The Difference Between Math and Logic

Perhaps the most controversial post I’ve written for this blog so far — if “controversy” can be anything other than a comical word when talking about the GRE — is this one, which I link to a lot, in which I point out that the quantitative section of the GRE is primarily a logic test, not a math test. Several very intelligent people pushed back in the comments, arguing, essentially, “But math IS logic.”

I found some very interesting statistics recently that I hope will clarify my point.

A professor at the University of North Texas compiled a list of average test scores, by major, for 2007-2008. Not surprisingly, math and physics majors scored, on average, the highest (160.0), with econ and philosophy majors closely following suit (157.4). Engineering (156.2) and chemistry (156.1) majors also put up a strong showing. Just goes to show, people who study a lot of math do better on the GRE, because sure, it’s a logic test, but math is logic, so same difference, right?

Right, except for one small thing. The average scores I’m referencing aren’t for the GRE. They’re for the LSAT.

Now the LSAT, if you’re unaware, is a 100 question multiple-choice test that people take to get into law school. There are two sections of logical reasoning, in which the questions are similar to the short, reasoning-based reading comp questions you’ll see on the GRE; one section of “pure” reading comp; and one section of “logic games,” in which you’re given a set of puzzle-like of instructions (e.g., “Bob lives in the house to the left of Jane,” etc) and have to answer questions about it (e.g., “If Perry lives in the fourth house, which of these can’t be the house that Bob lives in?”).

No math. No outside knowledge of any kind, for that matter. Just your noggin’ and you. And it’s super hard: as someone who teaches both the LSAT and the GRE, I’m qualified to say that you should thank your lucky stars that it’s the GRE you have to take, because the LSAT is a billion times harder.

And yet it has no math, of any kind. And yet math majors, of all people, beat the pants off everybody else, including philosophy, history, and English majors, whom you’d expect to clean house on a purely verbal test.

Which brings us to my initial claim that the GRE quantitative section is primarily a test of logic, not of math. “But isn’t math logic?” Sure. But that doesn’t mean that all logic is math! I’ve prepared hundreds of students for the GRE, and I’ve never had a problem teaching someone — no matter how “bad at math” they are — how to divide fractions, solve a system of equations, or use the combinations formula. In fact, many of my students come to class already knowing how to do all of these things. Is dividing fractions or solving a system of equations an exercise in logic, as well as math? Of course. But that’s not the logic that puts the screws on people. It’s the non-mathematical logic that students struggle with: the questions that ask “which of the following could be false?”, or present a medley of simple information in a series of complex-sounding sentences.

People who are really good at math are good at this other kind of logic, too. But — logic time! — this merely shows that math fluency is sufficient for success on the GRE, not necessary. If you’re not good at math, that’s okay, as long as you’re willing to rise to the challenge and develop your ability to reason logically.