GMAT Math : Understanding work problems

Study concepts, example questions & explanations for GMAT Math

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Example Questions

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Example Question #1 : Understanding 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:

None of the other answers are correct

 

Correct answer:

 

Explanation:

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.

Example Question #2 : Understanding 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.

Example Question #3 : Understanding Work Problems

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 field?

Possible Answers:

Correct answer:

Explanation:

First, find the area of the triangular field:

The garden takes up 40% of the field, therefore:

Area of garden=

Area of garden=

Example Question #4 : 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:

Correct answer:

Explanation:

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.

Example Question #5 : 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:

Correct answer:

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  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 

Example Question #6 : Understanding 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:

44 widgets

110 widgets

176 widgets

55 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.

Example Question #7 : 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:

Correct answer:

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  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.

Example Question #8 : Understanding Work Problems

What is the sum of the first seven prime numbers?

Possible Answers:

Correct answer:

Explanation:

The first seven prime numbers are:

To find the sum, all numbers must be added:

Example Question #9 : Understanding Work Problems

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

Possible Answers:

New volume is  times the old volume

New volume is  times the old volume

New volume is  times the old volume

New volume is  times the old volume

Cannot be determined without the original dimensions

Correct answer:

New volume is  times the old volume

Explanation:

Then, the new volume is  times the old volume.

Example Question #10 : 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  shoes. How many hours will it take for the factory to complete the packages necessary to ship the order?

Possible Answers:

 hours

 hours

 hours

 hours

 hours

Correct answer:

 hours

Explanation:

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.

 

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