A Math Test: What the GRE Quantitative Section Isn’t
A lot of you say this to me. “I’ve always been terrible at math!” It’s an expression of exasperation, but it’s also an excuse. It’s another way of saying, “If I don’t do well on the GRE, it’s not my fault. After all, I can’t help it: I’m just bad at math!”
My response to every variation of “I hate math!” is always the same: who cares? The GRE isn’t a math test. You might as well be saying, “I hate Justin Bieber!” Well, that’s fine, we all do, but what does that have to do with the GRE? It’s not a test of the Beebs.
Oh, sure, math is on the GRE. But it’s on the GRE in the same way that commas and periods are on the GRE: it’s needed to construct some of the problems. The presence of math on the GRE doesn’t make it a math test, any more than the presence of commas and periods makes it a punctuation test. I’ll prove it to you with an example. Try this problem:
If x and y aren’t both odd, which of the following must be odd?
B) x + y
C) xy + 1
Note that I’ve only shown you three of the answer choices, even though a typical GRE Quantitative problem will have five — three is enough to illustrate my point here.
Now let’s solve the question. If x and y aren’t both odd, that means one of two things: either they are (1) both even, or (2) one of them is even and the other is odd. One way to solve the problem, then, is to pick numbers for both cases.
If x = 1 and y = 2, then choice A is 2, choice B is 3, and choice C is 3. You can eliminate choice A, since the problem asks for the choice that’s always odd.
If x = 2 and y = 2, then choice B is 4 and choice C is 5. Again, you only want the odd choice, so B is out. That means C is the answer.
When I teach problems like this, there’s usually at least one student who asks, “But wait. When x was 1 and y was 2, choice B was odd. So why isn’t it the right answer?” And the question I want you to chew on is this: what is the source of the student’s confusion?
In fact, maybe you share the student’s confusion. And if you do, you’re probably sitting at your computer thinking, “I’m confused because I’M BAD AT MATH!” To which I say: that’s an utter load of baloney. Look at the math in this problem. Seriously, look at it:
1 * 2 = 2
1 + 2 = 3
1 * 2 + 1 = 3
2 + 2 = 4
2 * 2 + 1 = 5
That’s it. That’s the “math” of this problem. Most of the math on the GRE Quantitative section is this easy, which is why, if you’re preparing for the GRE, I simply do not care how much you hate math (!). I care about your success and I believe in you, but if you successfully got an undergraduate degree and are about to go to grad school, you cannot possibly convince me that you lack the intellectual capacity to multiply and add numbers.
The source of confusion around choice B isn’t math — it’s logic. The question asks for the choice that must be odd. That means that the correct answer is always odd, 100% of the time — which means, in turn, that if a choice is odd once, that doesn’t mean it’s right; but if a choice is even once, that does mean it’s wrong.
And that’s what the GRE is: a logic test. Understanding the phrase “must be odd” is a logic problem, not a math problem. Math is innocent: if you’re going to hate something on the GRE, at least hate the right thing.