm each . how many such small cubes can be obtained ?
Options: a ) 125 , b ) 127 , c ) 152 , d ) 140 , e ) 190
Rationale: "along one edge , the number of small cubes that can be cut = 550 / 110 = 5 along each edge 5 cubes can be cut . ( along length , breadth and height ) . total number of small cubes that can be cut = 5 * 5 * 5 = 125 answer : a"
Answer: a
Question (general): rates for having a manuscript typed at a certain typing service are $ 5 per page for the first time a page is typed and $ 2 per page each time a page is revised . if a certain manuscript has 100 pages , of which 40 were revised only once , 10 were revised twice , and the rest required no revisions , what was the total cost of having the manuscript typed ?
Options: a ) $ 430 , b ) $ 620 , c ) $ 650 , d ) $ 680 , e ) $ 770
Rationale: "for 100 - 40 - 10 = 50 pages only cost is 5 $ per page for the first time page is typed - 50 * 5 = 250 $ ; for 40 pages the cost is : first time 5 $ + 2 $ of the first revision - 40 * ( 5 + 2 ) = 280 $ ; for 10 pages the cost is : first time 5 $ + 2 $ of the first revision + 2 $ of the second revision - 10 ( 5 + 2 + 2 ) = 90 $ ; total : 250 + 280 + 90 = 620 $ . answer : b ."
Answer: b
Question (physics): some persons can do a piece of work in 32 days . two times the number of these people will do half of that work in ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: 32 / ( 2 * 2 ) = 8 days answer : e
Answer: e
Question (general): what is the units digit of 33 ^ 2 * 17 ^ 3 * 39 ^ 2 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "the units digit of 33 ^ 2 is the units digit of 3 * 3 = 9 which is 9 . the units digit of 17 ^ 3 is the units digit of 7 * 7 * 7 = 343 which is 3 . the units digit of 39 ^ 2 is the units digit of 9 * 9 = 81 which is 1 . the units digit of 9 * 3 * 1 = 27 is 7 . the answer is d ."
Answer: d
Question (general): a department of 10 people - 6 men and 4 women - needs to send a team of 5 to a conference . if they want to make sure that there are no more than 3 members of the team from any one gender , how many distinct groups are possible to send ?
Options: a ) 120 , b ) 150 , c ) 180 , d ) 210 , e ) 240
Rationale: they can make a team of 3 men and 2 women . the number of ways to do this is 6 c 3 * 4 c 2 = 20 * 6 = 120 they can make a team of 2 men and 3 women . the number of ways to do this is 6 c 2 * 4 c 3 = 15 * 4 = 60 the total number of distinct groups is 180 . the answer is c .
Answer: c
Question (gain): an error 3 % in excess is made while measuring the side of a square . what is the percentage of error in the calculated area of the square ?
Options: a ) 9.09 % , b ) 4.02 % , c ) 4 % , d ) 3 % , e ) 2 %
Rationale: "percentage error in calculated area = ( 3 + 3 + ( 3 ã — 3 ) / 100 ) % = 9.09 % answer : a"
Answer: a
Question (gain): uncle bruce is baking chocolate chip cookies . he has 40 ounces of dough ( with no chocolate ) and 20 ounces of chocolate . how much chocolate is left over if he uses all the dough but only wants the cookies to consist of 25 % chocolate ?
Options: a ) 8.5 , b ) 9.5 , c ) 10.5 , d ) 6.7 , e ) 6.5
Rationale: "first , you must find the total weight of the mixture given that 80 % of it will be dough . 75 % * total = 40 = > ( 75 / 100 ) total = 40 = > total = 4000 / 75 = > total = 53.33 oz , from there , you must find 25 % of the total 53.33 oz of the mixture . 25 % * total = > ( 25 / 100 ) ( 53.33 ) = 13.33 oz choclate used , not forgetting that the question asks how much chocolate is left over we must subtract the chocolate used from the initial chocolate . 20 - 13.3 = 6.7 oz chocolate left over . answer : d"
Answer: d
Question (physics): two pipes a and b can separately fill a tank in 10 and 15 minutes respectively . a third pipe c can drain off 20 liters of water per minute . if all the pipes are opened , the tank can be filled in 15 minutes . what is the capacity of the tank ?
Options: a ) 150 liters , b ) 540 liters , c ) 200 liters , d ) 560 liters , e ) 580 liters
Rationale: "1 / 10 + 1 / 15 - 1 / x = 1 / 15 x = 10 10 * 20 = 200 answer : c"
Answer: c
Question (gain): a and b started a business investing rs . 90,000 and rs 25,000 respectively . in what ratio the profit earned after 2 years be divided between a and b respectively ?
Options: a ) 9 : 2 , b ) 3 : 2 , c ) 18 : 20 , d ) 18 : 5 , e ) 17 : 4
Rationale: "a : b = 90000 : 25000 = 90 : 25 = 18 : 5 answer : d"
Answer: d
Question (gain): we invested a total of $ 1,000 . we invested one part of the money at 3 % and the rest of the money at 4 % . the total investment with interest at the end of the year was $ 1 , 036.70 . how much money did we invest at 3 % ?
Options: a ) $ 300 , b ) $ 330 , c ) $ 360 , d ) $ 390 , e ) $ 420
Rationale: "let x be the money invested at 3 % . 1.03 x + 1.04 ( 1000 - x ) = 1036.70 . 0.01 x = 1040 - 1036.70 . 0.01 x = 3.30 . x = 330 . the answer is b ."
Answer: b
Question (probability): how many positive integers less than 400 can be formed using the numbers 1 , 2 , 3 and 5 for the digits ?
Options: a ) 48 , b ) 52 , c ) 66 , d ) 84 , e ) 68
Rationale: "notice that we can find the number of 2 and 3 digit numbers by just assuming the first digit can also be zero : 0 1 1 1 2 2 2 3 3 3 5 5 number of possibilities = 4 * 4 * 4 = 64 . then , just add up the number of 1 digits numbers = 4 , so total is 64 + 4 = 68 . answer : e"
Answer: e
Question (other): forks , spoons , and knives in drawer are in the ratio of 4 : 4 : 3 . if there are 16 forks , the number of knives in the drawer is :
Options: a ) 8 , b ) 4 , c ) 12 , d ) 16 , e ) 14
Rationale: explanation : let forks = 4 x , spoons = 4 x & knives = 3 x . now , 4 x = 16 hence x = 4 . number of knives = 3 x = 12 . answer : c
Answer: c
Question (geometry): what is the smallest positive integer x such that 450 x is the cube of a positive integer ?
Options: a ) 2 , b ) 15 , c ) 30 , d ) 60 , e ) 120
Rationale: "450 = 2 x 3 ^ 2 x 5 ^ 2 now we need two 2 s , one 3 and one 5 to make it perfect cube . so x = 2 ^ 2 x 3 x 5 = 60 . answer is c ."
Answer: c
Question (gain): in an election between two candidates , one got 55 % of the total valid votes , 20 % of the votes were invalid . if the total number of votes was 6000 , the number of valid votes that the other candidate got , was :
Options: a ) 2800 , b ) 2700 , c ) 2160 , d ) 2200 , e ) 2300
Rationale: "c number of valid votes = 80 % of 6000 = 4800 . valid votes polled by other candidate = 45 % of 4800 = ( 45 / 100 x 4800 ) = 2160 ."
Answer: c
Question (physics): 10 : 4 seconds : : ? : 6 minutes
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: "10 * 6 = 4 * x x = 15 answer : b"
Answer: b
Question (physics): a train passes a platform in 36 seconds . the same train passes a man standing on the platform in 20 seconds . if the speed of the train is 54 km / hr , the length of the platform is
Options: a ) 240 , b ) 250 , c ) 260 , d ) 230 , e ) 220
Rationale: "speed of the train = 54 km / hr = ( 54 × 10 ) / 36 m / s = 15 m / s length of the train = speed × time taken to cross the man = 15 × 20 = 300 m let the length of the platform = l time taken to cross the platform = ( 300 + l ) / 15 = > ( 300 + l ) / 15 = 36 = > 300 + l = 15 × 36 = 540 = > l = 540 - 300 = 240 meter answer is a ."
Answer: a
Question (gain): rs . 6000 is lent out in two parts . one part is lent at 2 % p . a simple interest and the other is lent at 10 % p . a simple interest . the total interest at the end of one year was rs . 450 . find the ratio of the amounts lent at the lower rate and higher rate of interest ?
Options: a ) 5 : 11 , b ) 5 : 6 , c ) 5 : 2 , d ) 5 : 8 , e ) 5 : 2
Rationale: "let the amount lent at 2 % be rs . x amount lent at 10 % is rs . ( 6000 - x ) total interest for one year on the two sums lent = 2 / 100 x + 10 / 100 ( 6000 - x ) = 600 - 3 x / 100 = > 600 - 3 / 100 x = 450 = > x = 1875 amount lent at 10 % = 4125 required ratio = 5 : 11 answer : a"
Answer: a
Question (probability): if two dice are thrown together , the probability of getting a doublet on the dice is
Options: a ) 1 / 6 , b ) 1 / 5 , c ) 1 / 4 , d ) 1 / 3 , e ) 1 / 2
Rationale: "the number of exhaustive outcomes is 36 . let e be the event of getting doublet on the dies is 6 / 36 = 1 / 6 p ( e ) = 1 / 6 . a )"
Answer: a
Question (other): how many different positive integers are factors of 64 ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "8 × 8 = 4 ^ 2 × 2 ^ 2 so total factors = ( 3 + 1 ) ( 3 + 1 ) = 16 answer : d"
Answer: d
Question (geometry): the ratio of the volumes of two cubes is 343 : 512 . what is the ratio of their total surface areas ?
Options: a ) 12 : 24 , b ) 8 : 16 , c ) 45 : 25 , d ) 18 : 56 , e ) 49 : 64
Rationale: "ratio of the sides = â ³ â ˆ š 343 : â ³ â ˆ š 512 = 7 : 8 ratio of surface areas = 49 : 64 answer : e"
Answer: e
Question (gain): a 6 % stock yields 9 % . the market value of the stock is :
Options: a ) rs 66.55 , b ) rs 68.55 , c ) rs 69.55 , d ) rs 65.55 , e ) rs 66.66
Rationale: "explanation : for an income of rs . 9 , investment = rs . 100 . for an income of rs 6 , investment = rs . 100 / 9 x 6 = rs 66.66 market value of rs . 100 stock = rs . 66.66 answer is e"
Answer: e
Question (general): jean drew a gumball at random from a jar of pink and blue gumballs . since the gumball she selected was blue and she wanted a pink one , she replaced it and drew another . the second gumball also happened to be blue and she replaced it as well . if the probability of her drawing the two blue gumballs was 25 / 36 , what is the probability that the next one she draws will be pink ?
Options: a ) 1 / 6 , b ) 4 / 7 , c ) 3 / 7 , d ) 16 / 49 , e ) 40 / 49
Rationale: "the probability of drawing a pink gumball both times is the same . the probability that she drew two blue gumballs = 25 / 36 = ( 5 / 6 ) * ( 5 / 6 ) therefore probability that the next one she draws is pink = 1 / 6 option ( a )"
Answer: a
Question (general): if each participant of a chess tournament plays exactly one game with each of the remaining participants , then 253 games will be played during the tournament . what is the number of participants ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: "let n be the number of participants . the number of games is nc 2 = n * ( n - 1 ) / 2 = 253 n * ( n - 1 ) = 506 = 23 * 22 ( trial and error ) the answer is c ."
Answer: c
Question (physics): it takes 10 days for digging a trench of 100 m long , 50 m broad and 10 m deep . what length of trench , 25 m broad and 15 m deep can be dug in 30 days ?
Options: a ) 400 m , b ) 200 m , c ) 100 m , d ) 89 m , e ) 79 m
Rationale: more days , more length ( direct ) less breadth , more length ( indirect ) more depth , less length ( indirect days 10 : 30 ; breadth 25 : 50 ; : : 100 : x depth 15 : 10 ; : . 10 * 25 * 15 * x = 30 * 50 * 10 * 100 x = ( 30 * 50 * 10 * 100 ) / 10 * 25 * 15 = 400 so the required length = 400 m answer : a
Answer: a
Question (physics): if 20 men can build a water fountain 56 metres long in 3 days , what length of a similar water fountain can be built by 35 men in 3 days ?
Options: a ) 40 m , b ) 64 m , c ) 77 m , d ) 89 m , e ) 98 m
Rationale: "explanation : let the required length be x metres more men , more length built ( direct proportion ) less days , less length built ( direct proportion ) men 20 : 35 days 3 : 3 : : 56 : x therefore ( 20 x 3 x x ) = ( 35 x 3 x 56 ) x = ( 35 x 3 x 56 ) / 60 = 98 hence , the required length is 98 m . answer : e"
Answer: e
Question (general): p has $ 63 more than what q and r together would have had if both b and c had 1 / 9 of what p has . how much does p have ?
Options: a ) $ 69 , b ) $ 72 , c ) $ 75 , d ) $ 78 , e ) $ 81
Rationale: p = ( 2 / 9 ) * p + 63 ( 7 / 9 ) * p = 63 p = 81 the answer is e .
Answer: e
Question (physics): a train running at the speed of 110 km / hr crosses a pole in 9 sec . what is the length of the train ?
Options: a ) 298 m , b ) 275 m , c ) 208 m , d ) 988 m , e ) 299 m
Rationale: "speed = 110 * 5 / 18 = 275 / 9 m / sec length of the train = speed * time = 275 / 9 * 9 = 275 m answer : b"
Answer: b
Question (general): if 2 ^ y = 4 ^ ( 5 x + 3 ) and 3 ^ ( x - 7 ) = 9 ^ y , what is the value of x + y ?
Options: a ) - 10 , b ) - 5 , c ) - 4 , d ) 3 , e ) 7
Rationale: 2 ^ y = 4 ^ ( 5 x + 3 ) 2 ^ y = 2 ^ 2 ( 5 x + 3 ) y = 10 x + 6 . . . . . . . . . . . 1 3 ^ ( x - 7 ) = 9 ^ y 3 ^ ( x - 7 ) = 3 ^ 2 y x - 7 = 2 y . . . . . . . . . . . . . 2 put value of y = 10 x + 6 in eq 2 x - 7 = 2 ( 10 x + 6 ) x - 7 = 20 x + 12 19 x = - 19 x = - 1 therefore , y = - 10 + 6 y = - 4 x + y = - 1 - 4 = - 5 answer : b
Answer: b
Question (general): a jogger running at 9 km / hr along side a railway track is 240 m ahead of the engine of a 140 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?
Options: a ) 28 sec , b ) 16 sec , c ) 38 sec , d ) 18 sec , e ) 17 sec
Rationale: "speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 240 + 140 = 380 m . time taken = 380 / 10 = 38 sec . answer : c"
Answer: c
Question (other): of the 75 house in a development , 50 have a two - car garage , 40 have an in - the - ground swimming pool , and 35 have both a two - car garage and an in - the - ground swimming pool . how many houses in the development have neither a two - car garage nor an in - the - ground swimming pool ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: "neither car nor garage = total - garage - ( swim - common ) = 75 - 50 - ( 40 - 35 ) = 75 - 55 = 20 answer c"
Answer: c
Question (general): if the price of a certain computer increased 30 percent from a dollars to 351 dollars , then 2 a =
Options: a ) 540 , b ) 570 , c ) 619 , d ) 649 , e ) 700
Rationale: "before price increase price = a after 30 % price increase price = a + ( 30 / 100 ) * a = 1.3 a = 351 ( given ) i . e . a = 351 / 1.3 = $ 270 i . e . 2 a = 2 * 270 = 540 answer : option a"
Answer: a
Question (other): in a certain large company , the ratio of college graduates with a graduate degree to non - college graduates is 1 : 8 , and ratio of college graduates without a graduate degree to non - college graduates is 2 : 3 . if one picks a random college graduate at this large company , what is the probability w this college graduate has a graduate degree ?
Options: a ) 1 / 11 , b ) 1 / 12 , c ) 1 / 13 , d ) 3 / 19 , e ) 3 / 43
Rationale: "in believe the answer is d . please see below for explanation . 0 ) we are told the following ratios cgd - college graduate with degree ncg - non college graduate cgn - college graduate no degree cgd ncg cgn 1 8 3 2 in order to make cgd and cgn comparable we need to find the least common multiple of 8 and 3 and that is 24 multiplying the first ratio by 3 and the second ratio by 8 we get cgd ncg cgn 3 24 16 if one picks a random college graduate at this large company , what is the probability this college graduate has a graduate degree ? nr of cgd = 3 nr of cg = 3 + 16 = 19 probability w of cgd / ( cg ) - > 3 / 19 answer d"
Answer: d
Question (gain): what profit percent is made by selling an article at a certain price , if by selling at 2 / 3 rd of that price , there would be a loss of 25 % ?
Options: a ) 20 % , b ) 26 % , c ) 42 % , d ) 27 % , e ) 12.5 %
Rationale: "sp 2 = 2 / 3 sp 1 cp = 100 sp 2 = 75 2 / 3 sp 1 = 75 sp 1 = 112.50 100 - - - 12.5 = > 12.5 % answer : e"
Answer: e
Question (general): how many 5 - digit numbers are there , if the two leftmost digits are even , the other digits are odd and the digit 2 can not appear more than once in the number .
Options: a ) 2200 , b ) 2295 , c ) 2375 , d ) 2380 , e ) 2385
Rationale: n = ( 4 * 5 - 1 ) * 5 * 5 * 5 = 2375 where 4 cases of first digit { 2,4 , 6,8 } 5 cases of second digit { 0 , 2,4 , 6,8 } 1 case of 22 for two leftmost digit 5 cases of third digit { 1 , 3,5 , 7,9 } 5 cases of fourth digit { 1 , 3,5 , 7,9 } 5 cases of fifth digit { 1 , 3,5 , 7,9 } c
Answer: c
Question (general): a bucket full of nuts was discovered by the crow living in the basement . the crow eats a sixth of the total number of nuts in 4 hours . how many hours i total will it take the crow to finish a quarter of the nuts ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "in one hour , the crow eats 1 / 24 of the nuts . ( 1 / 4 ) / ( 1 / 24 ) = 6 hours the answer is a ."
Answer: a
Question (general): alok ordered 16 chapatis , 5 plates of rice , 7 plates of mixed vegetable and 6 ice - cream cups . the cost of each chapati is rs . 6 , that of each plate of rice is rs . 45 and that of mixed vegetable is rs . 70 . the amount that alok paid the cashier was rs . 1081 . find the cost of each ice - cream cup ?
Options: a ) 25 , b ) 66 , c ) 77 , d ) 99 , e ) 45
Rationale: "let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 1081 96 + 225 + 490 + 6 x = 1081 6 x = 270 = > x = 45 . answer : e"
Answer: e
Question (gain): selling an kite for rs . 30 , a shop keeper gains 40 % . during a clearance sale , the shopkeeper allows a discount of 10 % on the marked price . his gain percent during the sale is ?
Options: a ) 8 % , b ) 10 % , c ) 11 % , d ) 15 % , e ) 26 %
Rationale: "explanation : marked price = rs . 30 c . p . = 100 / 140 * 30 = rs . 21.42 sale price = 90 % of rs . 30 = rs . 27 required gain % = 5.57 / 21.42 * 100 = 26 % . answer : e"
Answer: e
Question (other): how many factors of 30 are odd numbers greater than 1 ?
Options: a ) 3 , b ) 3 , c ) 5 , d ) 6 , e ) 7
Rationale: "prime factors of 30 are 2 ^ 1,3 ^ 1,5 ^ 1 total divisors = ( power if a prime factor + 1 ) total no . of odd factors ( 3,5 , ) = ( 1 + 1 ) ( 1 + 1 ) = 4 since we need odd divisors other than 1 = > 4 - 1 = 3 odd divisors b is the answer"
Answer: b