GMAT Math : GMAT Quantitative Reasoning

Study concepts, example questions & explanations for GMAT Math

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Example Questions

Example Question #1 : Understanding 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:

Correct answer:

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:

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.

 

Example Question #31 : Problem Solving Questions

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?

Possible Answers:

Correct answer:

Explanation:

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.

 

Example Question #32 : Problem Solving Questions

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?

Possible Answers:

Correct answer:

Explanation:

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

Example Question #11 : Understanding Work Problems

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?

Possible Answers:

Correct answer:

Explanation:

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.

Example Question #11 : Work Problems

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?

Possible Answers:

Correct answer:

Explanation:

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.

Example Question #33 : Problem Solving Questions

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?

Possible Answers:

Correct answer:

Explanation:

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.

Example Question #34 : Problem Solving Questions

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?

Possible Answers:

Correct answer:

Explanation:

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!

Example Question #35 : Problem Solving Questions

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? 

Possible Answers:

Correct answer:

Explanation:

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.

Example Question #31 : Word Problems

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.)

Possible Answers:

Correct answer:

Explanation:

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, .

.

 

Example Question #31 : Problem Solving Questions

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?

Possible Answers:

Correct answer:

Explanation:

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.

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