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!

5.3: Percents and Proportions

This problem illustrates one of the basic rules of GRE math: whenever you see percentages, turn them into decimals if at all possible. Decimals are much easier to work with and, in my experience, less likely to yield errors in calculation. In word problems (which we’ll see later), turning percentages into decimals also forces you to be clear about the role of any markups, discounts, or other percent changes.

We could think of this problem as a “word problem lite,” where our first task is to translate the written phrases into mathematical expressions. “4 percent of s” becomes

0.04s

and “3 percent of t” becomes

0.03t

Putting the two together, we get

0.04s = 0.03t

From here, we can divide out the coefficient of 0.04 from both sides of the equation:

s = (0.03/0.04)t
s = (3/4)t
s = 0.75t

Because both s and t are positive, we now have enough information to conclude that quantity A (meaning s) is less than quantity B (that is, t). So our answer is (B).

To see this more clearly, try plugging in a number for t. If t = 4, then

s = 0.75(4) = 3

It doesn’t matter what value of t you plug in — as long as you choose a positive number (as the problem instructs), you’ll find that s is less than t. You could even start your solution by plugging in for t, then simplify from there. For this problem, though, I find it easier to simplify the expression first.

Math Review Reference

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

• 1.7: Percent (pp. 9-12)