GMAT combinatorics

Misplaced Math Anxiety: The Evil Four

As an independent GMAT tutor with an unorthodox streak, I tend to be the GMAT resource of last resort for many test-takers. The majority of my NYC students have already taken at least one GMAT prep course, and most have taken the test at least once (one of my students took the test seven times before she called me, and cracked 700 for the first time ever this weekend... yay!). I love the challenge of trying to help students beat the GMAT after they've already exhausted every other resource, and I'm always honored when somebody puts their faith in me after months--or years--of falling short of their score goal. Because the prospective students who contact me tend to have so much GMAT experience already, I usually ask the same question: what do you think is holding your GMAT score back? As you might guess, I get a huge variety of answers, but there's one common thread: nearly everybody blames combinatorics (combinations and permutations), probability, rates, and/or overlapping sets for at least part of their struggles on the quant section. Let's call those four topics the Evil Four.

I'm not going to tell you that rate questions aren't important. I'm not going to tell you that combinatorics, probability, and overlapping sets aren't important. But I will tell you that the Evil Four are never the difference between, say, a 650 and a 700 on the GMAT.

Here's the thing: when you really look hard at the GMAT, none of the Evil Four seem to appear all that often. It's possible that you'll see two rate problems, but it's more likely that you'll see only one. It's possible that you'll see a combined total of three probability and combinatorics questions, but it's also possible that you'll see exactly none--even if you're doing well on the exam. And overlapping sets questions aren't so common either: very few test-takers claim to see more than one or two of them on the GMAT.

Think of it this way: you might only see a grand total of four or five questions from the Evil Four on the actual GMAT. That's only a tiny proportion of the 78 questions on the test, yet I routinely speak with people who seem to spend as much as 50% of their study time on these topics. But if the Evil Four appear in less than 10% of GMAT test questions, why is everybody so stressed out about them?

Honestly, I think that test-takers tend to focus on these questions because they're so damned memorable compared with the rest of the questions on the GMAT. You won't necessarily remember the algebra questions (too boring), the arithmetic questions (too pedestrian), or the number properties questions (too abstract); the crazy rate questions with two trains headed toward each other seem to stick in our heads much more easily.

But the unglamorous reality is that algebra (including word problems and functions), arithmetic (including word problems, percents, exponents, roots, and estimation), and number properties (including all sorts of fun with factors, multiples, and remainders) questions are the core of your GMAT quant score. If your accuracy on these three topics is less than stellar, your GMAT score will also be less than stellar.

Again, I'm not saying that rates, combinatorics, probability, and overlapping sets aren't worth studying. I just think that these questions cause a disproportionate amount of anxiety, and I think it's crucial to keep them in perspective. If you're trying to raise your GMAT score from, say, a 47 to a 51, you probably need to study the living hell out of everything. But if your goals and starting score are more modest--or if you need to substantially improve your composite score--don't overemphasize this stuff.

At the very least, make sure that you don't focus on the Evil Four at the expense of more important topics. If you need to make a big improvement in your GMAT quant score, spend the bulk of your time developing your accuracy on algebra, arithmetic, and number properties. Since those three topics appear in more than two-thirds of GMAT quant questions, it would be wise to keep them at the front of your mind as you create your GMAT study plan.

GMAT Focus quirks

For the most part, I'm a fan of GMAC, the company that produces the GMAT. I've spent a good chunk of the last decade working as an SAT, ACT, GRE, and TOEFL tutor, and I respect that fact that the GMAT is much more complicated, precise, and nuanced than any of the aforementioned exams. And GMAC is also fairly generous about publishing retired test questions; some of us whine about the GMAT OG's lack of hard questions, but the official guides for GRE and TOEFL are far worse, offering only a handful of (ancient, moldy) practice questions. So while I generally think that GMAC does its job really, really well, they seem to have been a little bit sloppy with GMAT Focus lately. In some ways, GMAT Focus is the best of the GMAT practice material. Sure, it's overpriced ($25 for one test, or $65 for three... basically, you'll pay almost $1 per question). And I think it's weird that they sell the tests in groups of three--you can actually take the test four times before questions start to repeat. And you're given only 45 minutes to complete 24 questions--a little bit odd, since you'll ultimately need to get used to doing 37 GMAT questions in 75 minutes. But GMAT Focus still contains an impressive bank of difficult, fresh GMAT questions; I'm convinced that GMAT Focus questions are much closer to the real thing than any other practice resource available. If you're serious about improving your quant score, GMAT Focus is absolutely not optional.

Unfortunately, the GMAT Focus questions are no longer all that unique. Many of them appear in the 12th edition of the official guide, and I have a funny feeling that even more will show up in the next edition of the Quantitative Review guide. So you might be paying $1 for questions that you've already purchased in another book. That's really annoying, especially if you're already paying for a GMAT tutor.

Even more annoying: the GMAT Focus might not be as representative of the real test as I once thought. For a long time, it seemed that the GMAT Focus would give you a pretty good idea of the composition of the quantitative section--specifically, GMAT Focus included a lot more tricky logic, combinatorics, and "creative algebra" questions than the official guides, and GMAT Focus seemed to be an extremely accurate representation of the actual test. Sadly, something might have shifted, at least a little bit. In the past month, several of my students (all with quant raw scores above 40) whined that the real test didn't have any of the tough combination/permutation/probability questions that appear on GMAT Focus. It makes me wonder whether the GMAT Focus is becoming somehow less indicative of the actual test. Again, I find that a little bit irritating--if it's actually true.

Here's the strangest report of all: one of my GMAT students swears that he saw a GMAT Focus question on the real exam last weekend. He claims that the question was absolutely identical, with the same numbers and everything. He didn't share the details of the question (that would be illegal), but I find that pretty alarming if it's true. Is GMAC getting sloppy? Was the "retread" GMAT Focus question tossed back into the real test as some sort of experiment, or as a statistical control for other questions? Or was my student just hallucinating after a long, stressful few hours of test-taking?

Either way, it's interesting. I still think that it's worth spending $90 for all four GMAT Focus tests, but I couldn't really blame a budget-conscious GMAT student who comes to a different conclusion.