GMAT Math : Understanding work problems

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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

$30\; min$

$13.7\; min$

$63.3\; min$

$20.3\; min$

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.

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

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

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

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

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

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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.

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Example Question #2 : 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:

$8:26\textrm{ AM}$

$8:18\textrm{ AM}$

$8:21\textrm{ AM}$

$8:30\textrm{ AM}$

$8:35\textrm{ AM}$

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.

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Example Question #2 : 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:

$1:42 \textrm{ PM}$

$1:08 \textrm{ PM}$

$1:27 \textrm{ PM}$

$1:35 \textrm{ PM}$

$1:19 \textrm{ PM}$

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 $1:19 \textrm{ PM}$ .

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Example Question #3 : 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:

176 widgets

55 widgets

44 widgets

220 widgets

110 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:

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

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Example Question #4 : 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:

$112\ minutes$

$140\ minutes$

$70\ minutes$

$56\ minutes$

$35\ minutes$

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.

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Example Question #6 : Work Problems

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

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Example Question #7 : 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

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.

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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

7.5 hours

hours

4.25 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.

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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.

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GMAT Math : Understanding work problems

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1 : Understanding Work Problems

Example Question #1 : Work Problems

Example Question #2 : Work Problems

Example Question #2 : Work Problems

Example Question #3 : Work Problems

Example Question #4 : Work Problems

Example Question #6 : Work Problems

Example Question #7 : Work Problems

Example Question #5 : Understanding Work Problems

Example Question #8 : Work Problems

All GMAT Math Resources

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