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!

5.12: To Market, To Market

In GRE word problems, the underlying algebra is usually fairly simple. The real challenge is finding a mathematical expression that accurately captures all of the relevant details of the situation, without including any extraneous information. Fortunately, this section and the next provide plenty of practice in translating from words to equations.

Here, we can begin by finding an expression for the rate at which space is rented out, as stated in the first sentence of the problem stem:

Sanity check: It’s important to keep track of units, especially in word problems. In this case, we’re looking for a difference in dollars. Keeping track of the dollars, square feet, and days in our calculations will allow us to catch errors caused by multiplying or dividing incorrectly. If our answer comes back in square feet, for example, we know that a mistake has been made somewhere along the way.

Next, each woman’s “rental commitment” can be expressed in terms of the square feet rented times the duration of the rental:

To find out what each woman paid, we multiply her rental commitment by the rate we found in step one:

Cancelling out units gives the cost in dollars:

Finally, subtracting Alice’s cost from Betty’s cost yields our answer:

Betty paid $90 more than Alice, so our answer is (D).

Math Review Reference

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

• 2.7: Applications (pp. 25-28)