What Makes Tough Quantitative Questions Tough?

January 23, 2007

Right after "How do I get a 700?", I get this question more than any other. Unfortunately, just like the answer to the "700″ question, there's no quick and easy answer.

There is, however, a smart-aleck answer. A question is hard if lots of people can't do it. That's all. As I described in my tip about experimental questions, the difficulty level of GMAT questions is established by how well test-takers perform on them. If 90% of test-takers get a question wrong and the question makes it into the GMAT item pool, it's a 90th percentile question. It doesn't matter why it's difficult.

Of course, there are plenty of more specific issues involved. That's what I'll focus on today.

Content Areas

If you spend a lot of time around people preparing for the GMAT, you'll be exposed to a lot of anxiety regarding just a few topics. You'll hear fretting about probability, confusion about combinations, and perhaps kvetching about standard deviation. These are relatively difficult topics (compared to dividing fractions, anyway), and they require some study.

On the other hand, they involve content you can learn. There are a few rules that will help you answer just about any probability question the test will throw at you. Once you understand how standard deviation is included on the GMAT, you should have no fear of those problems.

In short, the content on the GMAT is the easy part. Flip through the subject review in either The GMAT Official Guide or The GMAT Quantitative Review and you'll get a good idea of what you might need to brush up on. The basic rules are an important foundation, but they are just the beginning.

Putting Two and Two Together

Many of the most difficult problems are those that cover multiple content areas at once. For instance, Problem Solving #248 in The Official Guide is a tricky permutations problem disguised within coordinate geometry. The coordinate geometry concepts are basic; the permutations content isn't that hard, but recognizing what you'll have to do is much more challenging.

More frequently, the GMAT will mix and match content in word problems. When the numbers are laid out for you, it may just be a matter of remembering an algebra rule, doing a little mental math, and clicking on the right answer. When the question is a long paragraph, you have to figure out which numbers are which, and do all of the same things you have to do on the non-word problem equivalent.

To more effectively combat these sorts of questions, learn to recognize key words that trigger certain kinds of math concepts. For instance, in Official Guide #248, the question includes the phrase "how many different triangles." That should suggest permutations or combinations. If a word problem contains the word "per," it's probably looking for a rate.

Abstraction

Especially on Data Sufficiency, the test challenges you by making you think at a more abstract level. I've written about this at greater length elsewhere. It's one thing to know that 2+3 is 5; it's another to immediately recognize that a+b is odd when a is even and b is odd. Instead of thinking about one case, a question will expect you to think about multiple cases simultaneously, or recognize what one case will effectively stand in for an entire class of examples.

This is one of the more difficult parts of the test to practice. Of course, there are plenty of practice questions that make you think this way, but on these, it's even more crucial than usual that you analyze your performance, learn from the explanation, and figure out how you can apply one question's worth of skill to a larger subset of test material.

Intuition

Everyone has seen a handful of GMAT questions that look impossible. There's usually some trick to them, and once you figure it out, you feel a little silly for not having seen it. But, in a way, that's what the GMAT is after: can you recognize the trick before it's too late?

A great example of that is Problem Solving #195 in The GMAT Official Guide. Most people (at least 95%, I'd estimate) look at it the first time with confusion, or try to come up with a "brute force" approach that could take four or five minutes. There's an easy way to do it, but almost no one recognizes it.

Mathematical intuition is a very tough thing to learn, but you should notice it increasing somewhat with practice. More than anything else, the method to improving in this area is simply exposing yourself to as much math as possible. If you're practicing GMAT math on a daily basis, you should improve your intuition, as well.

No matter how much you improve, though, you're always going to see a problem or two that simply confounds you. (I'm a bit embarrassed to admit that this happened to me once the last time I took the GMAT.) It's okay–you can get a great score and miss a few questions. Just don't let yourself spend too much time trying to figure it out. It's better to skip a question than to waste five or six minutes trying to puzzle it out.

Combating Tough GMAT Math

As you can tell, the key to dealing with the toughest GMAT Quantitative questions is not learning rules and practicing the basics. That's important, especially if you're just starting out, but it isn't enough. Make sure you expose yourself to plenty of difficult questions–especially word problems–from sources such as The GMAT Official Guide.

As frequent GMAT Daily Tips readers are well aware, the GMAT is not a generalized math test. It is not an algebra or geometry test. On the contrary, it's a thinking skills test that happens to require a bit of math knowledge. The toughest questions place demands on your thinking skills, not your mathematical technique. The most successful test-takers prepare accordingly.

About the author: Jeff Sackmann is a GMAT tutor based in New York City. He has created many resources for GMAT preparation, including the popular Total GMAT Math and Total GMAT Verbal, as well as 1,800 practice GMAT math questions.

• Older: How To Study GMAT Sentence Correction
• Newer: All About the GMAT AWA
• General GMAT Math: more articles
• All articles at GMAT HACKS