GMAT Math : Understanding work problems

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Work Problems

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?

Possible Answers:

$20.3\; min$

$63.3\; min$

$30\; min$

None of the other answers are correct

$13.7\; min$

Correct answer:

$20.3\; min$

Explanation:

Think of this as a rate problem, with rate being measured in "tanks per minute".

$Work = rate \times time$

The pipes can fill the tank up at rates of $\frac{1}{60}$ , $\frac{1}{80}$ , and $\frac{1}{50}$ tanks per minute, respectively.

In the time it takes to fill the tank, the three pipes fill up $\frac{1}{60}t$ of the tank, $\frac{1}{80}t$ of the tank, and $\frac{1}{50}t$ of the tank, respectively. Add the amounts of work done by the three tanks to get the total amount of work - one job.

$\frac{1}{60}t +\frac{1}{80}t +\frac{1}{50}t = 1$

$\left (\frac{1}{60} +\frac{1}{80} +\frac{1}{50} \right ) t= 1$

$\left (\frac{20}{1,200} +\frac{15}{1,200} +\frac{24}{1,200} \right ) t= 1$

$\frac{59}{1,200}t= 1$

$t= \frac{1,200}{59} \approx 20.3 \; min$

Report an Error

Example Question #1 : Work Problems

Which of the following is not a prime number?

Possible Answers:

Correct answer:

Explanation:

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.

Report an Error

Example Question #1 : Understanding Work Problems

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?

Possible Answers:

$8:18\textrm{ AM}$

$8:30\textrm{ AM}$

$8:21\textrm{ AM}$

$8:26\textrm{ AM}$

$8:35\textrm{ AM}$

Correct answer:

$8:26\textrm{ AM}$

Explanation:

Look at the work rates as "tanks per minute", not "minutes per tank".

The two pipes can fill the tank up at $\frac{1}{45}$ tanks per minute and $\frac{1}{40}$ 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 t-10 .

Since rate multiplied by time is equal to work, then the two pipes fill up $\frac{1}{45} t$ and $\frac{1}{40} \left ( t-10\right )$ tanks; together, they filled up $\frac{1}{45} t + \frac{1}{40} \left ( t-10\right )$ tank - one tank. This sets up the equation to be solved:

$\frac{1}{45} t + \frac{1}{40} \left ( t-10\right ) =1$

$360 \cdot \left [ \frac{1}{45} t + \frac{1}{40} \left ( t-10\right ) \right ] =360 \cdot 1$

$\frac{360}{45} t + \frac{360}{40} \left ( t-10\right ) =360$

$8 t + 9 \left ( t-10\right ) =360$

8 t + 9 t-90=360

17t-90=360

17t=450

$t = 450 \div17 \approx 26.47$

This rounds to 26 minutes after the first pipe is opened, or 8:26 AM.

Report an Error

Example Question #2 : Understanding Work Problems

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?

Possible Answers:

$1:08 \textrm{ PM}$

$1:35 \textrm{ PM}$

$1:27 \textrm{ PM}$

$1:42 \textrm{ PM}$

$1:19 \textrm{ PM}$

Correct answer:

$1:19 \textrm{ PM}$

Explanation:

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 $\frac{1}{4}$ greenhouse per hour.

Sharon can paint one greenhouse in four and a half hours, or $\frac{1}{4 \frac{1}{2}} = \frac{1}{ \left ( \frac{9}{2} \right )} = \frac{2} {9}$ greenhouses per hour. Grag can paint one greenhouse in three and a half hours, or $\frac{1}{3 \frac{1}{2}} = \frac{1}{ \left ( \frac{7}{2} \right )} = \frac{2} {7}$ 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 $\frac{1}{4} t$ , $\frac{2}{9} t$ , and $\frac{2}{7} t$ of the greenhouse, respectively; these three shares add up to one greenhouse, so we can set up and solve this equation:

$\frac{1}{4} t + \frac{2}{9} t + \frac{2}{7} t = 1$

$\frac{ 252}{1} \cdot \left ( \frac{1}{4} t + \frac{2}{9} t + \frac{2}{7} t \right )=252 \cdot 1$

$\frac{ 252}{1} \cdot \frac{1}{4} t +\frac{ 252}{1} \cdot \frac{2}{9} t +\frac{ 252}{1} \cdot \frac{2}{7} t =252$

63 t +56 t +72 t =252

191 t =252

$191 t \div 191 =252 \div 191$

$t = \frac{252}{191 }$

Let's convert this to minutes by multiplying by 60:

$\frac{252}{191 } \times 60 \approx 79.2$

This rounds to one hour and 19 minutes, so the three finish at $1:19 \textrm{ PM}$ .

Report an Error

Example Question #2 : Work Problems

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?

Possible Answers:

110 widgets

55 widgets

44 widgets

176 widgets

220 widgets

Correct answer:

110 widgets

Explanation:

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:

$5 machines\cdot 11widgets/min \cdot 2min = 110 widgets$ .

Report an Error

Example Question #4 : Understanding Work Problems

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?

Possible Answers:

$35\ minutes$

$140\ minutes$

$56\ minutes$

$112\ minutes$

$70\ minutes$

Correct answer:

$56\ minutes$

Explanation:

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 $\small \frac{1}{25}$ 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 $\small -\small \frac{1}{45}$ jobs per minute.

Now, think of this as a rate problem. In minutes, the drain does

$\small \small \frac{1}{25} x$ jobs

and the pipe does

$\small \small -\small \frac{1}{45} x$ jobs.

Together they do 1 job, the draining of the whole tank.

Set up an equation to solve for x:

$\small \small \small \frac{1}{25}x + \left (- \frac{1}{45} \right )x = 1$

$\small \small \small \small \frac{1}{25}x - \frac{1}{45} \right )x = 1$

$\small \small \left (\small \small \frac{1}{25} - \frac{1}{45} \right ) \right )x = 1$

$\small \small \small \left (\small \small \frac{9}{225} - \frac{5}{225} \right ) \right )x = 1$

$\small \small \small \small \left (\small \small \frac{4}{225} \right )x = 1$

$\small \small \small \small \small \left (\small \small \frac{225}{4} \right )\small \small \small \small \left (\small \small \frac{4}{225} \right )x = \small \small \small \small \left (\small \small \frac{225}{4} \right )1$

x=56.25 , which rounds to 56 minutes.

Report an Error

Example Question #26 : Problem Solving Questions

What is the sum of the first seven prime numbers?

Possible Answers:

Correct answer:

Explanation:

The first seven prime numbers are: 2,3,5,7,11,13,17

To find the sum, all numbers must be added:

2+3+5+7+11+13+17=58

Report an Error

Example Question #27 : Problem Solving Questions

What happens to the volume of a rectangular prism if the length, width, and height are doubled?

Possible Answers:

Cannot be determined without the original dimensions

New volume is times the old volume

Correct answer:

New volume is times the old volume

Explanation:

$V=l\cdot w\cdot h$

$New\ V=2l\cdot 2w\cdot 2h$

$New\ V=8\cdot l\cdot w\cdot h$

Then, the new volume is times the old volume.

Report an Error

Example Question #5 : Understanding Work Problems

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 250 shoes. How many hours will it take for the factory to complete the packages necessary to ship the order?

Possible Answers:

hours

2.5 hours

4.25 hours

hours

7.5 hours

Correct answer:

hours

Explanation:

If in an hour produces packages and produces packages respectively, then both machines produce 35 + 15 = 50 packages in an hour altogether.

Since the order requires 250 packages, the factory will take:

$\frac{250}{50}=5 \text{ hours}$

Therefore, it will take 5 hours for the factory to complete the packages necessary for the shipment.

Report an Error

Example Question #8 : Work Problems

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?

Possible Answers:

$\frac{7}{2}$

$\frac{7}{12}$

$\frac{5}{12}$

$\frac{1}{6}$

$\frac{5}{12}$

Correct answer:

$\frac{7}{2}$

Explanation:

The following table shows the amount of work done by each pump during the hour when they are both working.

Work_problem

The total work done by both pumps in an hour is:

$\frac{1}{4}+\frac{1}{6}=\frac{5}{12}$

The remaining work to be completed by the slowest pump is:

$1-\frac{5}{12}=\frac{7}{12}$

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:

$\frac{7}{12}\div\frac{1}{6}=\frac{7}{12}\times6=\frac{7}{2}$

It will take the slowest pump 7/2 hours to complete filling the pool.

Report an Error

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Algebra Tutors in Chicago, Statistics Tutors in Denver, Biology Tutors in Atlanta, Chemistry Tutors in Seattle, ACT Tutors in Chicago, LSAT Tutors in Los Angeles, Computer Science Tutors in Boston, LSAT Tutors in Denver, GRE Tutors in Denver, SAT Tutors in Washington DC

Popular Courses & Classes

GMAT Courses & Classes in Denver, SSAT Courses & Classes in San Francisco-Bay Area, SAT Courses & Classes in Phoenix, ACT Courses & Classes in Denver, Spanish Courses & Classes in Washington DC, MCAT Courses & Classes in Phoenix, MCAT Courses & Classes in Washington DC, SAT Courses & Classes in Seattle, MCAT Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in Philadelphia

Popular Test Prep

LSAT Test Prep in Washington DC, LSAT Test Prep in San Francisco-Bay Area, ISEE Test Prep in Seattle, MCAT Test Prep in Philadelphia, ISEE Test Prep in New York City, ACT Test Prep in Philadelphia, MCAT Test Prep in Chicago, GMAT Test Prep in Phoenix, GMAT Test Prep in Dallas Fort Worth, SSAT Test Prep in San Francisco-Bay Area

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

Email address:
Your name:
Feedback:

GMAT Math : Understanding work problems

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1 : Work Problems

Example Question #1 : Work Problems

Example Question #1 : Understanding Work Problems

Example Question #2 : Understanding Work Problems

Example Question #2 : Work Problems

Example Question #4 : Understanding Work Problems

Example Question #26 : Problem Solving Questions

Example Question #27 : Problem Solving Questions

Example Question #5 : Understanding Work Problems

Example Question #8 : Work Problems

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details