GMAT Tip: Tackling the Toughest Data Sufficiency Questions

Photograph by Michael Krinke

This tip on improving your GMAT score was provided by Brian Galvin at Veritas Prep.

Like any good strategy game, the GMAT’s data sufficiency questions have two levels of proficiency: There’s “knowing how to play the game” (for example, answer choice C means “both statements together are sufficient, but neither alone is”) and there’s “knowing how to play your opponent.” The latter is always a little more challenging and requires mastery of the former but usually has its rewards, once you get comfortable with it. And one way to read your data sufficiency opponent—the test-maker—is this:

The GMAT isn’t likely to reward you for nothing.

When the author of a data sufficiency question makes one (or both) of the statements easy to decide on, the question has to be challenging somewhere else. So if you’re breezing through a data sufficiency question, it’s a good idea to try to find the difficulty. That’s especially true if you’ve been able to quickly determine that neither statement alone is sufficient. Consider this example:

For nonnegative integers x and y, what is the remainder when x is divided by y?

(1) x/y = 13.8

(2) The numbers x and y have a combined total of less than 5 digits.

(A) Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient to answer the question asked

(B) Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient to answer the question asked

(C) Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient

(D) EACH statement ALONE is sufficient to answer the question asked

(E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed

It should be clear fairly quickly that neither statement alone is sufficient. For a lot of students, the phrase “well it could be anything”—the kind of massive generality that should be avoided on the GMAT—will follow them all the way to E without much thought or elbow grease.

But if you’re playing your opponent, you should realize that if it’s pretty easy to get to the “C vs. E” decision, they’ll make you work—at least a little—to make that decision. So in a case like this, it pays to put pencil to paper (rather, pen to noteboard) and do some work.  Even if it doesn’t seem “mathematical” or “smart,” just putting down some potential values that might work can help you get a feel for the question.

For example, what’s an easy x and y pair to give you x/y = 13.8? 138/10 can get you there quickly … and when you hold that up to the light of statement two, you should see that 138/10 isn’t valid for these purposes, as that’s five total digits and you’re only allowed a maximum of four. So you need to take 138/10 and reduce the number of digits. The only way to do that is to factor it down by dividing both numerator and denominator by 2.  That gives you 69/5; because 5 is prime, you can’t break the denominator down any further. That means, for this question, that x has to be 69 and y has to be 5, so the remainder has to be 4.

More important is the takeaway: that the “C vs. E” decision generally requires work. If neither statement alone is sufficient, then together they’re either just barely sufficient or just a whisker away from being sufficient, and it’s up to you to put in a minute’s work to find out. When the decision is E or C, it’s never as easy as it might look.

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