Datasets:
marcuscedricridia
/
brew-genpt-qwen32b-distill

Dataset card Data Studio Files
xet
Community
1
prompt
stringlengths
5
2.87k
response
stringlengths
1
2.73k
what is ( 19 ^ 7 + 19 ) / 19 ?
( 19 ^ 7 + 19 ) / 19 = 19 * ( 19 ^ 6 + 1 ) / 19 = 19 ^ 6 + 1 clearly this is a number which ends with a 2 in the units place . the answer is c .
a certain galaxy is known to comprise approximately 6 x 10 ^ 11 stars . of every 50 million of these stars , one is larger in mass than our sun . approximately how many stars in this galaxy are larger than the sun ?
6 * 10 ^ 11 50 mln = 5 * 10 ^ 7 we divide 10 ^ 11 by 10 ^ 7 and we get ( 10 ^ 4 ) * 6 = 60,000 and divide by 5 . the result is 12,000 d
what is the remainder when 4 ^ 381 is divided by 5 ?
i also agree that the remainder is ' 4 ' ( using the last digit of the powers of 7 ) . could we have the official answer please ? e
the present population of a town is 1000 . population increase rate is 25 % p . a . find the population of town before 1 years ?
p = 1000 r = 25 % required population of town = p / ( 1 + r / 100 ) ^ t = 1000 / ( 1 + 25 / 100 ) = 1000 / ( 5 / 4 ) = 800 answer is a
a garrison of 400 men had a provision for 31 days . after 28 days 300 persons re - enforcement leave the garrison . find the number of days for which the remaining ration will be sufficient ?
400 - - - 31 400 - - - 3 100 - - - ? 400 * 3 = 100 * x = > x = 12 days .
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 ?
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 .
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 ?
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 .
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 ?
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 %
for the positive integers x , x + 2 , x + 4 , x + 7 , and x + 17 , the mean is how much greater than the median ?
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
a man rows his boat 84 km downstream and 60 km upstream , taking 4 hours each time . find the speed of the stream ?
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
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 :
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
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 .
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
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 ?
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 .
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 ?
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
how many 4 - digit positive integers are multiple of each integer from 1 to 10
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
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 ?
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 .
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
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
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 ?
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 .
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 .
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 .
the speed of a train is 80 kmph . what is the distance covered by it in 6 minutes ?
80 * 6 / 60 = 8 kmph
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 ?
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
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 :
sol . sum = s . i . * t . d . / ( s . i ) - ( t . d . ) = 85 * 70 / ( 85 - 70 ) = rs . 396.7 . answer e
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 ?
x + y = 10 2 x – 3 y = 5 x = 7 y = 3 a )
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 ?
let see d / t = v then x / 20 + ( 400 - x ) / 70 = 8 x = 64 kmh t = 64 / 20 = 3.2 hr
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 ?
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
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 :
solution speed in still water = 1 / 2 ( 13 + 9 ) kmph . = 11 kmph . answer c
if 5 spiders make 2 webs in 8 days , then how many days are needed for 1 spider to make 1 web ?
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
an employee ’ s annual salary was increased $ 5,000 . if her new annual salary now equals $ 25000 what was the percent increase ?
new annual salary = $ 25000 salary increase = $ 5000 . original salary = $ 25000 - $ 5,000 . = $ 20,000 % increase = ( $ 15,000 / $ 75,000 ) * 100 = 80 % hence b .
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
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 %
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 ?
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
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 ?
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
by selling an article at rs . 250 , a profit of 25 % is made . find its cost price ?
sp = 250 cp = ( sp ) * [ 100 / ( 100 + p ) ] = 250 * [ 100 / ( 100 + 25 ) ] = 250 * [ 100 / 125 ] = rs . 200
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 ?
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
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 .
solution : c . 250 * 2 = 500 for 2 guy without discount , for other 2 ( 250 * 2 ) with 25 % is 375 . total cost 500 + 375 = 875
if x and y are integers and | x - y | = 11 , what is the minimum possible value of xy ?
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
15 : 5 seconds : : ? : 10 minutes
15 * 10 = 5 * x x = 30
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 ?
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
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 ?
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 .
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 ?
125 / 25 = 5 the answer is c .
what is the value of 3 x ^ 2 − 1.8 x + 0.5 for x = 0.6 ?
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
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 ?
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
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 ?
w = 62 % l = 38 % 62 % - 38 % = 24 % 24 % - - - - - - - - 288 62 % - - - - - - - - ? = > 744
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 ?
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 .
in how many ways can 7 boys be seated in a circular order ?
number of arrangements possible = ( 7 − 1 ) ! = 6 ! = 6 x 5 x 4 x 3 x 2 x 1 = 720
if n = 8 ^ 9 – 8 , what is the units digit of n ?
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
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 ?
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
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 ?
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 .
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 ?
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 .
what is the smallest positive integer x such that 120 - x is the cube of a positive integer ?
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
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 ?
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
a shopkeeper forced to sell at cost price , uses a 850 grams weight for a kilogram . what is his gain percent ?
shopkeeper sells 850 g instead of 1000 g . so , his gain = 1000 - 850 = 150 g . thus , % gain = ( 150 * 100 ) / 850 = 17.65 % .
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 ?
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 .
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 ?
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
the price of a coat in a certain store is $ 500 . if the price of the coat is to be reduced by $ 200 , by what percent is the price to be reduced ?
price of a coat in a certain store = $ 500 the price of the coat is to be reduced by $ 200 % change = ( final value - initial value ) * 100 / initial value % reduction = ( reduction in price ) * 100 / initial value i . e . % reduction = ( 200 ) * 100 / 500 = 40 %
bob wants to run a mile in the same time as his sister . if bob ’ s time for a mile is currently 10 minutes 40 seconds and his sister ’ s time is currently 10 minutes 8 seconds , by what percent does bob need to improve his time in order run a mile in the same time as his sister ?
bob ' s time = 640 secs . his sis ' time = 608 secs . percent increase needed = ( 640 - 608 / 640 ) * 100 = 32 / 640 * 100 = 5 % . ans ( b ) .
when a mobile is sold for rs . 24000 , the owner loses 40 % . at what price must that mobile be sold in order to gain 40 % ?
60 : 24000 = 140 : x x = ( 24000 x 140 ) / 60 = 56000 . hence , s . p . = rs . 56,000 .
bella is taking a trip in her car from new york ( point a ) chicago , illinois ( point b ) . she is traveling at an average speed of 50 miles per hour , if the total distance from point a to point b is 790 miles , in approximately how long will bella reach her destination ?
answer is ( c ) . if she is traveling at a speed of 50 miles per hour and her trip is a total of 790 miles , 790 miles divided by 50 miles per hours would equal 15.80 hours , just shy of 16 hours .
because he ’ s taxed by his home planet , mork pays a tax rate of 10 % on his income , while mindy pays a rate of 20 % on hers . if mindy earned 3 times as much as mork did , what was their combined tax rate ?
say morks income is - 100 so tax paid will be 10 say mindys income is 3 * 100 = 300 so tax paid is 20 % * 300 = 60 total tax paid = 10 + 60 = 70 . combined tax % will be 70 / 100 + 300 = 15.5 %
three numbers are in the ratio 4 : 5 : 6 and their average is 36 . the largest number is :
let the numbers be 4 x , 5 x and 6 x . therefore , ( 4 x + 5 x + 6 x ) / 3 = 36 15 x = 108 x = 7.2 largest number = 6 x = 43.2 . answer c
the probability that event a occurs is 0.4 , and the probability that events a and b both occur is 0.25 . if the probability that either event a or event b occurs is 0.6 , what is the probability that event b will occur ?
p ( a or b ) = p ( a ) + p ( b ) - p ( a n b ) 0.6 = 0.4 + p ( b ) - 0.25 p ( b ) = 0.45
there are 437 doctors and nurses in a hospital . if the ratio of the doctors to the nurses is 8 : 11 , then how many nurses are there in the hospital ?
given , the ratio of the doctors to the nurses is 8 : 11 number of nurses = 11 / 19 x 437 = 253
two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 14 kmph and 21 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ?
1 h - - - - - 5 ? - - - - - - 60 12 h rs = 14 + 21 = 35 t = 12 d = 35 * 12 = 420 .
if the length of the sides of two cubes are in the ratio 4 : 1 , what is the ratio of their total surface area ?
let x be the length of the small cube ' s side . the total surface area of the small cube is 6 x ^ 2 . the total surface area of the large cube is 6 ( 4 x ) ^ 2 = 96 x ^ 2 . the ratio of surface areas is 16 : 1 . the answer is d .
how many integers from 0 to 50 inclusive have a remainder of 3 when divided by 8 ?
the numbers should be of the form 8 c + 3 . the minimum is 3 when c = 0 . the maximum is 43 when c = 5 . there are six such numbers . the answer is b .
two brothers took the gmat exam , the higher score is x and the lower one is y . if the difference between the two scores is 1 / 5 , what is the value of x / y ?
answer is b : 5 x - y = ( x + y ) / 2 solving for x / y = 5
how much interest will $ 10,000 earn in 9 months at an annual rate of 3 % ?
soln : - 9 months = 3 / 4 of year ; 3 % = 3 / 100 = 3 / 100 ; $ 10,000 ( principal ) * 3 / 100 ( interest rate ) * 3 / 4 ( time ) = $ 225 .
the average weight of 20 persons sitting in a boat had some value . a new person added to them whose weight was 47 kg only . due to his arrival , the average weight of all the persons decreased by 5 kg . find the average weight of first 20 persons ?
20 x + 47 = 21 ( x – 5 ) x = 58
p can do a work in 24 days . q can do the samework in 9 days & r can do the same work in 12 days . q & r start the work and leave after 3 days . p finishes the remaining work in how many days .
work done by p in 1 day = 1 / 24 work done by q in 1 day = 1 / 9 work done by r in 1 day = 1 / 12 work done by q and r in 1 day = 1 / 9 + 1 / 12 = 7 / 36 work done by q and r in 3 days = 3 × 7 / 36 = 7 / 12 remaining work = 1 – 7 / 12 = 5 / 12 number of days in which p can finish the remaining work = ( 5 / 12 ) / ( 1 / 24 ) = 10 b
what is the difference between the c . i . on rs . 8000 for 1 1 / 2 years at 4 % per annum compounded yearly and half - yearly ?
c . i . when interest is compounded yearly = [ 8000 * ( 1 + 4 / 100 ) * ( 1 + ( 1 / 2 * 4 ) / 100 ] = 8000 * 26 / 25 * 51 / 50 = rs . 8486.4 c . i . when interest is compounded half - yearly = [ 8000 * ( 1 + 2 / 100 ) 2 ] = ( 8000 * 51 / 50 * 51 / 50 * 51 / 50 ) = rs . 8489.66 difference = ( 8489.66 - 8486.4 = rs . 3.26 .
the number of timeshare condos available at sunset beach is 2 / 5 the number of timeshare condos available at playa del mar . if the total number of timeshare condos available at the two beaches combined is 210 , what is the difference between the number of condos available at sunset beach and the number of condos available at playa del mar ?
let x be the number of timeshare condos available at playa del mar . then number of timeshare condos available at sunset beach = 3 / 5 x we know , x + 2 / 5 x = 210 hence , x = 150 . so , number of timeshare condos available at playa del mar = 150 the difference between the number of condos available at sunset beach and the number of condos available at playa del mar = x - 2 / 5 x = 2 / 5 x = 3 / 5 ( 150 ) = 90 the correct answer is b
a can do a particular work in 6 days . b can do the same work in 8 days . a and b signed to do it for rs . 3840 . they completed the work in 3 days with the help of c . how much is to be paid to c ?
amount of work a can do in 1 day = 1 / 6 amount of work b can do in 1 day = 1 / 8 amount of work a + b can do in 1 day = 1 / 6 + 1 / 8 = 7 / 24 amount of work a + b + c can do = 1 / 3 amount of work c can do in 1 day = 1 / 3 - 7 / 24 = 1 / 24 work a can do in 1 day : work b can do in 1 day : work c can do in 1 day = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 amount to be paid to c = 3840 × ( 1 / 8 ) = 480
on dividing 13698 by a certain number , we get 89 as quotient and 14 as remainder . what is the divisor ?
divisor * quotient + remainder = dividend divisor = ( dividend ) - ( remainder ) / quotient ( 13698 - 14 ) / 89 = 154 answer ( b )
a store owner estimates that the average price of type a products will increase by 30 % next year and that the price of type b products will increase by 10 % next year . this year , the total amount paid for type a products was $ 4500 and the total price paid for type b products was $ 8300 . according to the store owner ' s estimate , and assuming the number of products purchased next year remains the same as that of this year , how much will be spent for both products next year ?
cost of type a products next year = 1.30 * 4500 = 5850 cost of type b products next year = 1.1 * 8300 = 9130 total 5850 + 9130 = 14980 option a
a father said his son , ` ` i was as old as you are at present at the time of your birth . ` ` if the father age is 38 now , the son age 5 years back was
let the son ' s present age be x years . then , ( 38 - x ) = x x = 19 . son ' s age 5 years back = ( 19 - 5 ) = 14 years
the number of people who purchased book a is twice the number of people who purchased book b . the number of people who purchased both books a and b is 500 , which is twice the number of people who purchased only book b . what is the number of people x who purchased only book a ?
this is best solved using overlapping sets or a venn diagram . we know that a = 2 b , and that 500 people purchased both a and b . further , those purchasing both was double those purchasing b only . this gives us 250 people purchasing b only . with the 500 that pruchased both , we have a total of 750 that purchased b and this is 1 / 2 of those that purchased a . so , 1500 purchased a . less the 500 that purchased both , x = 1000 purchased a only . ( this is much simpler to solve using the venn diagram ) . correct answer is d . 1000
a sum of money at simple interest amounts to rs . 825 in 3 years and to rs . 854 in 4 years . the sum is ?
s . i . for 1 year = ( 854 - 825 ) = rs . 29 s . i . for 3 years = 29 * 3 = rs . 87 principal = ( 825 - 87 ) = rs . 738 .
in how many seconds will a train 150 meters long pass an oak tree , if the speed of the train is 54 km / hr ?
speed = 54 * 5 / 18 = 15 m / s time = 150 / 15 = 10 seconds the answer is c .
cereal a is 10 % sugar by weight , whereas healthier but less delicious cereal b is 3 % sugar by weight . to make a delicious and healthy mixture that is 4 % sugar , what should be the ratio of cereal a to cereal b , by weight ?
ratio of a / ratio of b = ( average wt of mixture - wt of b ) / ( wt of a - average wt of mixture ) = > ratio of a / ratio of b = ( 4 - 3 ) / ( 10 - 4 ) = 1 / 6 so they should be mixed in the ratio 1 : 6 answer - c
in a certain game , each player scores either 2 points or 5 points . if n players score 2 points and m players score 5 points , and the total number of points scored is 50 , what is the least possible positive e difference between n and m ?
we have equation 2 n + 5 m = 50 we have factor 2 in first number and we have factor 5 in second number . lcm ( 2 , 5 ) = 10 so we can try some numbers and we should start from 5 because it will be less list than for 2 2 * 5 = 10 and n should be equal 20 4 * 5 = 20 and n should be equal 15 6 * 5 = 30 and n should be equal 10 8 * 5 = 40 and n should be equal 5 10 * 5 = 50 and n should be equal 0 third variant give us the mininal difference n - m = 10 - 6 = 4 and there is some mistake in my way of thinking because we do n ' t have such answer ) if we change the task and will seek for difference between m and n than minimal result e will be 8 - 5 = 3 and answer b
4 years ago , paula was 4 times as old as karl . in 4 years , paula will be twice as old as karl . what is the sum of their ages now ?
p - 4 = 4 ( k - 4 ) and so p = 4 k - 12 p + 4 = 2 ( k + 4 ) ( 4 k - 12 ) + 4 = 2 k + 8 k = 8 p = 20 p + k = 28 the answer is d .
a palindrome is a word or a number that reads the same forward and backward . for example , 2442 and 111 are palindromes . if 5 - digit palindromes are formed using one or more of the digits 1 , 2 , 3 , 4 , and 5 , how many palindromes are possible ?
there are 5 choices for each of the first three digits . the number of possible palindromes is 5 ^ 3 = 125 . the answer is c .
if the personal income tax rate is lowered from 40 % to 33 % , what is the differential savings for a tax payer having an annual income before tax to the tune of $ 45000 ?
saving = ( 40 - 33 ) % of 45000 = 3150 .
the length of minute hand of a clock is 5.4 cm . what is the area covered by this in 10 minutes
area of circle is pi * r ^ 2 but in 10 minutes area covered is ( 10 / 60 ) * 360 = 60 degree so formula is pi * r ^ 2 * ( angle / 360 ) = 3.14 * ( 5.4 ^ 2 ) * ( 60 / 360 ) = 15.27 cm ^ 2
a pipe takes a hours to fill the tank . but because of a leakage it took 4 times of its original time . find the time taken by the leakage to empty the tank
pipe a can do a work 60 min . lets leakage time is x ; then 1 / 60 - 1 / x = 1 / 240 x = 80 min
the compound interest on $ 30,000 at 7 % per annum is $ 4347 . the period ( in years ) is :
amount = $ ( 30000 + 4347 ) = $ . 34347 . let the time be n years . then , 30000 1 + 7 n = 34347 100 107 n = 34347 = 11449 = 107 2 100 30000 10000 100 n = 2 years . answer a - 2
jonathan can type a 50 page document in 40 minutes , susan can type it in 30 minutes , and jack can type it in 24 minutes . working together , how much time will it take them to type the same document ?
you may set up common equation like this : job / a + job / b + job / c = job / x memorize this universal formula , you will need it definitely for gmat . and find x from this equation in this specific case , the equation will look like this : 50 / 40 + 50 / 30 + 50 / 24 = 50 / x if you solve this equation , you get the same answer b ( 10 )
find the annual income derived by investing $ 6800 in 30 % stock at 136 .
by investing $ 136 , income obtained = $ 30 . by investing $ 6800 , income obtained = $ [ ( 30 / 136 ) * 6800 ] = $ 1500 . answer b .
joe ’ s average ( arithmetic mean ) test score across 4 equally weighted tests was 90 . he was allowed to drop his lowest score . after doing so , his average test score improved to 85 . what is the lowest test score that was dropped ?
the arithmetic mean of 4 equally weighted tests was 90 . so what we can assume is that we have 4 test scores , each 90 . he dropped his lowest score and the avg went to 95 . this means that the lowest score was not 90 and other three scores had given the lowest score 5 each to make it up to 90 too . when the lowest score was removed , the other 3 scores got their 5 back . so the lowest score was 3 * 5 = 15 less than 90 . so the lowest score = 90 - 15 = 75 answer ( d )
the average age of 6 men increases by 2 years when two women are included in place of two men of ages 10 and 12 years . find the average age of the women ?
10 + 12 + 6 * 2 = 34 / 2 = 17
it takes 35 identical printing presses 15 hours to print 500,000 papers . how many hours would it take 25 of these printing presses to print 500,000 papers ?
35 printing presses can do 1 / 15 of the job each hour . 25 printing presses can do 5 / 7 * 1 / 15 = 1 / 21 of the job each hour . the answer is c .
3639 + 11.95 - x = 3054 . find the value of x .
let 3639 + 11.95 – x = 3054 then , x = ( 3639 + 11.95 ) – 3054 = 3650.95 – 3054 = 596.95
a pharmaceutical company received $ 3 million in royalties on the first $ 20 million in sales of and then $ 9 million in royalties on the next $ 108 million in sales . by approximately what percentage did the ratio of royalties to sales decrease from the first $ 20 million in sales to the next $ 104 million in sales ?
( 9 / 104 ) / ( 3 / 20 ) = 30 / 54 = 57,6 % it means that 9 / 108 represents only 57,6 % . therefore a decrease of 42 % . answer d
the cost per pound of milk powder and coffee were the same in june . in july , the price of coffee shot up by 300 % and that of milk powder dropped by 80 % . if in july , a mixture containing equal quantities of milk powder and coffee costs $ 6.30 for 3 lbs , how much did a pound of milk powder cost in july ?
lets assume price of coffee in june = 100 x price of milk powder in june = 100 x price of coffee in july = 400 x ( because of 300 % increase in price ) price of milk powder in july = 20 x ( because of 80 % decrease in price ) price of 1.5 pound of coffee 1.5 pound of milk powder in july will be = 600 x + 30 x = 630 x as per question 630 x = 6.30 $ x = 0.01 s so the price of milk powder in july = 20 x = 20 x 0.01 = 0.2 $ / pound answer b
a certain class of students is being divided into teams . the class can either be divided into 18 teams with an equal number of players on each team or 24 teams with an equal number of players on each team . what is the lowest possible number of students in the class ?
prime factorization of 18 = 2 * 3 ^ 2 prime factorization of 24 = 2 ^ 3 * 3 lcm of the given numbers = 2 ^ 3 * 3 ^ 2 = 72 answer e
a bus started its journey from mumbai and reached pune in 44 min with its average speed of 50 km / hr . if the average speed of the bus is increased by 5 km / hr , how much time will it take to cover the same distance ?
sol . distance between ramgarh and devgarh = ( 50 * 44 ) / 60 = 110 / 3 average speed of the bus is increased by 5 km / hr then the speed of the bus = 55 km / hr required time = 110 / 3 * 60 / 55 = 40 min d
daniel went to a shop and bought things worth rs . 25 , out of which 30 paise went on sales tax on taxable purchases . if the tax rate was 10 % , then what was the cost of the tax free items ?
total cost of the items he purchased = rs . 25 given that out of this rs . 25 , 30 paise is given as tax = > total tax incurred = 30 paise = rs . 30 / 100 let the cost of the tax free items = x given that tax rate = 10 % ∴ ( 25 − 30 / 100 − x ) 10 / 100 = 30 / 100 ⇒ 10 ( 25 − 0.3 − x ) = 30 ⇒ ( 25 − 0.3 − x ) = 3 ⇒ x = 25 − 0.3 − 3 = 21.7 d
how many positive integers less than 250 are there such that they are multiples of 15 or multiples of 16 ?
250 / 15 = 16 ( plus remainder ) so there are 16 multiples of 15 250 / 16 = 15 ( plus remainder ) so there are 15 multiples of 16 we need to subtract 1 because 15 * 16 is a multiple of both so it was counted twice . the total is 16 + 15 - 1 = 30 the answer is c .
if ( 5 - x ) / ( 5 + x ) = x , what is the value of x ^ 2 + 6 x - 5 ?
( 5 - x ) = x * ( 5 + x ) ( 5 - x ) = 5 x + x ^ 2 0 = x ^ 2 + 6 x - 5 the answer is d .
1 / 2 - [ ( 2 / 7 * 7 / 32 ) + 1 ] + 9 / 16 =
1 / 2 - [ ( 2 / 7 * 7 / 32 ) + 1 ] + 9 / 16 = 1 / 2 - [ ( 1 / 16 ) + 1 ] + 9 / 16 = 1 / 2 - [ 17 / 16 ] + 9 / 16 = 8 / 16 - 17 / 16 + 9 / 16 = 0 the answer is e .
if a person buy radio worth rs 2468 and pay 7 % sales . how much price of radio should reduce to pay only rs 2468 .
( x + . 07 x ) = 2468 1.07 x = 2468 x = 2306 reduce = 2468 - 2306 = 162