GRE Reading Comp: Quantitative Vocabulary

When I say “GRE vocabulary,” you might think I mean words like panacea and moribund. But in the past year, I’ve discovered that (aherm) esoteric words aren’t the only ones to give my students headaches. Seemingly (cough) innocuous words like “some,” “many,” and “most” instigate no end of consternation on the new GRE‘s logic-based reading comp problems.

Have a look at what I’m talking about:

Most of Bob’s students are graduate students, and most graduate students at Bob’s university are in a PhD program. Bob owns a hamster, as do many of his students, and most of Bob’s students think he’s a great teacher.

If the statements above are true, which of the following must also be true? Select all that apply.

A) Most of Bob’s students are in a PhD program.

B) Some hamster-owning students think Bob is a great teacher.

C) Some graduate students think Bob is a great teacher.

Let’s examine these statements one by one. First, is it true that most of Bob’s students are in a PhD program? The relevant information is this:

• Most of Bob’s students are grad students
• Most grad students are PhD students

If your intuition is confused, you can pick numbers to make sense of the situation, even though this is a verbal problem!

Suppose that Bob has 5 students. On the GRE (and, for that matter, in real life), the word “most” means “more than half.” So, at minimum 3 of Bob’s students are grad students. Now suppose that there are 1,000 grad students. If “most” of them are getting a PhD, that means there are at least 501 PhD-chasers. This leaves up to 499 students who AREN’T getting a PhD — and Bob’s 3 grad students could easily be among them.

So, no: choice (A) doesn’t have to be true. It could be true, sure, but it doesn’t have to be. Avoid the GRE’s “could be true” answers on “must be true” questions!

Next, check out (B): Some hamster-owning students think Bob is a great teacher. The relevant information this time is this:

• Most of Bob’s students think he’s great
• Many of his students own a hamster

This is cake if you know what “many” means. For some reason, many (cough!) of you think it means “most,” perhaps because both words are four letters long and start with “m.” Not so! “Many” is actually a synonym for “some:” it means, for the precise purposes of the GRE, “at least one.”

(Side note: if you don’t think that’s true — if you think that “many” means “a lot more than one” or some such — consider that “many” is a subjective word that hangs on context. One hair on my head isn’t very many at all, but one cockroach in my soup, I think you’ll agree, is already too “many!”)

So all we’ve got from the stimulus is that at least one of Bob’s students owns a hamster. And that one hamster-owning student could easily be among the few who think Bob sucks. This is another choice that could be true but doesn’t have to be.

On Test Day, there will always be at least one right choice on an “all that apply” question, so if you ever cross out (A) and (B), you know that (C) is right without even checking it. For practice’s sake here, though, let’s give it a look: Some graduate students think Bob is a great teacher.

Well. You know that most of Bob’s students think he’s a great teacher, and you also know that most of Bob’s students are grad students. If Bob has 5 students, that means there has to be a minimum of 3 in each category. Here’s what that could look like:

Student 1: Grad Student
Student 2: Grad Student
Student 3: Grad Student, Thinks Bob is Great
Student 4: Thinks Bob is Great
Student 5: Thinks Bob is Great

Notice that despite my best effort to avoid overlap, some overlap was unavoidable: with 3 grad students, 3 fans of Bob, and only 5 total students, at least one student had to be both. So yes: “some” (i.e., at least one) students are both grad students AND think Bob is great.

These problems don’t just test your ability to make good deductions. They also test your ability to not make bad deductions. On Test Day, think everything through, picking numbers if you have to — and before Test Day, ask us in the comments if you’re confused about these or other examples you’ve encountered!