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# Understanding the Relationship Between Cost, Sales Price, and Profit on GMAT Quant Questions

A common type of word problem you’ll encounter on the GMAT quantitative section involves merchant services, namely the buying and selling of goods or services. The math itself needs to be learned for these types of questions, to be sure, but for some of my students, particularly my international students, the hardest part is actually deciphering the terminology used in the questions themselves.

Let’s go through a couple of examples together and clearly define all of the business terms you’ll encounter on these questions.

The easiest way to understand what’s going on in GMAT “business” questions is to think about the very nature of business in its simplest form.

Imagine you’ve decided to open a store selling ice cream cones. Your objective would be to make money, right? But exactly how would that happen? In short, you would need to charge your customers more money than it costs you to actually make the ice cream cones, and that additional money would represent your profit.

Pretty easy, right?

Let’s break it down even further and define a few terms.

Let’s assume you can buy all of the materials to make an ice cream cone for \$0.50. That is your cost (or cost of production), i.e. the value of money that has been used up to produce your product.

Then, you turn around and charge your customers \$1.25 for the ice cream cone. That is your sales price (or retail price), i.e. the price you charge your customers for your product or service. That extra \$0.75? That is called your markup, the extra money you charge your customers above your product costs per item.

Now, let’s say you have 10 customers buy ice cream cones from you. In that case, you would earn 10 x \$1.25 = \$12.50. That is called revenue, the income that your company receives from the sale of goods and services to your customers.

But how much of that \$12.50 do you get to keep? Well, remember that it costs you \$0.50 per ice cream cone, so your costs for those 10 sales are 10 x \$0.50 = \$5.00. Thus, your total profit is your revenue minus your costs, or \$12.50 – \$5.00 = \$7.50. Profit (also gross profit, return, or net income), then, is a financial benefit that is realized when the amount of revenue gained from a business activity exceeds the expenses, costs, and taxes needed to sustain the activity. Note: In this example, we’re assuming that your only costs are the purchase of the materials to make the cones. That is almost always the case on the GMAT as well.

Profit (per unit sold) = Sales Price – Cost

One other quick thing. Sometimes businesses will run a sale and offer their products at a discount. The sale price is the price you sell your product for after subtracting the discount. Your sale price, by definition, is less than your retail sales price.

To continue this example, let’s assume you offer a sale of \$0.25 off each ice cream cone. Your new sale price, then, is \$1.00 instead of \$1.25. As such, the sale of 10 ice cream cones would now only net you a revenue of \$10.00 and a profit of \$5.00. However, if the sale attracts more customers because of the reduced price (e.g. 15 instead of 10), you could actually make more money through higher volume.

Here’s a diagram that illustrates everything we’ve just discussed:

### Application Example

Try your hand at this example:

A merchant made a gross profit of \$40 from the sale of a vase. If this gross profit was 25 percent of the cost of the vase to the merchant, for how many dollars more should the merchant have sold the vase for the gross profit to have been 30 percent of the cost?

(A) \$2
(B) \$5
(C) \$8
(D) \$10
(E) \$12

What do you think? Was this question easy or difficult for you?

The key with this question is to determine the merchant’s cost of the vase, right? We’re told that the profit on the sale of the vase is \$40. Based on our definitions above, that means that Sales Price – Cost = \$40.

Uh-oh. That’s one equation with two variables. Can we solve it? Not in its current form. But the question does tell us the relationship between the profit (gross profit) and the cost. Specifically, it tells us that Profit = .25 * Cost. That we can solve, since profit is given as \$40. So, \$40 = .25 * Cost. Thus, Cost = \$40 / .25 = \$160.

Now we can go back to our original profit formula to solve for the missing variable, Sales Price. If Profit = Sales Price – Cost, then \$40 = Sales Price – \$160. So, Sales Price = \$160 + \$40 = \$200.

At this point we can just work backwards from the answer choices to find the right answer. Following our rules for applying the “Working Backwards Strategy” (see our Free Session video to learn more), let’s assume the answer is C, i.e. that the merchant sold the vase for \$8 more, or \$200 + \$8 = \$208. The profit it that case would be \$208 – \$160 = \$48. Does a profit of \$48 equal 30% of the cost? Yep, absolutely, since \$160 * .30 = \$48. Thus, the correct answer is C.

Note: Rather than working backwards from the answer choices to finish out the question, you could also have just figured out that 30% of the Cost is \$160 * .30 = \$48. Given that the current profit is \$40, the merchant would have to charge \$48 – \$40 = \$8 extra dollars to produce that desired profit outcome.