Work Problems - GMAT Quantitative
Card 1 of 160
If 2 machines working at the same rate create 88 widgets in 4 minutes, how many widgets can 5 machines make in 2 minutes, working at the same rate?
If 2 machines working at the same rate create 88 widgets in 4 minutes, how many widgets can 5 machines make in 2 minutes, working at the same rate?
Tap to reveal answer
To find the number of widgets created by each machine separately, divide 88 by 2:
88/2=44
This is the number of widgets created by 1 machine in 4 minutes.
To find the number of widgets in 1 minute, divide 44 by 4: 44/4minutes = 11widgets/min
Use this rate to find the answer:
5 machinescdot 11widgets/min cdot 2min = 110 widgets.
To find the number of widgets created by each machine separately, divide 88 by 2:
88/2=44
This is the number of widgets created by 1 machine in 4 minutes.
To find the number of widgets in 1 minute, divide 44 by 4: 44/4minutes = 11widgets/min
Use this rate to find the answer:
5 machinescdot 11widgets/min cdot 2min = 110 widgets.
← Didn't Know|Knew It →
The inlet pipe leading into a water tank can fill the tank in 45 minutes; the drain can empty the tank in 25 minutes.
One day while draining the tank, someone left the inlet pipe on.
To the nearest minute, how long did it take for the tank to drain completely?
The inlet pipe leading into a water tank can fill the tank in 45 minutes; the drain can empty the tank in 25 minutes.
One day while draining the tank, someone left the inlet pipe on.
To the nearest minute, how long did it take for the tank to drain completely?
Tap to reveal answer
Let 
be the number of minutes that it takes to drain the tank.
Think of emptying the tank as one job. Then the drain can do one job in 25 minutes, or 
jobs per minute.
Now, think of the inlet pipe as doing a "negative" job - it is doing the opposite of emptying the tank, working against the drain. It is doing "negative one" job in 45 minutes, or 
jobs per minute.
Now, think of this as a rate problem. In 
minutes, the drain does
jobs
and the pipe does
jobs.
Together they do 1 job, the draining of the whole tank.
Set up an equation to solve for x:
, which rounds to 56 minutes.
Let
Think of emptying the tank as one job. Then the drain can do one job in 25 minutes, or
Now, think of the inlet pipe as doing a "negative" job - it is doing the opposite of emptying the tank, working against the drain. It is doing "negative one" job in 45 minutes, or
Now, think of this as a rate problem. In
and the pipe does
Together they do 1 job, the draining of the whole tank.
Set up an equation to solve for x:
← Didn't Know|Knew It →
To the nearest hour, how many hours would it take three koala bears - Stuffy, Fluffy, and Muffy - to eat all of the leaves on Mr. Meany's farm if:
Stuffy can eat all the leaves alone in three times as much time that the three together can eat them;
Fluffy can eat all the leaves alone in four times as much time that the three together can eat them; and,
Muffy can eat all the leaves in twenty-four hours?
To the nearest hour, how many hours would it take three koala bears - Stuffy, Fluffy, and Muffy - to eat all of the leaves on Mr. Meany's farm if:
Stuffy can eat all the leaves alone in three times as much time that the three together can eat them;
Fluffy can eat all the leaves alone in four times as much time that the three together can eat them; and,
Muffy can eat all the leaves in twenty-four hours?
Tap to reveal answer
Let 
be the number of hours it takes the three koala bears together to eat the leaves. Then Stuffy can eat the leaves in 
hours, Fluffy can eat them in 
hours, and Muffy can eat them in 24 hours. Therefore, in one hour, Stuffy, Fluffy, and Muffy can eat 
, 
, and 
of the leaves, respectively, and in 
hours, Stuffy can eat 
of the leaves, Fluffy can eat 
of the leaves, and Muffy can eat 
of the leaves. Since together they are eating all of the leaves, the sum of the three amounts is one task, so we solve for 
in the equation:
It takes 10 hours for all three koalas together to eat all the leaves on Mr. Meany's farm.
Let
It takes 10 hours for all three koalas together to eat all the leaves on Mr. Meany's farm.
← Didn't Know|Knew It →
A tank has three inlet pipes. One, by itself, can fill the tank in one hour; another, by itself, can fill the tank in one hour and twenty minutes ; a third, by itself, can fill the tank in fifty minutes alone. If all three are on, then, to the nearest tenth of a minute, how long does it take to fill the tank?
A tank has three inlet pipes. One, by itself, can fill the tank in one hour; another, by itself, can fill the tank in one hour and twenty minutes ; a third, by itself, can fill the tank in fifty minutes alone. If all three are on, then, to the nearest tenth of a minute, how long does it take to fill the tank?
Tap to reveal answer
Think of this as a rate problem, with rate being measured in "tanks per minute".
The pipes can fill the tank up at rates of 
, 
, and 
tanks per minute, respectively.
In the time 
it takes to fill the tank, the three pipes fill up 
of the tank, 
of the tank, and 
of the tank, respectively. Add the amounts of work done by the three tanks to get the total amount of work - one job.
Think of this as a rate problem, with rate being measured in "tanks per minute".
The pipes can fill the tank up at rates of
In the time
← Didn't Know|Knew It →
In a subdivision, several houses of uniform size and design need to be painted; there are two crews working together to paint them. Without the second crew, the first crew painted the first house in twelve hours; together, the two crews painted the second house in five hours. The second crew will paint the third house without the first crew; how long should it take them?
In a subdivision, several houses of uniform size and design need to be painted; there are two crews working together to paint them. Without the second crew, the first crew painted the first house in twelve hours; together, the two crews painted the second house in five hours. The second crew will paint the third house without the first crew; how long should it take them?
Tap to reveal answer
Let 
be the amount of time it takes for the second crew to paint a house without the first.
Think of this as a rate problem, with rate being measured in "houses per hour" rather than "hours per house". The first crew alone can paint 
house per hour; the second alone can paint 
house per hour; both together can paint 
house per hour.
We can find the portion of the house each crew does in an amount of time by multiplying its rate in house per hour by the time in hourse elapsed.
Let's look at what happens when the two crews are working together over five hours, adding their efforts:
or
The third house will be painted in about 8.6 hours.
Let
Think of this as a rate problem, with rate being measured in "houses per hour" rather than "hours per house". The first crew alone can paint
We can find the portion of the house each crew does in an amount of time by multiplying its rate in house per hour by the time in hourse elapsed.
Let's look at what happens when the two crews are working together over five hours, adding their efforts:
or
The third house will be painted in about 8.6 hours.
← Didn't Know|Knew It →
Which of the following is not a prime number?
Which of the following is not a prime number?
Tap to reveal answer
By definition, a prime number is any number that is greater than 
and is only divisible by 
and itself. Therefore, by definition 
is not a prime number.
By definition, a prime number is any number that is greater than
← Didn't Know|Knew It →
What is the sum of the first seven prime numbers?
What is the sum of the first seven prime numbers?
Tap to reveal answer
The first seven prime numbers are: 
To find the sum, all numbers must be added:
The first seven prime numbers are:
To find the sum, all numbers must be added:
← Didn't Know|Knew It →
If a triangular field has a base of 
and a height of 
, and a garden is taking up 40% of the field. What is the area of the garden?
If a triangular field has a base of
Tap to reveal answer
First, find the area of the triangular field:
The garden takes up 40% of the field, therefore:
Area of garden= 
Area of garden= 
First, find the area of the triangular field:
The garden takes up 40% of the field, therefore:
Area of garden=
Area of garden=
← Didn't Know|Knew It →
What happens to the volume of a rectangular prism if the length, width, and height are doubled?
What happens to the volume of a rectangular prism if the length, width, and height are doubled?
Tap to reveal answer
Then, the new volume is 
times the old volume.
Then, the new volume is
← Didn't Know|Knew It →
Two inlet pipes lead into a large water tank. One pipe can fill the tank in 45 minutes; the second pipe can fill it in 40 minutes. At 8:00 AM, the first pipe is opened; at 8:10 AM, the second one is opened. To the nearest minute, at what time is the tank full?
Two inlet pipes lead into a large water tank. One pipe can fill the tank in 45 minutes; the second pipe can fill it in 40 minutes. At 8:00 AM, the first pipe is opened; at 8:10 AM, the second one is opened. To the nearest minute, at what time is the tank full?
Tap to reveal answer
Look at the work rates as "tanks per minute", not "minutes per tank".
The two pipes can fill the tank up at 
tanks per minute and 
tanks per minute.
Let 
be the time it took, in minutes, to fill the tank up. Then this is the amount of time that the first pipe had to let in water; the amount of time that the second pipe had, in minutes, is 
.
Since rate multiplied by time is equal to work, then the two pipes fill up 
and 
tanks; together, they filled up 
tank - one tank. This sets up the equation to be solved:
This rounds to 26 minutes after the first pipe is opened, or 8:26 AM.
Look at the work rates as "tanks per minute", not "minutes per tank".
The two pipes can fill the tank up at
Let
Since rate multiplied by time is equal to work, then the two pipes fill up
This rounds to 26 minutes after the first pipe is opened, or 8:26 AM.
← Didn't Know|Knew It →
Philip, his wife Sharon, and their son Greg are planning to paint a greenhouse together. Philip can paint the greenhouse alone in four hours; Sharon can paint it alone in four and a half hours; Greg can paint it alone in three and a half hours. If they start at noon and don't stop, when, to the nearest minute, will they finish painting the greenhouse?
Philip, his wife Sharon, and their son Greg are planning to paint a greenhouse together. Philip can paint the greenhouse alone in four hours; Sharon can paint it alone in four and a half hours; Greg can paint it alone in three and a half hours. If they start at noon and don't stop, when, to the nearest minute, will they finish painting the greenhouse?
Tap to reveal answer
This can be solved by looking at their work rates in terms of "greenhouses per hour".
Philip can paint one greenhouse in four hours, or 
greenhouse per hour.
Sharon can paint one greenhouse in four and a half hours, or 
greenhouses per hour. Grag can paint one greenhouse in three and a half hours, or 
greenhouses per hour. If 
is the number of hours that it takes for the three to paint the greenhouse, then Philip, Sharon, and Grag will paint 
, 
, and 
of the greenhouse, respectively; these three shares add up to one greenhouse, so we can set up and solve this equation:
Let's convert this to minutes by multiplying by 60:
This rounds to one hour and 19 minutes, so the three finish at 
.
This can be solved by looking at their work rates in terms of "greenhouses per hour".
Philip can paint one greenhouse in four hours, or
Sharon can paint one greenhouse in four and a half hours, or
Let's convert this to minutes by multiplying by 60:
This rounds to one hour and 19 minutes, so the three finish at
← Didn't Know|Knew It →
A shoe factory has two pieces of equipment to package the shoes: 
and 
.
is a better performer and makes 
packages an hour while 
produces only 
packages an hour.
The company has an order to ship 
shoes. How many hours will it take for the factory to complete the packages necessary to ship the order?
A shoe factory has two pieces of equipment to package the shoes:
The company has an order to ship
Tap to reveal answer
If in an hour 
produces 
packages and 
produces 
packages respectively, then both machines produce 
packages in an hour altogether.
Since the order requires 
packages, the factory will take:
Therefore, it will take 5 hours for the factory to complete the packages necessary for the shipment.
If in an hour
Since the order requires
Therefore, it will take 5 hours for the factory to complete the packages necessary for the shipment.
← Didn't Know|Knew It →
A large water tank has an inlet pipe that can fill the tank completely in three hours, and a drain that can empty it completely in five hours. On one occasion, two hours after the filling of the tank started, the drain was accidentally opened. The error was not immediately discovered, and the drain was not closed until the tank was completely filled. Which of the following comes closest to the number of hours it took to fill the tank?
A large water tank has an inlet pipe that can fill the tank completely in three hours, and a drain that can empty it completely in five hours. On one occasion, two hours after the filling of the tank started, the drain was accidentally opened. The error was not immediately discovered, and the drain was not closed until the tank was completely filled. Which of the following comes closest to the number of hours it took to fill the tank?
Tap to reveal answer
Let 
be the number of hours it took to fill the tank.
The inlet pipe takes three hours to fill the tank, so it can fill 
tank in one hour, and 
tank in 
hours.
The drain can empty the tank in five hours, so it can remove 
tank in one hour; since it started two hours after the filling started, it worked for 
hours to empty 
tank worth of water.
The work performed by the drain was against that performed by the inlet pipe, so the difference of their results is one tank of water. Therefore, the equation to solve for 
is
Let
The inlet pipe takes three hours to fill the tank, so it can fill
The drain can empty the tank in five hours, so it can remove
The work performed by the drain was against that performed by the inlet pipe, so the difference of their results is one tank of water. Therefore, the equation to solve for
← Didn't Know|Knew It →
Two pumps are used to fill a pool. One pump can fill the pool by itself in 
hours while the oher can fill the pool by itself in 
hours. Both pumps are open for an hour when the fastest pump stops working. How long will it take the slower pump to complete filling the pool?
Two pumps are used to fill a pool. One pump can fill the pool by itself in
Tap to reveal answer
The following table shows the amount of work done by each pump during the hour when they are both working.
The total work done by both pumps in an hour is:
The remaining work to be completed by the slowest pump is:
The time taken by the slowest pump to complete filling the pool is the quotient of the remaining work by the work rate of the slowest pump:
It will take the slowest pump 7/2 hours to complete filling the pool.
The following table shows the amount of work done by each pump during the hour when they are both working.
The total work done by both pumps in an hour is:
The remaining work to be completed by the slowest pump is:
The time taken by the slowest pump to complete filling the pool is the quotient of the remaining work by the work rate of the slowest pump:
It will take the slowest pump 7/2 hours to complete filling the pool.
← Didn't Know|Knew It →
When working at the same constant rate, 
temporary workers at a company can classify 
files in a day. How many temporary workers would be needed to classify 
files in a day?
When working at the same constant rate,
Tap to reveal answer
All five workers have the same work rate, therefore they all complete an equal portion of the work done. Each worker's rate is:
Each worker can then classify 50 files in a day.
To classify 1250 files, the company therefore needs the following number of temporary workers:
Twenty-five workers are needed to classify the 1250 files in a day.
All five workers have the same work rate, therefore they all complete an equal portion of the work done. Each worker's rate is:
Each worker can then classify 50 files in a day.
To classify 1250 files, the company therefore needs the following number of temporary workers:
Twenty-five workers are needed to classify the 1250 files in a day.
← Didn't Know|Knew It →
Bryan and his brother Philip, working together, can paint their father's house in a total of sixteen hours. Bryan, working alone, would take twenty-five hours. Which of the following is closest to the number of hours it would take Philip to paint the house, working alone?
Bryan and his brother Philip, working together, can paint their father's house in a total of sixteen hours. Bryan, working alone, would take twenty-five hours. Which of the following is closest to the number of hours it would take Philip to paint the house, working alone?
Tap to reveal answer
Let 
be the amount of time it would take for Phillip to paint the house by himself. Then he can paint 
of a house per hour. Similarly, since Bryan can paint the house by himself in 25 hours, he can paint 
of the house per hour.
Since the two brothers together paint one house in 16 hours, Bryan's share of the work is to paint 
of one house. Phillip's share of the work is to paint 
of the house. Their shares together add up to one house, so the problem to be solved is
Cross-multiply and solve:
hours.
Of the given choices, 45 hours comes closest.
Let
Since the two brothers together paint one house in 16 hours, Bryan's share of the work is to paint
Cross-multiply and solve:
Of the given choices, 45 hours comes closest.
← Didn't Know|Knew It →
A large water tank has an inlet pipe that can fill the tank completely in two and one-half hours, and a drain that can empty it completely in three and one-half hours. On one occasion, when the tank was being filled, the drain was left open; the drain was not closed until the tank was completely full. Which of the following answers comes closest to the number of hours it took to fill the tank?
A large water tank has an inlet pipe that can fill the tank completely in two and one-half hours, and a drain that can empty it completely in three and one-half hours. On one occasion, when the tank was being filled, the drain was left open; the drain was not closed until the tank was completely full. Which of the following answers comes closest to the number of hours it took to fill the tank?
Tap to reveal answer
Let 
be the number of hours it took to fill the tank.
The inlet pipe takes 
hours to fill the tank, so it fills 
tank per hour. The drain empties the tank in 
hours, so it empties 
tank per hour. In 
hours, the inlet pipe filled 
tanks of water, but the drain let out 
tanks of water; the one tank of water was the difference of these amounts, so
This makes 9 hours the correct response.
Let
The inlet pipe takes
This makes 9 hours the correct response.
← Didn't Know|Knew It →
Together, Mary and I, can trade stocks at a rate of 
stocks every 
minutes. I alone on the other hand can only trade 
stock every 
minutes. How fast can Mary trade, alone?
Together, Mary and I, can trade stocks at a rate of
Tap to reveal answer
To solve this problem, we need to set up an equation as follows
,.
is Mary's rate.
By simply manipulating the terms, we end up with
, which is the final answer.
To solve this problem, we need to set up an equation as follows
By simply manipulating the terms, we end up with
← Didn't Know|Knew It →
It takes Samuel thirty minutes to make a notebook cover and forty-five minutes to make a book cover. How many hours will it take Samuel to make thirteen notebook covers and three times as many book covers?
It takes Samuel thirty minutes to make a notebook cover and forty-five minutes to make a book cover. How many hours will it take Samuel to make thirteen notebook covers and three times as many book covers?
Tap to reveal answer
To begin, convert minutes to hours for each project.
Notebook Cover: 
Samuel is making thirteen of these, so we need to multiply the result by thirteen. 
is the amount of time Samuel needs to make thirteen notebook covers.
Book Cover: 
Samuel is making three times as many book covers as he is making notebook covers. 
, so he is making 
book covers.
It will take Samuel 
to make 
book covers.
Add up the calculated times to get the total number of hours it will take Samuel to make the given number of notebook covers and book covers:
. That's almost a full work-week of work!
To begin, convert minutes to hours for each project.
Notebook Cover:
Samuel is making thirteen of these, so we need to multiply the result by thirteen.
Book Cover:
Samuel is making three times as many book covers as he is making notebook covers.
It will take Samuel
Add up the calculated times to get the total number of hours it will take Samuel to make the given number of notebook covers and book covers:
← Didn't Know|Knew It →
A doughnut factory has a machine that takes four hours and twenty minutes to make 
. Another machine is brought in that can do the same job in 
. It is decided to go ahead and allow both machines to work alongside each other until the older machine is worn out.
How long does it take for the 
working together to make 
(Choose the time that is closest to the actual time.)
A doughnut factory has a machine that takes four hours and twenty minutes to make
How long does it take for the
Tap to reveal answer
The first machine can make 
; this is
doughnuts per minute.
Similarly, the second machine can make 
; this is
doughnuts per minute.
Working together, the machines make
doughnuts per minute, or, equivalently, 
.
.
The first machine can make
Similarly, the second machine can make
Working together, the machines make
doughnuts per minute, or, equivalently,
← Didn't Know|Knew It →