All GMAT Math Resources
Example Question #1 : Calculating Profit
Mark buys 1,000 shares of stock for the current stock price of $20 per share. If the stock price goes up to $25 per share, by what percentage does Mark increase his money?
Mark spends $20 * 1,000 shares = $20,000. When the stock price increases to $25/share, he makes ($25 – $20) * 1,000 shares = $5,000.
$5,000 / $20,000 = = 25%
He does NOT increase his money by 125%, which would mean an additional $25,000, not $5,000.
Example Question #2 : Calculating Profit
Mary works at a clothing store. She makes $13/hour and works 40 hours a week. Working at the clothing store gives her a 25% discount on anything they sell. If she buys a sweater that retails for $50 and a jacket that retails for $144, what is her net profit for the week?
Mary makes $13/hour and works 40 hours. So she makes
However, we need to subtract the cost of the items that she bought. If the sweater retails for $50, Mary buys it for because of her 25% discount. Similarly, she buys the jacket for . So her net profit is
Example Question #3 : Calculating Profit
The profit equation for a certain manufacturing process is , where is the number of units.
How much money will the plant make/lose if it sells units?
Example Question #4 : Calculating Profit
Company B produces toy trucks for a shopping mall at a cost of $7.00 each for the first 500 trucks and $5.00 for each additional truck. If 600 trucks were produced by Company B and sold for $15.00 each, what was Company B’s gross profit?
First of all, we need to know that
There are 600 trucks produced. According to the question, the first 500 trucks cost $7.00 each. Therefore, the total cost of the first 500 trucks is .
The other 100 trucks cost $5.00 each for a cost of .
Add these together to find the cost of the 600 trucks:
The total profit is easier to calculate since the selling price doesn't change:
At this point we have both revenue and total cost, so the answer for gross profit is .
Example Question #5 : Calculating Profit
Abe is a big gambler. He is equally likely to win, lose, or break even. When he loses, his loss is . When he wins, he either makes or with equal probability. How much money does Abe win or lose on average?
Abe wins $200.
Abe loses $83.
Abe wins $83.
Abe loses $100.
Abe breaks even.
Abe loses $83.
To find the average, multiply each expected profit or loss by its probability:
Example Question #6 : 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?
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 #7 : Calculating Profit
Find the number of units, , that a company must sell to break even if the profit equation is .
Break even profit is . Plug this value into the equation to solve for the number of units:
Example Question #8 : Calculating Profit
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?
Calculate the net profit by subtracting the cost of the cars from the gross profit:
Example Question #9 : Calculating Profit
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?
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 #10 : Calculating Profit
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?
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