GMAT Data Sufficiency Example Problem

Annex - Rathbone, Basil (Adventures of Sherlock Holmes, The)_01

“Watson, when doing data sufficiency problems, one must remember that after one has eliminated the impossible, what remains, no matter how improbable, must be the truth!”

Data sufficiency questions can often be a thorn in the side for even the most diligent of GMAT test takers. Rather than test your ability to solve a math problem and get an answer at the end, data sufficiency problems really test your logical reasoning skills and knowledge of number properties and mathematical definitions. If you know how to approach them, though, they aren’t as bad as they might seem at first glance. Consider the following data sufficiency problem:

 

 

Is rst = 1?

(1) rs = 1

(2) st = 1

Remember, the answer choices for all data sufficiency problems are as follows:

(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 are needed.

So, let’s think about this a little. Because we have variables rather than actual numbers to work with in this question, we are going to use a picking numbers strategy in order to try out different possibilities and explore what is and isn’t possible within the limits of the various statements given in the question. For instance, consider that in order for the product of a given set of numbers to be 1, either the numbers must be equal to 1 themselves or they must be reciprocals of each other. So, if we were to pick numbers that would make rst = 1, we could let r = 1, s = 1, and t = 1; or we could have something like r = (1/3), s = (1/2), and t = 6. So, the question now is do either statement (1), statement (2), or both together suffice to assure us that one of these scenarios is the case?

First let’s consider statement (1), which says that rs = 1. This means that either r and s both equal 1 or they are reciprocals of one another: r = (1/2) and s = 2, for instance. This alone is not enough to insure that rst = 1, since t would have to be 1 if rs = 1 in order for rst = 1, and we have no guarantee that t = 1. So let’s look at statement (2), which says that st = 1. We can basically draw the same conclusions as we did for statement (1), since r would have to be 1 if st = 1 in order for rst = 1, and we have no guarantee that r = 1. So, neither of the statements alone is enough to prove that rst = 1. What happens when we consider them together?

If r, s, and t all equal 1, then it works fine. But statements (1) and (2) can be satisfied another way: suppose we let r = (1/2). In order to satisfy statement (1), s would have to equal 2. Then, if s = 2, in order to satisfy statement (2) t would have to equal (1/2). We can thus conclude from both statements (1) and (2) together that r = s, but we cannot conclude that rst = 1 will always equal 1, since in the preceding scenario:

rst = (1/2)(2)(1/2) = (1/2)

Thus, we must choose choice (E): Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed. If there had been an additional statement telling us that r = s = t, or even r = s or s = t, or a statement saying that one of the variables was equal to 1, then there would have been sufficient information to conclude that rst = 1 in all cases, but as things stand, it ain’t necessarily so!

The trick for data sufficiency questions is to try to come up with counterexamples that would disprove the statement the question is asking about. If one or both of the given statements makes it impossible to come up with a counterexample,  then they are indeed sufficient to conclude that the statement in question is true. Always remember, practice makes perfect, and if you feel you need extra practice with data sufficiency questions or any other part of the GMAT, you can always study with experts like me at Testmasters. Until then, keep up the good work, and good luck!

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