The Most Difficult Data Sufficiency Question to Answer

Photograph by David Elfstrom

This tip for improving your GMAT score was provided by David Newland at Veritas Prep.

Of all the Data Sufficiency questions, the simplest is most difficult to answer. By that, I mean that it requires the most information in order to be sufficient.

The question “x = ?” seems so straightforward, yet it takes more information to get a definite value for x (or any other variable) than it would to answer just about any other question.
Here is an example from the Veritas Prep Data Sufficiency book:
“Is x > y?
1) x = y + 2
2) x/2 = y – 1

The correct answer to this question (as it is written) is A. Statement 1 is sufficient because no matter what value x is, it will always be larger than y. For example, if x is 10 then y equals 8. Even if x is negative, y will be more negative. So if x is – 10 y will equal – 12.

Statement 2 is not sufficient because if you multiply both sides of the equation by 2 you get “x = 2y – 2.” If x equals 1, then y equals 1.5. But if x = 10, then y equals only 6. So x could be larger than y, but it could also be smaller than y, so this is not sufficient.

Getting a definite value
What happens if we alter this question slightly, so that it asks “x =?” Now you need to find a specific value for x in order to establish that a statement is sufficient. Statement 1 is no longer sufficient alone because an infinite number of values of x are possible. Statement 2 continues to be insufficient, as it was with the original question.

What about both statements together? Can you determine a single value for x? Yes, you can. Solving the system of equations (x = y + 2 and x = 2y – 2), you find that x = 6 and y = 4. This is the only set of values that satisfies both equations. So the correct answer is now C. As you can see, it takes more information (both statements in this case) to determine a single value for x and less information (just statement 1) to simply determine if x is always greater than y.

Here is an additional example:

“What is the value of m + n?
1) jm + kn + nj + km = 36
2) j + k = 12

It is clear that neither statement alone will be sufficient for this question. Statement 1 involves too many variables, and statement 2 does not even include m or n. However, both statements, taken together, are sufficient. By rearranging the terms in statement 1, it is possible to factor an “m” from two terms and an “n” from the other two. Statement 1 becomes m (j + k) + n (j + k). Statement 2 indicates that j + k = 12, so that m + n must equal 3 because 3 * 12 = 36. Therefore, the correct answer is C.

Note, however, that it is not possible to determine a distinct value for m or n; m could be 2 and n could be 1, or m could equal 0 and n could equal 3. M and n could even be non-integers, or one of the numbers could be negative. So if this question were to ask for a value for one of the variables, the answer would be E.

Often, less information is required to answer what seems to be a more complex question “m + n = ?” And it can take more information to answer the simpler question “m = ?”

When you are given a Data Sufficiency question that simply asks for the value of a single variable, realize that it takes more information to answer this type of question than to answer any other type. “x =?” may just be the most difficult Data Sufficiency question to answer.

Plan on taking the GMAT soon? Try our own new, 100 percent computer-adaptive, free GMAT practice test, and see how you do.

Before it's here, it's on the Bloomberg Terminal.