GMAT Math : GMAT Quantitative Reasoning

Study concepts, example questions & explanations for GMAT Math

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Example Questions

Example Question #4 : Calculating Profit

A non-profit organization is selling shirts to raise money. They purchase 500 shirts at a cost of $5 per shirt. During the course of the month, they are only able to sell 388 shirts. They donate the extra shirts. If the  shirts sell for $13 each, how much does the organization earn/lose during this campaign?

Possible Answers:

$3,104

$3,594

$2,544

$2,328

$4,000

Correct answer:

$2,544

Explanation:

To calculate profit, we find the total revenue and subtract the total expense.

The total revenue is the amount of money made from selling 388 shirts:

The total expense is the amount of money spent on buying 500 shirts:

 

Example Question #5 : Calculating Profit

Find the number of units, , that a company must sell to break even if the profit equation is .

Possible Answers:

Correct answer:

Explanation:

Break even profit is . Plug this value into the equation to solve for the number of units:

Example Question #151 : Word Problems

Last year, a car dealer purchased four cars for $5,000 each, and then later in the year he bought eight more cars for $7,000 each.  If this year the car dealer sells the 12 cars for a combined total of $126,000, what is his net profit?

Possible Answers:

Correct answer:

Explanation:

Calculate the net profit by subtracting the cost of the cars from the gross profit:

 

 

Example Question #152 : Word Problems

It costs $15,000 a month to operate Acme Widgets, Inc, plus $0.25 for every widgets produced.  Each widget sells for $0.35.  If gross profit is measured by the total dollar amount of sales minus operating and production costs, how many widgets would Acme Widgets, Inc. have to sell to make a profit of $25,000?

Possible Answers:

375,000

25,000

600,000

550,000

400,000

Correct answer:

400,000

Explanation:

We need to turn the word problem into a mathematical equation, and solve.

The basic profit equation is:

Where G = gross profit, R = revenue, F = fixed or operating costs, and V = variable or production costs.

We know that we want our gross profit to be $25,000, so .

Now, R is revenue, the money that the company earns by selling its product.  The company earns $0.35 for every widget sold, so , where w = number of widgets sold.

F is the operating cost, which is $15,000.

 

V is the cost of producing the widgets, which is $0.25 per widget.

 

Plugging in our variables, we get:

The company would have to sell 400,000 widgets to make a profit of $25,000

Example Question #153 : Word Problems

Read the problem below:

The French Club wants to make and sell cookies in order to raise $500 for a field trip. The equipment they want to use costs $400 to rent and to operate, and the ingredients for the cookies cost 45 cents per cookie. The French Club wants to sell the cookies for $2 each. At this price, how many cookies will they need to sell in order to earn back the money they paid for the ingredients and the equipment rental and make a profit of $500?

If  is the number of cookies sold, then which of the following equations represents the cost function?

Possible Answers:

Correct answer:

Explanation:

Each cookie costs 45 cents, or $0.45, to make, so the price of the ingredients will be $0.45 times the number of cookies, or 

The other expense is a flat price of the rental of the equipment, $400. 

Add the expressions to get the cost function

Example Question #151 : Word Problems

Read the problem below:

The German Club wants to make and sell cookies in order to raise $500 for a field trip. The equipment they want to use costs $400 to rent and to operate, and the ingredients for the cookies cost 45 cents per cookie. The German Club wants to sell the cookies for $2.25 each. At this price, how many cookies will they need to sell in order to earn back the money they paid for the ingredients and the equipment rental and make a profit of $500?

If  is the number of cookies sold, then which of the following equations represents the revenue function?

Possible Answers:

Correct answer:

Explanation:

The money raised from each cookie sold will be $2.25, so this is to be multilplied by number of cookies  to obtain the revenue in terms of . Therefore, the revenue function is .

Example Question #151 : Word Problems

Read the problem below:

The Russian Club wants to make and sell cookies in order to raise $800 for a field trip. The equipment they want to use costs $350 to rent and to operate, and the ingredients for the cookies cost 35 cents per cookie. The Russian Club wants to sell the cookies for $1.75 each. At this price, how many cookies will they need to sell in order to earn back the money they paid for the ingredients and the equipment rental and make a profit of $800?

If  is the number of cookies sold, then which of the following inequalities can be solved to obtain an answer to this question?

Possible Answers:

Correct answer:

Explanation:

Let  be the number of cookies sold. The Russian Club will need to spend 35 cents, or $0.35, per cookie for the ingredients, plus $350 flat for the ingredients, so the cost function will be

They will sell the cookies for $1.75 each, thereby earning a revenue of

They want to earn at least $800, so the profit  must be at least this - or

Replacing  and  with their definitions, the inequality becomes

Example Question #154 : Word Problems

The Spanish Club wants to make and sell cookies in order to raise  for a field trip. The equipment they want to use costs  to rent and to operate, and the ingredients for the cookies cost  cents per cookie. The Spanish Club wants to sell the cookies for  each. At this price, how many cookies will they need to sell in order to earn back the money they paid for the ingredients and the equipment rental and make a profit of ?

Possible Answers:

Correct answer:

Explanation:

Let  be the number of cookies sold. The Spanish Club will need to spend 75 cents, or $0.75, per cookie for the ingredients, plus $400 flat for the ingredients, so the cost function will be

They will sell the cookies for $2.50 each, thereby earning a revenue of

They want to earn at least $1,000, so the profit  must be at least this - or

Solve the inequality:

The Spanish Club will need to sell 800 cookies.

Example Question #152 : Word Problems

Adam buys 12 broken cell phones for $50 each. If he fixes the cell phones and sells them each for $80, what is his total profit?

Possible Answers:

$360

$800

$260

$960

$600

Correct answer:

$360

Explanation:

Adam first buys 12 cell phones for $50 each, which means he spends:

12($50) = $600

He then sells the phones for $80 each, which means he earns:

12($80) = $960

The profit is the earnings minus the expenses, so Adam's profit is:

$960 - $600 = $360

Example Question #152 : Word Problems

It costs a company an average of  to build one of their custom woodchippers. The company makes an average profit of  of the cost of building a machine. To the nearest dollar, what is the average net profit the company makes per unit sold?

Possible Answers:

Correct answer:

Explanation:

The company makes an average net profit that is  of the cost of building a machine. To calculate the average net profit in this case, simply do the following:

So, to the nearest dollar, the company's net profit is .

Note: avoid the trap answer . Our unrounded answer is , so we need to round down to  instead of rounding up to .

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