GMAT Tip: Strategies for Data Sufficiency Questions

This tip on improving your GMAT score was provided by Vivian Kerr at Veritas Prep.

Data Sufficiency is a unique question type and has the potential to look quite abstract, but as you’ll see, half the battle is making these questions concrete. These two strategies will help:

Count the Variables; Don’t Do the Math

Remember the “n equations with n variables” rule: If you have three unknowns, you’ll need three equations to solve for all three. If you only need the sum of two of those variables, however, you may need only two equations to solve. Let’s take a look at how this strategy can help us find a shortcut.

A total of 2,000 T-shirts was divided among a soccer team, two baseball teams, and a track team. How many shirts did the track team receive?

(1) The track team and one of the baseball teams together received 5/7 as many shirts as the other baseball team and the soccer team combined; and the two baseball teams each received the same number of shirts.

(2) Each baseball team received 400 fewer shirts than the soccer team and 400 more than the track team.

This is a value question for which we have four unknowns: the soccer shirts, baseball team A shirts, baseball team B shirts, and track team shirts. Statement (1) doesn’t allow us to solve for these four unknowns.

For (2), we’re given the relationship between one unknown (the soccer team) and the other three unknowns. That would allow us to choose a variable for the soccer team T-shirts and write the other unknowns with that same variable. We don’t even have to do any math to see that this is sufficient.

If we wanted to try this out algebraically, we could pick “x” for the number of shirts given out to the baseball teams. Because the baseball team received 400 more than one team and 400 less than another, that makes the other two totals (x + 400) and (x – 400). Since a total of 2,000 shirts were given out, x + x + (x + 400) + (x – 400) = 2,000. We have a linear equation with a single variable, so we know this choice is sufficient, according to the “n equations, n variable” rule.

Data sufficiency questions come with five answer choices asking test-takers to determine if one or both of the statements, alone or in combination, are sufficient to answer the question. In this case the answer is (B): statement (2) alone is sufficient, but statement (1) alone is not.

Plug in Values

This strategy comes in handy especially for “yes or no” data sufficiency questions. Here’s an example:

Given that A > 0 and C > 0, is (A + B) / (C + B) > A/C?

(1) B > 0

(2) A

For (1), we are given only that B is a positive number. Picking values is a good strategy here. If we can choose values such that we get a “yes” and choose values so that we get a “no,” we can quickly eliminate choices. If A = 1 and C = 1 and B = 1, then the inequality is NOT correct. If, however, A = 1, C = 2, and B = 3, we get 4/5 > 1/2, which IS correct. Statement (2) can also be proved insufficient. Combined, if B is positive and AC, then it will continue to INCREASE the left-hand side of the inequality no matter what values we pick. The answer is (C): Both statements (1) and (2) together are sufficient to answer the question, but neither statement alone is sufficient.

Remember, even the most seemingly complex data sufficiency questions can be overcome with solid strategy.

Vivian Kerr has been teaching and tutoring in the Los Angeles area since 2005. She graduated from the University of Southern California, studied abroad in London, and has worked for several test-prep giants tutoring, writing content, and blogging about all things SAT, ACT, GRE, and GMAT.

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