This page is part of my unofficial solutions manual to the GRE Paper Practice Book (2e), a free resource available on the ETS website. They publish the questions; I explain the answers. If you haven’t worked through the Practice Book, give Section 5 a shot before reading this!

5.25: Fixed and Variable Costs

This problem invokes a situation that is not explicitly mentioned in the GRE Math Review, but is important enough to merit its own formula:

Unlike the simple interest formula (see 5.13), which should be memorized, the total cost formula does not come into play frequently enough that you have to memorize it. As long as you understand the difference between fixed and variable costs, and how to account for each, you can skip straight to the application without writing down “T = F + V” or any such expression.

The variable costs, in this problem, consist of two parts: the number of units produced and the rate per unit. Substituting that into our initial formula gives

This expression that will serve as our template for solving the problem. Reading through the problem stem, we see that our target value is the fixed cost — which, true to its name, does not change from month to month. In order to find that value, we will first need to determine the variable cost and subtract it out from the totals provided for each month. Here’s what we know at the start of the problem:

We can use that information to populate two equations: one for each month.

Subtracting one equation from the other allows us to figure out the unit cost:

Once we have our unit cost, we can plug it back into the equation for either month and use it to determine the fixed cost:

Here, I’ve used the first equation (from the 20,000-unit month), but using the second equation (the month with 25,000 units) gives the same result. Either way, the correct answer is $30,000 (B).

Math Review Reference

For more on this topic, see the following section of the GRE Math Review:

• 2.7: Applications (pp. 25-28)