Oct
22
2012

# A Math Test: What the GRE Quantitative Section Isn’t

“I hate math!”

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?

A) xy

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.

## Related Posts

#### About the Author: Boris Dvorkin

After picking up degrees in English and computer science from Case Western, Boris Dvorkin worked for six unfortunate months as a computer programmer before finding a home at Kaplan in May 2008. He is now a full-time GRE faculty member on-site and online, and he's worked on Kaplan's curriculum for the recent GRE revision. Boris was named Kaplan's Teacher of the Year for 2010. When he's not gushing about standardized test trivia, Boris enjoys playing obscure strategy board games, and is the proud owner of no less than three different board games about Portuguese spice merchants.

• Anonymous

Yeah, well, most humanities types also hate logic, don’t they? That’s usually the _reason_ they hate math.

• Boris Dvorkin

Actually, no. You’re quite enlightened if you realize that disliking logic is the reason you dislike moth. Most people who hate math — and believe me, I’ve met a LOT of these people — believe that math is its “own thing” that exists in a vacuum from everything else.

• fsilber

It should be quite obvious that, far from being distinct from everything else, math is _abstracted_ from everything else. Maybe the problem is that humanities types have trouble with the concept of abstraction. (Though if that is the case, I cannot see how they could have any appreciation of formal logic, either.)

In the United States, math is taught very poorly. Tragically poor.

• fsilber

You should publicize what is being done wrong.

• Kristen

I will admit to being one of the “math haters” blaming math for my struggles with it. I took the GRE a year ago as an undergrad and was very discouraged by my quantitative results. I am, however, back at it with a new attitude. I really needed to hear “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.” That helped put things into perspective for me. Thanks for the article and enlightenment! Take care.

• Boris Dvorkin

Kristen, you’re very welcome! And thank you so much for posting — glad to hear the article was a positive one for you.

• Anonymous

Very good point!

• Boris Dvorkin

Thanks Bwin, glad you think so!

• hdavis

The sad thing here is I almost thought I was reading how high school students react to exams. These are nearly college graduates who want to enter graduate school and they can’t handle math which is at a high school level. Many of my friends complain for the opposite reason, why can’t they put a few calculus questions on there? At least make it a little challenging.

• Boris Dvorkin

If there GRE were a math test — even a math test at a high school level — it’d be completely fair for a lot of people to complain. Someone who wants to study French literature would be right to be angry if the GRE tested high school level trigonometry, just as a hopeful math PhD would be right to be angry if the GRE tested high school level French.

Thankfully neither of these things is the case.

• Orlandus

A math PhD candidate ought to be able to read mathematical papers and books in French!

• Boris Dvorkin

Haha! Knowledge of German would be handy too…

• teapartywonk

Boris, you are way too kind to the math haters. Imagine how they would react to you saying you hate literature or art. If they can’t do fifth grade math, maybe instead of grad school, their highest and best use is flipping burgers or cleaning toilets.

• Boris Dvorkin

I do find it odd how many people view math on a plane apart from other subjects. Lots of high school students argue that they shouldn’t have to take math because “I’m never gonna need any of this stuff!” That exclamation would be just as accurate in literature or history class, but you never hear it there.

Since I’m a representative of Kaplan here, professional decorum prohibits me from commenting on your other thoughts.

I heard plenty of business majors complain they wooould never use art, lit or history. Only math I ever used was one geometry proof or theorem, long before I even went on to get Bach degree.

• B_stein

I actually love math and think it is fun. And I still suck at it. I think where many people like myself get hung up, is we just get rusty, and forget a lot of it, since we do not use high level math, except for test taking reasons. Having said that, I thought the math question you posted for the example was insanely simple.

• Boris Dvorkin

If you thought that question was simple, then don’t take it for granted! Number properties questions aren’t a joke: they trip up a lot of other people, primarily because they use “could be/must be” phrasing that forces students to critically consider what does and doesn’t answer the question.

As for rustiness: that IS a real issue, because there are some things you need to memorize. It’s handy to know that x^2 – 9 is (x – 3)(x + 3), that 5 cubed is 125, that 1/8 is 0.125, that average speed = total distance / total time, and so on. None of that stuff is hard, though. And memorizing stuff for the quant section is no different than memorizing vocabulary for the verbal section!

Wow that question was really common sense easy. It took me 30 seconds to figure out and I have not been to college in over 35 years and i was an Art major.

• Boris Dvorkin

I daresay that just about proves my point.

• JoeB

If x is -1 and y is +1 then xy+1 is 0. Is that odd? I wouldn’t want you teaching me math!

• Jane

But both -1 and +1 are odd numbers, so your scenario doesn’t apply.

• JoeB

You’re right I am an idiot. To lazy to read the question.

• Boris Dvorkin

Not an idiot, Joe — just an unwitting demonstrator of my point.

Most students take several math courses by the time they’re nearly graduated, however, courses in Logic are rare. I wonder why the GRE is heavy on Logic and light on “math”?

• Boris Dvorkin

Y’know, Ben, the best answer I can think of is to swap your premise with your query. “The GRE is heavy on logic and light on math. I wonder why courses in logic are so rare?”

Mathematical reasoning IS logic.

• Boris Dvorkin

Well, yes. But then, all reasoning is logic, if we want to get very philosophical about it.

• Stephen

Math is a particularly powerful and abstract form of logic. I would call everything you’ve described above “math,” and the better math classes will teach the logic of math, not just the cookbook formulas.

You’re absolutely right, though, that if students could just calm down and apply reason, they could do much better at math. If calling it a different name helps the students get over their fear, then ok. But this is pedagogical marketing, not a fundamental distinction about content.

It reminds me of the power of Bill Clinton’s address at the Dems’ convention. Everyone else was saying that Romney’s math didn’t add up. Clinton didn’t call it math. He called it “arithmetic.” And that made a huge difference!

• Boris Dvorkin

With respect, Stephen, your logic is a little off. Just because all math is logic, doesn’t mean that all logic is math. For example, math and physics majors get the highest average scores on the LSAT than any other major, but it’d be ridiculous to claim that the LSAT is a math or physics test. Clearly THAT is a logic test, right?

I have zero doubt that a math major is better equipped than an average person off the street to understand and correctly answer a question that asks, “Which of the following must be false?” But that is not a math question.

If you throw some basic number properties and arithmetic into a question and THEN ask, “Which of the following must be false?”, now you have both a math component and a (non-mathematical) logic component to the question. Students will get tripped up on the logic and assume that their problem was with the math. That’s the point of this entry: not that the GRE has no math, or that math isn’t logic, but that the non-mathematical logic of the GRE is what’s really killing people.

• Stephen Weinberg

Boris,

I disagree with your claim that the logic called for on the GRE is non-mathematical. EVERY aspect of the examples given is math, and is something that, as a professor in a graduate program, I want my students to be capable of doing. And it’s something they should have learned in their high school math courses, regardless of whether the term “logic” is in the title,

I don’t just care that they can memorize their times tables or the formula for the area of a triangle. I need them to be able to THINK about numbers and formulas. That’s a critical element of mathematics. I find the argument presented here to be similar to saying that a reading comprehension question doesn’t test verbal skills because the only verbal skill is memorizing vocabulary words, not being able to have to put words together or see what they mean.

But it’s definitely the case that many students choke on the math GREs, even students who are capable of doing the thinking underlying the questions. Getting students to turn off their panic long enough to actually use their math skills is a useful service. If saying “this isn’t math” helps them do that, well, I will sadly accept the possible validity of such a strategy.

• welshmx

I blame math for most of the world’s problems, yet I find this article helpful. I passed the GRE with know knowledge of math whatsoever, beyond the ability to recognize that some numbers represent more stuff than other numbers. We even have a number for no stuff. The trouble started when we began giving numbers for less than no stuff and required others to restore the deficit. Things got worse when we allowed numbers to apply differently to stuff depending on peoples’ different relationships to the same stuff. Well, math just continues to promote misunderstanding and inequity, but there is no reason to fear the GRE. You came equipped with the same logic that everyone else has. Logic is fairly safe from the depredations of math.

If x=3 and y=5, than 3*5+1 is even so C must be wrong.

• Orlandus

Read the question again. It says that x and y are NOT BOTH odd.