Cheukting/mathqa huggingface dataset:
Question (general): a = { 0 , 1 , - 3 , 6 , - 8 } b = { - 1 , 2 , - 4 , 7 } if a is a number that is randomly selected from set a , and b is a number that is randomly selected from set b , what is the probability that ab > 0 ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 2 / 5 , d ) 4 / 9 , e ) 1 / 2
Rationale: for the product of 2 numbers to be positive either both of them must be positive or both of them must be negative : p ( positive , positive ) = 2 / 5 * 2 / 4 = 4 / 20 ; p ( negative , negative ) = 2 / 5 * 2 / 4 = 4 / 20 . p = 4 / 20 + 4 / 20 = 8 / 20 = 2 / 5 . answer : c .
Answer: c
Question (physics): two trains 140 m and 210 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
Options: a ) 12.6 sec , b ) 10.1 sec , c ) 10.6 sec , d ) 10.8 sec , e ) 10.2 sec
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 140 + 210 = 350 m . required time = 350 * 9 / 250 = 12.6 sec . answer : a"
Answer: a
Question (gain): john and david can finish a job together in 1 hours . if john can do the job by himself in 2 hours , what percent of the job does david do ?
Options: a ) 40 % , b ) 45 % , c ) 50 % , d ) 55 % , e ) 60 %
Rationale: you can also plug in numbers . for example , bob and alice work at a donut factory and make 10 donuts which is the job ( i picked this as a smart number ) . john on his own works 10 / 2 = 5 donuts per hour . john and david work 10 / 1 = 10 donuts per hour so david works 5 donuts / hour to find out the percentage , david works 5 donuts / hr x 1 hours = 5 donuts per hour . therefore 5 donuts / 10 donuts = 1 / 2 = 50 % answer : c
Answer: c
Question (general): for the positive integers x , x + 2 , x + 4 , x + 7 , and x + 17 , the mean is how much greater than the median ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 4 , e ) 7
Rationale: "mean = ( x + x + 2 + x + 4 + x + 7 + x + 17 ) / 5 = ( 5 x + 30 ) / 5 = x + 6 median = x + 4 thus mean - median = x + 6 - ( x + 4 ) = 2 answer = c"
Answer: c
Question (physics): a man rows his boat 84 km downstream and 60 km upstream , taking 4 hours each time . find the speed of the stream ?
Options: a ) 76 kmph , b ) 6 kmph , c ) 14 kmph , d ) 8 kmph , e ) 3 kmph
Rationale: "speed downstream = d / t = 84 / ( 4 ) = 21 kmph speed upstream = d / t = 60 / ( 4 ) = 15 kmph the speed of the stream = ( 21 - 15 ) / 2 = 3 kmph answer : e"
Answer: e
Question (geometry): an iron cube of side 10 cm is hammered into a rectangular sheet of thickness 0.5 cm . if the sides of the sheet are in the ratio 1 : 5 , the sides are :
Options: a ) 10 cm 20 cm
b ) 2 cm 10 cm
c ) 100 cm 20 cm
d ) 30 cm 100 cm
e ) none
Rationale: sol . let the sides of the sheet be x and 5 x . then , ⇒ x * 5 x * 1 / 2 = 10 * 10 * 10 ⇒ 5 x ² = 2000 ⇒ x ² = 400 ⇒ x = 20 . ∴ the sides are 20 cm and 100 cm . answer a
Answer: a
Question (physics): a train is moving at a speed of 132 km / hour . if the length of the train is 110 meters , how long will it take to cross a railway platform 165 meters long .
Options: a ) 7 second , b ) 7.5 second , c ) 8 second , d ) 8.5 second , e ) none of these
Rationale: explanation : as we need to calculate answer in seconds , so first convert speed into meter / sec . we know 1 km / hr = 1 * ( 5 / 18 ) m / sec so , speed = 132 * ( 5 / 18 ) = 110 / 3 m / sec distance need to be covered in passing the platform = length of train + length of platform = 110 + 165 = 275 meters time = distance / speed = > time = 275 ∗ 3 / 110 = 15 / 2 = 7.5 seconds option b
Answer: b
Question (physics): 10 machines , each working at the same constant rate , together can complete a certain job in 12 days . how many additional machines , each working at the same constant rate , will be needed to complete the job in 8 days ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 8
Rationale: "another solution which is faster is since each machine works at a constant rate . the time needs to bought down from 12 to 8 . so the new time is 2 / 3 of the original time . thus to achieve this we need the rate to be 3 / 2 of original . so 3 / 2 * 10 = 15 so we need 15 - 10 = 5 more machines . answer : d"
Answer: d
Question (probability): given a bag with 2 red balls and 3 yellow balls , you randomly select one of them , in order . if the second ball you take is yellow , what is the probability that the first one was also yellow ?
Options: a ) 1 / 2 , b ) 1 / 5 , c ) 3 / 4 , d ) 1 / 3 , e ) 3 / 5
Rationale: this is a conditional probability question . basically we are told that out of 2 balls picked one is yellow and are asked to find the probability of the other one also to be yellow . so , possible options for this other ball would be : w , w , b , b ( as one yellow is already picked ) so the probability for that ball to be yellow too is 2 / 4 = 1 / 2 . option a
Answer: a
Question (general): how many 4 - digit positive integers are multiple of each integer from 1 to 10
Options: a ) 1520 , b ) 2520 , c ) 3520 , d ) 5140 , e ) 7660
Rationale: "least no which could be divisible by integers [ 1,2 , 3,4 , 5,6 , 7,8 , 9,10 ] is the lcm of the said integers . lcm [ 1,2 , 3,4 , 5,6 , 7,8 , 9,10 ] = 2520 no the nos which are divisible by 2520 will be divisible by [ 1 , 2,3 , 4,5 , 6,7 , 8,9 ] there are 3 values possible between 1000 to 9999 they are 2520 x 1 = 2520 2520 x 2 = 5040 2520 x 3 = 7560 answer : b"
Answer: b
Question (physics): a water tank is one - fifth full . pipe a can fill a tank in 10 minutes and pipe b can empty it in 6 minutes . if both the pipes are open , how many minutes will it take to empty or fill the tank completely ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: the combined rate of filling / emptying the tank = 1 / 10 - 1 / 6 = - 1 / 15 since the rate is negative , the tank will be emptied . a full tank would take 15 minutes to empty . since the tank is only one - fifth full , the time is ( 1 / 5 ) * 15 = 3 minutes the answer is a .
Answer: a
Question (general): jar y has 10 % more marbles than jar x . what percent of marbles from jar y need to be moved into x so that both jars have equal marbles
Options: a ) 4.54 % , b ) 9.09 % , c ) 10 % , d ) 11 % , e ) 12.25 %
Rationale: no ; the choices will be approximated only when gmat question explicitly mentions that ; here the answer is very close 4.54 , not 5 . jar y has 10 % more marbles than x y = 1.1 x if k marbles are taken out of y . the remaining marbles in jar y = 1.1 x - k if k marbles are added to x . the new marbles ' count in jar x = x + k and we know they are equal ; x + k = 1.1 x - k 2 k = 0.1 x k = 0.05 x the marbles taken out of y = 0.05 x question is : 0.05 x is what percent of marbles that was originally there in y i . e . 1.1 x 0.05 x 1.1 x ∗ 1000.05 x 1.1 x ∗ 100 0.05 x 1.1 x ∗ 1000.05 x 1.1 x ∗ 100 5011 = 4.54 ¯ ≈ 4.545011 = 4.54 ¯ ≈ 4.54 answer : a
Answer: a
Question (probability): a bag contains 3 blue and 5 white marbles . one by one , marbles are drawn out randomly until only two are left in the bag . what is the probability that out of the two , one is white and one is blue ?
Options: a ) 15 / 56 , b ) 41 / 56 , c ) 13 / 28 , d ) 15 / 28 , e ) 5 / 14
Rationale: "the required probability = probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls . ways to select 6 out of total 8 = 8 c 6 ways to select 4 out of 5 white balls = 5 c 4 ways to select 2 out of 3 blue balls = 3 c 2 thus the required probability = ( 5 c 4 * 3 c 2 ) / 8 c 6 = 15 / 28 . d is thus the correct answer ."
Answer: d
Question (physics): a woman complete a journey in 10 hours . she travels first half of the journey at the rate of 21 km / hr and second half at the rate of 24 km / hr . find the total journey in km .
Options: a ) 334 km . , b ) 216 km . , c ) 314 km . , d ) 224 km . , e ) 544 km .
Rationale: "d 224 km . 0.5 x / 21 + 0.5 x / 24 = 10 - - > x / 21 + x / 24 = 20 - - > 15 x = 168 x 20 - - > x = ( 168 x 20 ) / 15 = 224 km ."
Answer: d
Question (physics): the speed of a train is 80 kmph . what is the distance covered by it in 6 minutes ?
Options: a ) 15 kmph , b ) 11 kmph , c ) 18 kmph , d ) 8 kmph , e ) 12 kmph
Rationale: "80 * 6 / 60 = 8 kmph answer : d"
Answer: d
Question (other): if 50 % of the 880 students at a certain college are enrolled in biology classes , how many students at the college are not enrolled in a biology class ?
Options: a ) 560 , b ) 540 , c ) 520 , d ) 440 , e ) 500
Rationale: we know 50 % people study biology , therefore the no of people not studying = 100 - 50 = 50 % > therefore the people not studying biology out of a total 880 people are = 50 % of 880 > ( 50 / 100 ) * 880 = 440 people d
Answer: d
Question (gain): the simple interest and the true discount on a certain sum for a given time and at a given rate are rs . 85 and rs . 70 respectively . the sum is :
Options: a ) 1360 , b ) 1450 , c ) 1600 , d ) 1800 , e ) none
Rationale: "sol . sum = s . i . * t . d . / ( s . i ) - ( t . d . ) = 85 * 70 / ( 85 - 70 ) = rs . 396.7 . answer e"
Answer: e
Question (general): sum of two numbers is 10 . two times of the first exceeds by 5 from the three times of the other . then the numbers will be ?
Options: a ) a ) 7 , b ) b ) 9 , c ) c ) 11 , d ) d ) 13 , e ) e ) 15
Rationale: "explanation : x + y = 10 2 x – 3 y = 5 x = 7 y = 3 a )"
Answer: a
Question (physics): ram covers a part of the journey at 20 kmph and the balance at 70 kmph taking total of 8 hours to cover the distance of 400 km . how many hours has been driving at 20 kmph ?
Options: a ) 3.2 hr , b ) 3.4 hr , c ) 3.6 hr , d ) 3.8 hr , e ) 4.2 hr
Rationale: let see d / t = v then x / 20 + ( 400 - x ) / 70 = 8 x = 64 kmh t = 64 / 20 = 3.2 hr answer : a
Answer: a
Question (gain): a shopkeeper sells 10 % of his stock at 20 % profit ans sells the remaining at a loss of 5 % . he incurred an overall loss of rs . 400 . find the total worth of the stock ?
Options: a ) 20000 , b ) 16000 , c ) 18000 , d ) 17000 , e ) 15000
Rationale: "let the total worth of the stock be rs . x . the sp of 20 % of the stock = 1 / 10 * x * 6 / 5 = 6 x / 50 the sp of 80 % of the stock = 9 / 10 * x * 0.95 = 171 x / 200 total sp = 24 x / 200 + 171 / 200 = 49 x / 50 overall loss = x - 195 / 20050 = 5 x / 200 5 x / 200 = 400 = > x = 16000 answer : b"
Answer: b
Question (physics): in one hour , a boat goes 13 km along the stream and 9 km against the stream . the speed of the boat in still water ( in km / hr ) is :
Options: a ) 3 , b ) 5 , c ) 11 , d ) 9 , e ) 10
Rationale: "solution speed in still water = 1 / 2 ( 13 + 9 ) kmph . = 11 kmph . answer c"
Answer: c
Question (physics): if 5 spiders make 2 webs in 8 days , then how many days are needed for 1 spider to make 1 web ?
Options: a ) 10 , b ) 15 , c ) 30 , d ) 20 , e ) 16
Rationale: "explanation : let , 1 spider make 1 web in x days . more spiders , less days ( indirect proportion ) more webs , more days ( direct proportion ) hence we can write as ( spiders ) 5 : 1 ( webs ) 1 : 8 } : : x : 2 â ‡ ’ 5 ã — 1 ã — 8 = 1 ã — 2 ã — x â ‡ ’ x = 20 answer : option d"
Answer: d
Question (general): an employee ’ s annual salary was increased $ 5,000 . if her new annual salary now equals $ 25000 what was the percent increase ?
Options: a ) 15 % , b ) 80 % , c ) 20 % , d ) 22 % , e ) 24 %
Rationale: "new annual salary = $ 25000 salary increase = $ 5000 . original salary = $ 25000 - $ 5,000 . = $ 20,000 % increase = ( $ 15,000 / $ 75,000 ) * 100 = 80 % hence b ."
Answer: b
Question (general): the price of a cycle is reduced by 25 per cent . the new price is reduced by a further 50 per cent . the two reductions together are equal to a single reduction of
Options: a ) 45 % , b ) 62.5 % , c ) 35 % , d ) 32.5 % , e ) 30 %
Rationale: "price = p initially price reduced by 25 % which means new price is 3 / 4 p now on this new price further 50 percent is reduced which means the new price is merely 50 percent of 3 / 4 p = = > ( 3 / 4 ) x ( 1 / 2 ) p = 3 / 8 p is the new price after both deduction which is 37.5 percent of the original value p . this implies this entire series of deduction is worth having discounted 62.5 % of p . so answer is b = 62.5 %"
Answer: b
Question (other): in a school 10 % of the boys are same in number as 1 / 2 th of the girls . what is the ratio of boys to the girls in the school ?
Options: a ) 5 : 1 , b ) 2 : 3 , c ) 1 : 4 , d ) 3 : 7 , e ) 2 : 5
Rationale: "10 % of b = 1 / 2 g 10 b / 100 = g / 2 b = 5 g / 1 b / g = 5 / 1 b : g = 5 : 1 answer is a"
Answer: a
Question (physics): audrey 4 hours to complete a certain job . ferris can do the same job in 3 hours . audrey and ferris decided to collaborate on the job , working at their respective rates . while audrey worked continuously , ferris took 6 breaks of equal length . if the two completed the job together in 2 hours , how many minutes long was each of ferris ’ breaks ?
Options: a ) 2 , b ) 5 , c ) 15 , d ) 20 , e ) 25
Rationale: audery and ferris collective work rate : 1 / 4 + 1 / 3 = 7 / 12 collective work time = 12 / 7 = 1.7 hrs job was actually done in = 2 ( includes breaks ) breaks = actual time taken - collective work time = 2 - 1.7 = . 3 hrs = 1 / 2 so ferrais took 6 breaks = . 3 / 6 = . 06 hrs = 5 m so answer is b ) 10 mins
Answer: b
Question (gain): by selling an article at rs . 250 , a profit of 25 % is made . find its cost price ?
Options: a ) s . 486 , b ) s . 455 , c ) s . 220 , d ) s . 480 , e ) s . 200
Rationale: "sp = 250 cp = ( sp ) * [ 100 / ( 100 + p ) ] = 250 * [ 100 / ( 100 + 25 ) ] = 250 * [ 100 / 125 ] = rs . 200 answer : e"
Answer: e
Question (physics): a can do a work in 6 days , b can do a work in 8 days and c can do it in 12 days . b left work after 6 days . for how many number of days should a and c should work together to complete the remaining work ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "b work 1 / 8 * 6 = 3 / 4 remaining work = 1 - 3 / 4 = 1 / 4 a and c work together = 1 / 6 + 1 / 12 = 3 / 12 = 1 / 4 take reciprocial 4 * remaining work = 4 * 1 / 4 = 1 answer : a"
Answer: a
Question (gain): 4 guys buy same cellphones cost them 250 each . two guy have 25 % of for his first cellphone . what is the total cost all of them pay to seller .
Options: a ) 1000 , b ) 850 , c ) 875 , d ) 775 , e ) 750
Rationale: solution : c . 250 * 2 = 500 for 2 guy without discount , for other 2 ( 250 * 2 ) with 25 % is 375 . total cost 500 + 375 = 875
Answer: c
Question (general): if x and y are integers and | x - y | = 11 , what is the minimum possible value of xy ?
Options: a ) - 10 , b ) - 18 , c ) - 28 , d ) - 30 , e ) - 32
Rationale: sometimes the answer choices to a given question provide a big ' hint ' as to how you can go about solving it . this prompt can also be solved without any complex math ideas - you just need to do a bit of ' brute force ' math and you ' ll have the answer relatively quickly . we ' re told that x and y are integers and | x - y | = 11 . we ' re asked for the minimum possible value of ( x ) ( y ) . since all of the answer choices are negative , this tells us that one of the two variables must be negative ( and the other must be positive ) , so we should restrict our work to those options . if . . . x = 10 , y = - 1 , then xy = - 10 x = 9 , y = - 2 , then xy = - 18 x = 8 , y = - 3 , then xy = - 24 x = 7 , y = - 4 , then xy = - 28 x = 6 , y = - 5 , then xy = - 30 x = 5 , y = - 6 , then xy = - 30 x = 4 , y = - 7 , then xy = - 28 from this , we can conclude the xy will start to get bigger as x continues to decrease down to 1 , so there ' s no need to do any additional work . final answer : d
Answer: d
Question (physics): 15 : 5 seconds : : ? : 10 minutes
Options: a ) 10 , b ) 15 , c ) 30 , d ) 25 , e ) 30
Rationale: "15 * 10 = 5 * x x = 30 answer : c"
Answer: c
Question (physics): a train 75 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 ) 35 kmph , b ) 40 kmph , c ) 45 kmph , d ) 50 kmph , e ) 55 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 75 / [ ( x + 5 ) * 5 / 18 ] = 6 30 ( x + 5 ) = 1350 x = 40 kmph answer is b"
Answer: b
Question (physics): two trains , each 100 m long , moving in opposite directions , cross other in 5 sec . if one is moving twice as fast the other , then the speed of the faster train is ?
Options: a ) 26 km / hr , b ) 17 km / hr , c ) 60 km / hr , d ) 42 km / hr , e ) 46 km / hr
Rationale: "let the speed of the slower train be x m / sec . then , speed of the train = 2 x m / sec . relative speed = ( x + 2 x ) = 3 x m / sec . ( 100 + 100 ) / 5 = 3 x = > x = 20 / 3 . so , speed of the faster train = 40 / 3 = 40 / 3 * 18 / 5 = 42 km / hr . answer : d"
Answer: d
Question (general): shreehari has 125 pencils . there are 25 students are studying in his class . he would like to give each student the same amount of pencils , how much should he give to each student ?
Options: a ) 12 , b ) 7 , c ) 5 , d ) 15 , e ) 6
Rationale: 125 / 25 = 5 the answer is c .
Answer: c
Question (general): what is the value of 3 x ^ 2 − 1.8 x + 0.5 for x = 0.6 ?
Options: a ) − 0.3 , b ) 0 , c ) 0.3 , d ) 1.08 , e ) 0.5
Rationale: "3 x ^ 2 - 1.8 x + 0.5 for x = 0.6 = 3 ( 0.6 * 0.6 ) - 3 * 0.6 * ( 0.6 ) + 0.5 = 0 + 0.5 = 0.5 answer : e"
Answer: e
Question (physics): the consumption of diesel per hour of a bus varies directly as square of its speed . when the bus is travelling at 60 kmph its consumption is 1 litre per hour . if each litre costs $ 60 and other expenses per hous is $ 60 , then what would be the minimum expenditure required to cover a distance of 600 km ?
Options: a ) 120 , b ) 1250 , c ) 1200 , d ) 1100 , e ) 1150
Rationale: "60 kmph consumption is 1 lt / hr so 600 km will take 10 hrs and the consumption is 10 lt for entire distance . 1 lt costs $ 60 so 10 lt costs $ 600 extra expenses for 1 hr - $ 60 10 hrs - $ 600 total expense - $ 600 + $ 600 = $ 1200 answer : c"
Answer: c
Question (gain): there were two candidates in an election . winner candidate received 62 % of votes and won the election by 288 votes . find the number of votes casted to the winning candidate ?
Options: a ) 456 , b ) 744 , c ) 912 , d ) 1200 , e ) 1400
Rationale: w = 62 % l = 38 % 62 % - 38 % = 24 % 24 % - - - - - - - - 288 62 % - - - - - - - - ? = > 744 answer : b
Answer: b
Question (general): there are 17 teams in the hockey league , and each team faces all the other teams 10 times each . how many games are played in the season ?
Options: a ) 980 , b ) 1150 , c ) 1360 , d ) 1540 , e ) 1720
Rationale: "the number of ways to choose two teams is 17 c 2 = 17 * 16 / 2 = 136 the total number of games in the season is 10 * 136 = 1360 . the answer is c ."
Answer: c
Question (probability): in how many ways can 7 boys be seated in a circular order ?
Options: a ) 110 , b ) 230 , c ) 720 , d ) 420 , e ) 680
Rationale: "number of arrangements possible = ( 7 − 1 ) ! = 6 ! = 6 x 5 x 4 x 3 x 2 x 1 = 720 answer : c"
Answer: c
Question (general): if n = 8 ^ 9 – 8 , what is the units digit of n ?
Options: a ) 4 , b ) 0 , c ) 1 , d ) 2 , e ) 3
Rationale: "8 ^ 9 - 8 = 8 ( 8 ^ 8 - 1 ) = = > 8 ( 2 ^ 24 - 1 ) last digit of 2 ^ 24 is 6 based on what explanation livestronger is saying . 2 ^ 24 - 1 yields 6 - 1 = 5 as the unit digit . now on multiply this with 8 , we get unit digit as 0 answer : b"
Answer: b
Question (general): a , b , c subscribe rs . 50,000 for a business . if a subscribes rs . 4000 more than b and b rs . 5000 more than c , out of a total profit of rs . 40,000 , what will be the amount a receives ?
Options: a ) 14700 , b ) 14500 , c ) 16800 , d ) 14300 , e ) 14000
Rationale: "total amount invested = 50000 assume that investment of c = x . then investment of b = 5000 + x , investment of a = 4000 + 5000 + x = 9000 + x x + 5000 + x + 9000 + x = 50000 ⇒ 3 x + 14000 = 50000 ⇒ 3 x = 50000 – 14000 = 36000 ⇒ x = 36000 / 3 = 12000 investment of c = x = 12000 investment of b = 5000 + x = 17000 investment of a = 9000 + x = 21000 ratio of the investment of a , b and c = 21000 : 17000 : 12000 = 21 : 17 : 12 share of a = total profit × 21 / 50 = 40000 × 21 / 50 = 16,800 answer is c"
Answer: c
Question (general): 30 carrots on a scale weigh 5.94 kg . when 3 carrots are removed from the scale , the average weight of the 27 carrots is 200 grams . what is the average weight ( in grams ) of the 3 carrots which were removed ?
Options: a ) 165 , b ) 170 , c ) 175 , d ) 180 , e ) 185
Rationale: 27 * 200 = 5400 . the other 3 carrots weigh a total of 540 grams . the average weight is 540 / 3 = 180 grams . the answer is d .
Answer: d
Question (general): two trains start at same time from two stations and proceed towards each other at the rate of 20 km / hr and 25 km / hr respectively . when they meet , it is found that one train has traveled 75 km more than the other . what is the distance between the two stations ?
Options: a ) 540 km , b ) 675 km , c ) 276 km , d ) 178 km , e ) 176 km
Rationale: "explanation : let us assume that trains meet after ' x ' hours distance = speed * time distance traveled by two trains = 20 x km and 25 x km resp . as one train travels 75 km more than the other , 25 x â € “ 20 x = 75 5 x = 75 x = 15 hours as the two trains are moving towards each other , relative speed = 20 + 25 = 45 km / hr therefore , total distance = 45 * 15 = 675 km . answer : b"
Answer: b
Question (general): what is the smallest positive integer x such that 120 - x is the cube of a positive integer ?
Options: a ) 10 , b ) 6 , c ) 5 , d ) 0 , e ) 1
Rationale: "given 130 - x is a perfect cube so we will take 125 = 5 * 5 * 5 130 - x = 125 x = 130 - 125 = 5 correct option is c"
Answer: c
Question (general): two ants , arthur and amy , have discovered a picnic and are bringing crumbs back to the anthill . amy makes twice as many trips and carries one and a half times as many crumbs per trip as arthur . if arthur carries a total of c crumbs to the anthill , how many crumbs will amy bring to the anthill , in terms of c ?
Options: a ) x / 2 , b ) x , c ) 3 x / 2 , d ) 2 x , e ) 3 x
Rationale: "lets do it by picking up numbers . let arthur carry 2 crumbs per trip , this means amy carries 3 crumbs per trip . also let arthur make 2 trips and so amy makes 4 trips . thus total crumbs carried by arthur ( c ) = 2 x 2 = 4 , total crumbs carried by amy = 3 x 4 = 12 . 12 is 3 times 4 , so e"
Answer: e
Question (gain): a shopkeeper forced to sell at cost price , uses a 850 grams weight for a kilogram . what is his gain percent ?
Options: a ) 17.65 % , b ) 9 % , c ) 11.11 % , d ) 12 % , e ) none of these
Rationale: "shopkeeper sells 850 g instead of 1000 g . so , his gain = 1000 - 850 = 150 g . thus , % gain = ( 150 * 100 ) / 850 = 17.65 % . answer : option a"
Answer: a
Question (general): in a mayoral election , candidate x received 2 / 3 more votes than candidate y , and candidate y received 1 / 3 fewer votes than z . if z received 27,000 votes how many votes did candidate x received ?
Options: a ) 18000 , b ) 22000 , c ) 24000 , d ) 26000 , e ) 30000
Rationale: "z = 27 - - > y received 2 / 3 fewer votes than z - - > y = z - 1 / 3 * z = 18 ; x received 2 / 3 more votes than y - - > x = y + 2 / 3 * y = 30 . answer : e ."
Answer: e
Question (geometry): a cubical block of metal weighs 4 pounds . how much will another cube of the same metal weigh if its sides are twice as long ?
Options: a ) 48 , b ) 32 , c ) 24 , d ) 18 , e ) 12
Rationale: "for example our cube have a side 1 meter , so we have 1 cubical meter in this cube and this cubical meter weigth 4 pounds if we take cube with side 2 meters we will have 8 cubical meters in this cube 8 meters * 4 pounds = 32 pounds so answer is b and similar but more theoretical approach : if we have sides a and b than they have equal ration with their areas : a / b = a ^ 2 / b ^ 2 and they have equal ration with their volumes : a / b = a ^ 3 / b ^ 3 we have two sides 1 / 2 so their volume will be in ratio 1 / 8 weight of one cube * volume of another cube 4 * 8 = 32 so answer is b"
Answer: b