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!

5.21: Judicial Appointees

This problem has some major similarities to 5.9. Both ask us to reason about a group of people based on a set of overlapping characteristics. Because there are two “dimensions” to this problem (gender and minority status), we can even use the same table setup as in 5.9, where the dimensions were sex and age.

Here’s our initial setup, with the target value represented by bold question marks:

Most of the remaining information is given in terms of percentages or fractions. Just as in 5.9, we need to translate the percentages and fractions into whole numbers, since this is the form our answer will have to take. We begin by considering women and minority groups separately:

• (0.30)(180) = 54 appointees were women
• (0.25)(180) = 45 appointees were from minority groups

Here’s what that looks like in chart form:

The next piece of the puzzle is the overlap between women and minority groups:

• (1/9)(54) = 6 appointees were women from minority groups

Adding that fact to our chart allows us to fill in all of the remaining blanks.

At this point, we can see that 87 of the judicial appointees were neither women nor from minority groups. Therefore, the correct answer is (C).

Math Review Reference

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

• 4.3: Counting Methods (pp. 73-75)