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!

5.9: A Very Good Year

Probability, along with quadratic equations and standard deviation, is what I call a “scare topic” — one that students perceive as inordinately difficult, even when the underlying math is relatively simple. The test makers know this and often employ the “P-word” to add an element of suspense and intimidation to an otherwise run-of-the-mill problem.

This problem is a great example. It uses the word “probability” multiple times, but it’s actually about counting. It’s true that some of the numbers are given as probabilities, but this is a minor inconvenience, because we know the total number of people in the group. Right away, we can translate the probabilities into integers.

If there’s a 0.44 probability that a group member is male, and there are 25 group members, then there are

males in the group. Likewise, if there’s a 0.28 probability that a group member is a “pre-1960” male (again, out of 25 total members), then there are

“pre-1960” males in the group. Just like that, we’ve turned a probability scenario into basic arithmetic.

Next, we can draw a quick chart to help us organize this information. (This, by the way, is the sort of scratch-paper diagram that I consider useful on the GRE. It takes just a few seconds to set up and pays big dividends in clarity.)

In this chart, the question marks represent values we can figure out from the information provided. The bolded question marks represent the value we need to figure out to solve the problem. Notice that we don’t have any information about the age distribution of the non-male group members.

By subtracting the “pre-1960” males from the total number of males, we find that there are 4 “1960 or later” males in the group. We can also determine that the number of non-males is 14, though we don’t need this information to solve.

So the number of males in the group who were born in 1960 or later (Quantity A) is equal to 4 (Quantity B). Because the quantities are equal, answer (C) is correct.

That’s all there is to it: no “ANDs,” “ORs,” or Venn diagrams required. The moral of this story? Even if probability isn’t your strong suit, don’t assume that a problem will be difficult just because it says “probability.” There’s a good chance (ha!) that the problem will involve nothing more than accurate bookkeeping and simple arithmetic.

Math Review Reference

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

• 4.4: Probability (pp. 78-79)