rootacess/math-qa-classification · Datasets at Hugging Face

Problem stringlengths 5 967	category class label 6 classes
what is the greatest value of positive integer x such that 2 ^ x is a factor of 100 ^ 90 ?	0general
alex takes a loan of $ 9,000 to buy a used truck at the rate of 9 % simple interest . calculate the annual interest to be paid for the loan amount .	2gain
last month , john rejected 0.7 % of the products that he inspected and jane rejected 0.8 percent of the products that she inspected . if total of 0.75 percent of the products produced last month were rejected , what fraction of the products did jane inspect ?	2gain
if the average ( arithmetic mean ) of x and y is 60 , and z – x = 80 , what is the average of y and z ?	0general
what is the smallest integer z for which 27 ^ z > 3 ^ 24 ?	0general
a is twice as good a work man as b and together they finish the work in 8 days . in how many days a alone can finish the work ?	1physics
the sum of two numbers is 21 and the sum of their squares is 527 . find the product of the numbers .	0general
thabo owns exactly 280 books , and each book is either paperback fiction , paperback nonfiction , or hardcover nonfiction . if he owns 20 more paperback nonfiction books than hardcover nonfiction books , and twice as many paperback fiction books as paperback nonfiction books , how many hardcover books nonfiction books does thabo own ?	0general
in the number 100 ab , a and b represent the tens and units digits , respectively . if 110 ab is divisible by 55 , what is the greatest possible value of b × a ?	0general
a train 350 m long , running with a speed of 63 km / hr will pass a tree in ?	1physics
a car travelling with 5 / 7 km of its actual speed covers 42 km in 1 hr 40 min 48 sec find the actual speed of the car ?	1physics
compare the rates of two trains , one travelling at 90 km / hr and other is at 50 m / s ?	2gain
a computer manufacturer produces a certain electronic component at a cost of $ 100 per component . shipping costs for delivering the components are $ 2 per unit . further , the manufacturer has costs of $ 10,000 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 1000 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?	0general
sari and ken climb up a mountain . at night , they camp together . on the day they are supposed to reach the summit , sari wakes up at 08 : 00 and starts climbing at a constant pace . ken starts climbing only at 10 : 00 , when sari is already 700 meters ahead of him . nevertheless , ken climbs at a constant pace of 500 meters per hour , and reaches the summit before sari . if sari is 50 meters behind ken when he reaches the summit , at what time did ken reach the summit ?	1physics
the average weight of a , b and c is 30 kg . if the average weight of a and b be 25 kg and that of b and c be 28 kg , then the weight of b is :	0general
the cost of a one - family home was $ 120000 in 1980 . in 1988 , the price had increased to $ 192000 . what was the percent increase in the cost of the home ?	0general
one fourth of one third of two fifth of a number is 20 . what will be 40 % of that number	2gain
a card board of 34 * 14 has to be attached to a wooden box and a total of 35 pins are to be used on the each side of the cardbox . find the total number of pins used .	0general
a 200 meter long train crosses a platform in 50 seconds while it crosses a signal pole in 42 seconds . what is the length of the platform ?	1physics
how much water should be added to 11 liters of a 20 % - solution of alcohol to reduce the concentration of alcohol in the solution by 75 % ?	0general
a van takes 5 hours to cover a distance of 600 km . what speed in kph should the van maintain to cover the same distance in 3 / 2 of the previous time ?	1physics
the ratio of ages of aman , bren , and charlie are in the ratio 5 : 8 : 7 respectively . if 8 years ago , the sum of their ages was 76 , what will be the age of bren 12 years from now ?	0general
a and b undertake to do a piece of work for $ 500 . a alone can do it in 5 days while b alone can do it in 10 days . with the help of c , they finish it in 2 days . find the share of c ?	1physics
a clock store sold a certain clock to a collector for 15 percent more than the store had originally paid for the clock . when the collector tried to resell the clock to the store , the store bought it back at 45 percent of what the collector had paid . the shop then sold the clock again at a profit of 85 percent on its buy - back price . if the difference between the clock ' s original cost to the shop and the clock ' s buy - back price was $ 80 , for how much did the shop sell the clock the second time ?	0general
angelina walked 100 meters from her home to the grocery at a constant speed . she then walked 180 meters to the gym at double the speed . she spent 40 seconds less on her way from the grocery to the gym than on her way from home to the grocery . what was angelina ' s speed , in meters per second , from the grocery to the gym ?	1physics
if 45 % of z is 39 % of y and y is 75 % of x , what percent of x is z ?	2gain
10 camels cost as much as 24 horses , 16 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants . if the cost of 10 elephants is rs . 130000 , find the cost of a camel ?	0general
a worker makes a toy in every 3 h . if he works for 150 h , then how many toys will he make ?	1physics
in one hour , a boat goes 11 km along the stream and 5 km against the stream . the speed of the boat in still water in ( km / hr ) is	1physics
45 workers work 8 hours to dig a hole 30 meters deep . how many extra workers should be hired to dig another hole 40 meters deep by working for 6 hours ?	1physics
if an amount of rs 42,900 is distributed equally amongst 22 persons , how much amount would each person get ?	0general
what is the perimeter , in meters , of a rectangular garden 8 meters wide that has the same area as a rectangular playground 16 meters long and 12 meters wide ?	3geometry
what is the value of : - 9 ^ 7 + 9 ^ 9 ?	0general
let the sides of a rectangular prism are consecutive multiples of 5 . which among the following could be the base area	3geometry
if teena is driving at 55 miles per hour and is currently 7.5 miles behind joe , who is driving at 40 miles per hour in the same direction then in how many minutes will teena be 45 miles ahead of joe ?	1physics
the sum of ages of 4 children born at the intervals of 10 years each is 80 years . what is the age of the youngest child ?	0general
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 x that out of the two , one is white and one is blue ?	4probability
one hour after yolanda started walking from x to y , a distance of 17 miles , bob started walking along the same road from y to x . if yolanda ' s walking rate was 3 miles per hour and bob т ' s was 4 miles per hour , how many miles had bob walked when they met ?	1physics
a dozen eggs and 10 pounds of oranges are currently at the same price . if the price of a dozen eggs rises by 9 percent and the price of oranges rises by 6 % . how much more will it cost to buy a dozen eggs and 10 pounds of oranges .	0general
at what price must an article costing rs . 47.50 be marked in order that after deducting 5 % from the list price . it may be sold at a profit of 40 % on the cost price ?	2gain
two friends decide to get together ; so they start riding bikes towards each other . they plan to meet halfway . each is riding at 6 mph . they live 36 miles apart . one of them has a pet carrier pigeon and it starts flying the instant the friends start traveling . the pigeon flies back and forth at 19 mph between the 2 friends until the friends meet . how many miles does the pigeon travel ?	1physics
in a river flowing at 2 km / hr , a boat travels 48 km upstream and then returns downstream to the starting point . if its speed in still water be 6 km / hr , find the total journey time .	0general
in smithtown , the ratio of right - handed people to left - handed people is 3 to 1 and the ratio of men to women is 3 to 2 . if the number of right - handed men is maximized , then what x percent of all the people in smithtown are left - handed women ?	0general
the number of degrees that the hour hand of a clock moves through between noon and 2.30 in the afternoon of the same day is ?	1physics
a rectangular tiled patio is composed of 30 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 30 tiles , and it will still be rectangular . how many rows are in the tile patio before the change in layout ?	3geometry
a row of ants comprised of 102 ants . a man walked upon it and all except 42 were crushed beneath his foot . how many ants are left alive ?	0general
at a certain food stand , the price of each apple is 40 ¢ and the price of each orange is 60 ¢ . mary selects a total of 10 apples and oranges from the food stand , and the average ( arithmetic mean ) price of the 10 pieces of fruit is 54 ¢ . how many oranges must mary put back so that the average price of the pieces of fruit that she keeps is 45 ¢ ?	0general
what percent is 50 gm of 1 kg ?	2gain
the dimensions of a rectangular solid are 6 inches , 5 inches , and 8 inches . if a cube , a side of which is equal to one of the dimensions of the rectangular solid , is placed entirely within thespherejust large enough to hold the cube , what the ratio of the volume of the cube to the volume within thespherethat is not occupied by the cube ?	3geometry
john purchased some shirts and trousers for $ 1300 . he paid $ 500 less for the shirts than he did for the trousers . if he bought 5 shirts and the cost of a shirt is $ 20 less than that of a trouser , how many trousers did he buy ?	0general
a contractor undertakes to complete the construction of a tunnel 720 meters long in 240 days and employs 50 men for the purpose . after 120 days , he finds that only 240 meters of the tunnel is complete . how many more men should be employ in order to complete the work in time ?	1physics
for all integers x > 1 . < x > = 2 x + ( 2 x - 1 ) + ( 2 x - 2 ) + . . . . . . 2 + 1 . what is the value of < 2 > * < 4 > ?	0general
two identical circles intersect such that their centers and the points at which they intersect form a square of side 4 cm . what is the area of the region where the two circles intersect ?	3geometry
pradeep has to obtain 35 % of the total marks to pass . he got 150 marks and failed by 25 marks . the maximum marks are	0general
if 4 people are selected from a group of 6 married couples , what is the probability that none of them would be married to each other ?	4probability
if the length of a rectangle is increased by 20 % and the breadth is reduced by 20 % , what will be the effect on its area ?	3geometry
each light bulb at a hotel is either incandescent or fluorescent . at a certain moment , forty percent of the incandescent bulbs are switched on , and eighty percent of the fluorescent bulbs are switched on . if 75 percent of all the bulbs are switched on at this moment , what percent of the bulbs that are switched on are incandescent ?	2gain
a and b can do a piece of work in 2 days and 6 days respectively . both work for 1 days and then a goes away . find how long will b take to complete the remaining work ?	1physics
karen places a bet with tom that she will beat tom in a car race by 4 miles even if karen starts 4 minutes late . assuming that karen drives at an average speed of 60 mph and tom drives at an average speed of 45 mph , how many h miles will tom drive before karen wins the bet ?	1physics
rs . 1210 were divided among 3 person p , q , r so that p : q = 5 : 4 and q : r = 9 : 10 . then r gets the amount .	0general
in what ratio should a variety of rice costing rs . 7 per kg be mixed with another variety of rice costing rs . 14.50 per kg to obtain a mixture costing rs . 9.75 per kg ?	5other
if 10 is added to thrice a number and this sum is multiplied by 5 , the result is the same as if the number is multiplied by 5 and 13 is added to the product . what is the number ?	0general
if a 2 + b 2 + c 2 = 390 and ab + bc + ca = 5 , then a + b + c is	0general
in an office in singapore there are 60 % female employees . 50 % of all the male employees are computer literate . if there are total 62 % employees computer literate out of total 1500 employees , then the no . of female employees who are computer literate ?	2gain
what will be the remainder when ( 27 ^ 27 ) + 27 is divided by 28 ?	0general
a man has some hens and cows . if the number of heads be 48 and the number of feet equals 140 , then the number of hens will be	0general
the cash realised on selling a 14 % stock is rs . 120.50 , brokerage being 1 / 4 % is	0general
a and b are two partially filled buckets of water . if 7 liters are transferred from a to b , then a would contain one - third of the amount of water in b . alternatively , if 7 liters are transferred from b to a , b would contain one - half of the amount of water in a . bucket a contains how many liters of water ?	0general
how many liters of water must be evaporated from 50 liters of a 2 percent sugar solution to get a 5 percent sugar solution ?	2gain
an equilateral triangle t 2 is formed by joining the mid points of the sides of another equilateral triangle t 1 . a third equilateral triangle t 3 is formed by joining the mid - points of t 2 and this process is continued indefinitely . if each side of t 1 is 50 cm , find the sum of the perimeters of all the triangles .	3geometry
three walls have wallpaper covering a combined area of 300 square meters . by overlapping the wallpaper to cover a wall with an area of 180 square meters , the area that is covered by exactly two layers of wallpaper is 40 square meters . what is the area that is covered with three layers of wallpaper ?	3geometry
a trained covered x km at 40 kmph and another 2 x km at 20 kmph . find the average speed of the train in covering the entire 4 x km .	0general
if n = 2.0254 and n * is the decimal obtained by rounding n to the nearest hundredth , what is the value of n * – n ?	0general
find the sum lend at c . i . at 5 p . c per annum will amount to rs . 240 in 2 years ?	0general
a bag contains 7 green balls and 7 white balls . if two balls are drawn simultaneously , what is the probability that both balls are the same colour ?	5other
a vendor sells 60 percent of apples he had and throws away 15 percent of the remainder . next day he sells 50 percent of the remainder and throws away the rest . what percent of his apples does the vendor throw ?	2gain
the radius of a cylinder is 8 m , height 14 m . the volume of the cylinder is :	3geometry
average of money that group of 4 friends pay for rent each month is $ 800 . after one persons rent is increased by 20 % the new mean is $ 880 . what was original rent of friend whose rent is increased ?	0general
when a student joe , weighing 43 kg , joins a group of students whose average weight is 30 kg , the average weight goes up by 1 kg . subsequently , if two students , excluding joe , leave the group the average weight comes back to 30 kg . what is the difference between the average weight of the two students who left and the weight of joe ?	0general
while working alone at their respective constant rates , server p uploads 480 files in 4 hours and server y uploads 480 files in 8 hours . if all files uploaded by these servers are the same size , how long would it take the two servers , working at the same time and at their respective constant rates , to process a total of 480 files ?	1physics
0.0203 x 2.92 / 0.0073 x 14.5 x 0.7 = ?	0general
the speed of a train is 90 kmph . what is the distance covered by it in 30 minutes ?	1physics
what is the smallest positive integer x such that 280 - x is the cube of a positive integer	0general
in a kilometer race , a beats b by 60 meters or 15 seconds . what time does a take to complete the race ?	1physics
in a certain diving competition , 5 judges score each dive on a scale from 1 to 10 . the point value of the dive is obtained by dropping the highest score and the lowest score and multiplying the sum of the remaining scores by the degree of difficulty . if a dive with a degree of difficulty of 3.2 received scores of 7.5 , 8.3 , 9.0 , 6.0 , and 8.6 , what was the point value of the dive ?	0general
train starts from amritsar to bombay at 9 am . it reaches destination after 3 days at 9 : 30 am . every day a train starts . how many trains does it come across on the way ?	1physics
if a ( a - 9 ) = 10 and b ( b - 9 ) = 10 , where a ≠ b , then a + b =	0general
there are 12 teams in a certain league and each team plays each of the other teams exactly twice . if each game is played by 2 teams , what is the total number of games played ?	0general
at what rate percent per annum will the simple interest on a sum of money be 1 / 5 of the amount in 10 years ?	2gain
a man can do a job in 15 days . his father takes 10 days and his son finishes it in 25 days . how long will they take to complete the job if they all work together ?	1physics
in a neighborhood having 90 households , 11 did not have either a car or a bike . if 22 households had a both a car and a bike and 44 had a car , how many had bike only ?	5other
the 3 digits of a number add up to 11 . the number is divisible by 5 . the leftmost digit is double the middle digit . what is the product of the 3 digits ?	0general
if a randomly selected positive single digit multiple of 3 is multiplied by a randomly selected prime number less than 20 , what is the probability t that this product will be a multiple of 45 ?	0general
uba capital recently bought brand new vehicles for office use . uba capital only went for toyota and honda and bought more of toyota than honda at the ratio of 8 : 2 . if 80 % of the toyota bought and 20 % of the honda bought were suv â € ™ s . how many suv â € ™ s did uba capital buy in the aforementioned purchase ?	5other
10 ^ ( 655 ) ã · 10 ^ ( 650 ) = ?	0general
a corporation that had $ 115.19 billion in profits for the year paid out $ 250.10 million in employee benefits . approximately what percent of the profits were the employee benefits ? ( note : 1 billion = 10 ^ 9 )	0general
a reduction of 10 % in the price of salt enables a lady to obtain 10 kgs more for rs . 100 , find the original price per kg ?	2gain
the average ( arithmetic mean ) of 16 students first quiz scores in a difficult english class is 62.5 . when one student dropped the class , the average of the remaining scores increased to 62.0 . what is the quiz score of the student who dropped the class ?	0general
the triplicate ratio of 2 : 3 is ?	5other
if 15 lions can kill 15 deers in 15 minutes how long will it take 100 lions to kill 100 deers ?	1physics

what is the greatest value of positive integer x such that 2 ^ x is a factor of 100 ^ 90 ?

0general

alex takes a loan of $ 9,000 to buy a used truck at the rate of 9 % simple interest . calculate the annual interest to be paid for the loan amount .

2gain

last month , john rejected 0.7 % of the products that he inspected and jane rejected 0.8 percent of the products that she inspected . if total of 0.75 percent of the products produced last month were rejected , what fraction of the products did jane inspect ?

2gain

if the average ( arithmetic mean ) of x and y is 60 , and z – x = 80 , what is the average of y and z ?

0general

what is the smallest integer z for which 27 ^ z > 3 ^ 24 ?

0general

a is twice as good a work man as b and together they finish the work in 8 days . in how many days a alone can finish the work ?

1physics

the sum of two numbers is 21 and the sum of their squares is 527 . find the product of the numbers .

0general

thabo owns exactly 280 books , and each book is either paperback fiction , paperback nonfiction , or hardcover nonfiction . if he owns 20 more paperback nonfiction books than hardcover nonfiction books , and twice as many paperback fiction books as paperback nonfiction books , how many hardcover books nonfiction books does thabo own ?

0general

in the number 100 ab , a and b represent the tens and units digits , respectively . if 110 ab is divisible by 55 , what is the greatest possible value of b × a ?

0general

a train 350 m long , running with a speed of 63 km / hr will pass a tree in ?

1physics

a car travelling with 5 / 7 km of its actual speed covers 42 km in 1 hr 40 min 48 sec find the actual speed of the car ?

1physics

compare the rates of two trains , one travelling at 90 km / hr and other is at 50 m / s ?

2gain

a computer manufacturer produces a certain electronic component at a cost of $ 100 per component . shipping costs for delivering the components are $ 2 per unit . further , the manufacturer has costs of $ 10,000 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 1000 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?

0general

sari and ken climb up a mountain . at night , they camp together . on the day they are supposed to reach the summit , sari wakes up at 08 : 00 and starts climbing at a constant pace . ken starts climbing only at 10 : 00 , when sari is already 700 meters ahead of him . nevertheless , ken climbs at a constant pace of 500 meters per hour , and reaches the summit before sari . if sari is 50 meters behind ken when he reaches the summit , at what time did ken reach the summit ?

1physics

the average weight of a , b and c is 30 kg . if the average weight of a and b be 25 kg and that of b and c be 28 kg , then the weight of b is :

0general

the cost of a one - family home was $ 120000 in 1980 . in 1988 , the price had increased to $ 192000 . what was the percent increase in the cost of the home ?

0general

one fourth of one third of two fifth of a number is 20 . what will be 40 % of that number

2gain

a card board of 34 * 14 has to be attached to a wooden box and a total of 35 pins are to be used on the each side of the cardbox . find the total number of pins used .

0general

a 200 meter long train crosses a platform in 50 seconds while it crosses a signal pole in 42 seconds . what is the length of the platform ?

1physics

how much water should be added to 11 liters of a 20 % - solution of alcohol to reduce the concentration of alcohol in the solution by 75 % ?

0general

a van takes 5 hours to cover a distance of 600 km . what speed in kph should the van maintain to cover the same distance in 3 / 2 of the previous time ?

1physics

the ratio of ages of aman , bren , and charlie are in the ratio 5 : 8 : 7 respectively . if 8 years ago , the sum of their ages was 76 , what will be the age of bren 12 years from now ?

0general

a and b undertake to do a piece of work for $ 500 . a alone can do it in 5 days while b alone can do it in 10 days . with the help of c , they finish it in 2 days . find the share of c ?

1physics

a clock store sold a certain clock to a collector for 15 percent more than the store had originally paid for the clock . when the collector tried to resell the clock to the store , the store bought it back at 45 percent of what the collector had paid . the shop then sold the clock again at a profit of 85 percent on its buy - back price . if the difference between the clock ' s original cost to the shop and the clock ' s buy - back price was $ 80 , for how much did the shop sell the clock the second time ?

0general

angelina walked 100 meters from her home to the grocery at a constant speed . she then walked 180 meters to the gym at double the speed . she spent 40 seconds less on her way from the grocery to the gym than on her way from home to the grocery . what was angelina ' s speed , in meters per second , from the grocery to the gym ?

1physics

if 45 % of z is 39 % of y and y is 75 % of x , what percent of x is z ?

2gain

10 camels cost as much as 24 horses , 16 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants . if the cost of 10 elephants is rs . 130000 , find the cost of a camel ?

0general

a worker makes a toy in every 3 h . if he works for 150 h , then how many toys will he make ?

1physics

in one hour , a boat goes 11 km along the stream and 5 km against the stream . the speed of the boat in still water in ( km / hr ) is

1physics

45 workers work 8 hours to dig a hole 30 meters deep . how many extra workers should be hired to dig another hole 40 meters deep by working for 6 hours ?

1physics

if an amount of rs 42,900 is distributed equally amongst 22 persons , how much amount would each person get ?

0general

what is the perimeter , in meters , of a rectangular garden 8 meters wide that has the same area as a rectangular playground 16 meters long and 12 meters wide ?

3geometry

what is the value of : - 9 ^ 7 + 9 ^ 9 ?

0general

let the sides of a rectangular prism are consecutive multiples of 5 . which among the following could be the base area

3geometry

if teena is driving at 55 miles per hour and is currently 7.5 miles behind joe , who is driving at 40 miles per hour in the same direction then in how many minutes will teena be 45 miles ahead of joe ?

1physics

the sum of ages of 4 children born at the intervals of 10 years each is 80 years . what is the age of the youngest child ?

0general

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 x that out of the two , one is white and one is blue ?

4probability

one hour after yolanda started walking from x to y , a distance of 17 miles , bob started walking along the same road from y to x . if yolanda ' s walking rate was 3 miles per hour and bob т ' s was 4 miles per hour , how many miles had bob walked when they met ?

1physics

a dozen eggs and 10 pounds of oranges are currently at the same price . if the price of a dozen eggs rises by 9 percent and the price of oranges rises by 6 % . how much more will it cost to buy a dozen eggs and 10 pounds of oranges .

0general

at what price must an article costing rs . 47.50 be marked in order that after deducting 5 % from the list price . it may be sold at a profit of 40 % on the cost price ?

2gain

two friends decide to get together ; so they start riding bikes towards each other . they plan to meet halfway . each is riding at 6 mph . they live 36 miles apart . one of them has a pet carrier pigeon and it starts flying the instant the friends start traveling . the pigeon flies back and forth at 19 mph between the 2 friends until the friends meet . how many miles does the pigeon travel ?

1physics

in a river flowing at 2 km / hr , a boat travels 48 km upstream and then returns downstream to the starting point . if its speed in still water be 6 km / hr , find the total journey time .

0general

in smithtown , the ratio of right - handed people to left - handed people is 3 to 1 and the ratio of men to women is 3 to 2 . if the number of right - handed men is maximized , then what x percent of all the people in smithtown are left - handed women ?

0general

the number of degrees that the hour hand of a clock moves through between noon and 2.30 in the afternoon of the same day is ?

1physics

a rectangular tiled patio is composed of 30 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 30 tiles , and it will still be rectangular . how many rows are in the tile patio before the change in layout ?

3geometry

a row of ants comprised of 102 ants . a man walked upon it and all except 42 were crushed beneath his foot . how many ants are left alive ?

0general

at a certain food stand , the price of each apple is 40 ¢ and the price of each orange is 60 ¢ . mary selects a total of 10 apples and oranges from the food stand , and the average ( arithmetic mean ) price of the 10 pieces of fruit is 54 ¢ . how many oranges must mary put back so that the average price of the pieces of fruit that she keeps is 45 ¢ ?

0general

what percent is 50 gm of 1 kg ?

2gain

the dimensions of a rectangular solid are 6 inches , 5 inches , and 8 inches . if a cube , a side of which is equal to one of the dimensions of the rectangular solid , is placed entirely within thespherejust large enough to hold the cube , what the ratio of the volume of the cube to the volume within thespherethat is not occupied by the cube ?

3geometry

john purchased some shirts and trousers for $ 1300 . he paid $ 500 less for the shirts than he did for the trousers . if he bought 5 shirts and the cost of a shirt is $ 20 less than that of a trouser , how many trousers did he buy ?

0general

a contractor undertakes to complete the construction of a tunnel 720 meters long in 240 days and employs 50 men for the purpose . after 120 days , he finds that only 240 meters of the tunnel is complete . how many more men should be employ in order to complete the work in time ?

1physics

for all integers x > 1 . < x > = 2 x + ( 2 x - 1 ) + ( 2 x - 2 ) + . . . . . . 2 + 1 . what is the value of < 2 > * < 4 > ?

0general

two identical circles intersect such that their centers and the points at which they intersect form a square of side 4 cm . what is the area of the region where the two circles intersect ?

3geometry

pradeep has to obtain 35 % of the total marks to pass . he got 150 marks and failed by 25 marks . the maximum marks are

0general

if 4 people are selected from a group of 6 married couples , what is the probability that none of them would be married to each other ?

4probability

if the length of a rectangle is increased by 20 % and the breadth is reduced by 20 % , what will be the effect on its area ?

3geometry

each light bulb at a hotel is either incandescent or fluorescent . at a certain moment , forty percent of the incandescent bulbs are switched on , and eighty percent of the fluorescent bulbs are switched on . if 75 percent of all the bulbs are switched on at this moment , what percent of the bulbs that are switched on are incandescent ?

2gain

a and b can do a piece of work in 2 days and 6 days respectively . both work for 1 days and then a goes away . find how long will b take to complete the remaining work ?

1physics

karen places a bet with tom that she will beat tom in a car race by 4 miles even if karen starts 4 minutes late . assuming that karen drives at an average speed of 60 mph and tom drives at an average speed of 45 mph , how many h miles will tom drive before karen wins the bet ?

1physics

rs . 1210 were divided among 3 person p , q , r so that p : q = 5 : 4 and q : r = 9 : 10 . then r gets the amount .

0general

in what ratio should a variety of rice costing rs . 7 per kg be mixed with another variety of rice costing rs . 14.50 per kg to obtain a mixture costing rs . 9.75 per kg ?

5other

if 10 is added to thrice a number and this sum is multiplied by 5 , the result is the same as if the number is multiplied by 5 and 13 is added to the product . what is the number ?

0general

if a 2 + b 2 + c 2 = 390 and ab + bc + ca = 5 , then a + b + c is

0general

in an office in singapore there are 60 % female employees . 50 % of all the male employees are computer literate . if there are total 62 % employees computer literate out of total 1500 employees , then the no . of female employees who are computer literate ?

2gain

what will be the remainder when ( 27 ^ 27 ) + 27 is divided by 28 ?

0general

a man has some hens and cows . if the number of heads be 48 and the number of feet equals 140 , then the number of hens will be

0general

the cash realised on selling a 14 % stock is rs . 120.50 , brokerage being 1 / 4 % is

0general

a and b are two partially filled buckets of water . if 7 liters are transferred from a to b , then a would contain one - third of the amount of water in b . alternatively , if 7 liters are transferred from b to a , b would contain one - half of the amount of water in a . bucket a contains how many liters of water ?

0general

how many liters of water must be evaporated from 50 liters of a 2 percent sugar solution to get a 5 percent sugar solution ?

2gain

an equilateral triangle t 2 is formed by joining the mid points of the sides of another equilateral triangle t 1 . a third equilateral triangle t 3 is formed by joining the mid - points of t 2 and this process is continued indefinitely . if each side of t 1 is 50 cm , find the sum of the perimeters of all the triangles .

3geometry

three walls have wallpaper covering a combined area of 300 square meters . by overlapping the wallpaper to cover a wall with an area of 180 square meters , the area that is covered by exactly two layers of wallpaper is 40 square meters . what is the area that is covered with three layers of wallpaper ?

3geometry

a trained covered x km at 40 kmph and another 2 x km at 20 kmph . find the average speed of the train in covering the entire 4 x km .

0general

if n = 2.0254 and n * is the decimal obtained by rounding n to the nearest hundredth , what is the value of n * – n ?

0general

find the sum lend at c . i . at 5 p . c per annum will amount to rs . 240 in 2 years ?

0general

a bag contains 7 green balls and 7 white balls . if two balls are drawn simultaneously , what is the probability that both balls are the same colour ?

5other

a vendor sells 60 percent of apples he had and throws away 15 percent of the remainder . next day he sells 50 percent of the remainder and throws away the rest . what percent of his apples does the vendor throw ?

2gain

the radius of a cylinder is 8 m , height 14 m . the volume of the cylinder is :

3geometry

average of money that group of 4 friends pay for rent each month is $ 800 . after one persons rent is increased by 20 % the new mean is $ 880 . what was original rent of friend whose rent is increased ?

0general

when a student joe , weighing 43 kg , joins a group of students whose average weight is 30 kg , the average weight goes up by 1 kg . subsequently , if two students , excluding joe , leave the group the average weight comes back to 30 kg . what is the difference between the average weight of the two students who left and the weight of joe ?

0general

while working alone at their respective constant rates , server p uploads 480 files in 4 hours and server y uploads 480 files in 8 hours . if all files uploaded by these servers are the same size , how long would it take the two servers , working at the same time and at their respective constant rates , to process a total of 480 files ?

1physics

0.0203 x 2.92 / 0.0073 x 14.5 x 0.7 = ?

0general

the speed of a train is 90 kmph . what is the distance covered by it in 30 minutes ?

1physics

what is the smallest positive integer x such that 280 - x is the cube of a positive integer

0general

in a kilometer race , a beats b by 60 meters or 15 seconds . what time does a take to complete the race ?

1physics

in a certain diving competition , 5 judges score each dive on a scale from 1 to 10 . the point value of the dive is obtained by dropping the highest score and the lowest score and multiplying the sum of the remaining scores by the degree of difficulty . if a dive with a degree of difficulty of 3.2 received scores of 7.5 , 8.3 , 9.0 , 6.0 , and 8.6 , what was the point value of the dive ?

0general

train starts from amritsar to bombay at 9 am . it reaches destination after 3 days at 9 : 30 am . every day a train starts . how many trains does it come across on the way ?

1physics

if a ( a - 9 ) = 10 and b ( b - 9 ) = 10 , where a ≠ b , then a + b =

0general

there are 12 teams in a certain league and each team plays each of the other teams exactly twice . if each game is played by 2 teams , what is the total number of games played ?

0general

at what rate percent per annum will the simple interest on a sum of money be 1 / 5 of the amount in 10 years ?

2gain

a man can do a job in 15 days . his father takes 10 days and his son finishes it in 25 days . how long will they take to complete the job if they all work together ?

1physics

in a neighborhood having 90 households , 11 did not have either a car or a bike . if 22 households had a both a car and a bike and 44 had a car , how many had bike only ?

5other

the 3 digits of a number add up to 11 . the number is divisible by 5 . the leftmost digit is double the middle digit . what is the product of the 3 digits ?

0general

if a randomly selected positive single digit multiple of 3 is multiplied by a randomly selected prime number less than 20 , what is the probability t that this product will be a multiple of 45 ?

0general

uba capital recently bought brand new vehicles for office use . uba capital only went for toyota and honda and bought more of toyota than honda at the ratio of 8 : 2 . if 80 % of the toyota bought and 20 % of the honda bought were suv â € ™ s . how many suv â € ™ s did uba capital buy in the aforementioned purchase ?

5other

10 ^ ( 655 ) ã · 10 ^ ( 650 ) = ?

0general

a corporation that had $ 115.19 billion in profits for the year paid out $ 250.10 million in employee benefits . approximately what percent of the profits were the employee benefits ? ( note : 1 billion = 10 ^ 9 )

0general

a reduction of 10 % in the price of salt enables a lady to obtain 10 kgs more for rs . 100 , find the original price per kg ?

2gain

the average ( arithmetic mean ) of 16 students first quiz scores in a difficult english class is 62.5 . when one student dropped the class , the average of the remaining scores increased to 62.0 . what is the quiz score of the student who dropped the class ?

0general

the triplicate ratio of 2 : 3 is ?

5other

if 15 lions can kill 15 deers in 15 minutes how long will it take 100 lions to kill 100 deers ?

1physics