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.
I'm toward the end of my second full month of tutoring in NYC, and it's been interesting to see how my GMAT students here differ from the gang that I taught in DC. I had an amazing range of students in DC, including a couple of people who started at or above 700, quite a few others who started in the high 300s or low 400s, and pretty much everything in between. My first group of NYC GMAT students, on the other hand, consists almost entirely of ass-kickers, gunning for something close to a 700. I've met two guys who have gone through every official GMAT question twice; both of them diligently kept notebooks of all of their mistakes, and still didn't get the scores they wanted. Pretty much everybody else I've met has graduated from a Kaplan, Veritas, Princeton Review, or Manhattan course. With only one exception, all of my students have consistently scored in the 600s on the real GMAT, and in the 600s and 700s on practice test.
So all of these guys know the GMAT really, really well. Generally, they start by asking questions about the tough stuff--combinatorics, hard rate problems, set theory, conditional probability, and the most vicious of sentence correction problems. Hardly any of these guys are the least bit worried about their algebra or arithmetic skills when they call me.
I have a few little files of "easy" GMAT questions, mostly consisting of basic algebra, arithmetic, and geometry. Eighth-grade level math, at most. Over the past few weeks, I've given the set to most of these veteran GMAT warriors.
How did they do? Well, one GMAT student got a perfect score, which is exactly what he should have done if he wants to get a 700. (I'm very proud of you, Mr. V. May the GMAT gods grant you a 750 and admission to the MBA program of your dreams.) Everybody else got ripped to shreds, missing somewhere between 15% and 30% of the questions. That would be fine on medium-to-hard (say, 600- or 700-level) GMAT questions, but nobody with dreams of admits from Harvard or Stanford should miss this kind of stuff.
Here are a few examples of reasonably easy questions that caused problems:
1. You drop a ball from a height of 16 meters. Each time you drop the ball, it bounces to a level half as high as its starting point. If you catch the ball after the fourth bounce, how far did the ball travel? (A) 30 meters (B) 31 meters (C) 40 meters (D) 41 meters (E) 45 meters
2. If x and y are two-digit integers such that x < 40, which of the following is closest to the maximum possible value of xy ? (A) 400 (B) 1,600 (C) 4,000 (D) 16,000 (E) 40,000
3. If the numbers 13/24, 9/16, 1/2, 2/3, and 5/8 were ordered from greatest to least, the middle number of the resulting sequence would be (A) 13/24 (B) 9/16 (C) 1/2 (D) 2/3 (E) 5/8
I'm not sure that any of these questions are much more than 500-level questions, but some good GMAT math students screw these up regularly, just because they don't read carefully, or because they rush through their calculations. Sometimes it seems that arithmetic and algebra questions cause 600+ scorers to immediately think "this is easy, I'm going to destroy this question in 25 seconds so I can move on to harder stuff"... and then they make a dumb mistake. I call this phenomenon "getting GMAT-ed."
The GMAT writes questions specifically to test your precision, and they're trying to get you to fall into traps by being imprecise or careless. If you don't count the bounces carefully, you won't get (E) for question 1. If you jump to conclusions on #2 (i.e. by misreading an inequality sign or by missing the word "two-digit"), you might not know that the answer is (C). There's nothing magical about question #3, but it's easy to get overconfident and make a calculation or comparison error. The answer, incidentally, is (B). Easily 30% of my 600+ students have missed a version of that last one, even though it's just a simple numerical comparison.
The moral of the story? If you read a GMAT math question and you think that it's easy, watch your back. Don't let overconfidence get in the way of your GMAT score. Check your answer twice--it's always worth spending an extra 15 seconds to make sure that you haven't done something silly that can damage your GMAT score.