Data Sufficiency (Beginner's Guide)

Note: Today's article is the sixth in a series I'm running throughout January and February called "The Beginner's Guide to the GMAT." Here are parts one, two, three, four, and five.

Data Sufficiency is a challenge that is unique to the GMAT. You won't find a Data Sufficiency problem anywhere else in the world, but if you want a respectable score on the Quantitative part of the test, you'll need to spend a lot of time getting comfortable with the Data Sufficiency question type.

The Data Sufficiency Format

If you're a complete novice, it's necessary to familiarize yourself with the basic format. Here's what a Data Sufficiency item looks like:

If x is positive, is x a prime number?
(1) x is odd.
(2) x < 8

There are three important components to any DS question:

• Information given in the question. Here, we know that x is positive. That will never change. (There isn't always information given in the question.)
• The question itself. We want to know whether x is prime.
• The statements. (1) and (2) give us information that may or may not allow us to answer the question.

The Process

Evaluate each statement on its own. If there is information given in the question, keep that in mind as well.

First, look at (1). Using (1) alone, we know that x is positive, and that it is odd. Is that enough information to answer the question? If x is a positive odd number, it could be prime: for instance, if x = 3. However, it might not be prime: for instance, if x = 9. Thus, we say that statement (1) is insufficient.

Next, look at (2) alone. The tricky part is that you have to temporarily forget what you learned in (1). (It may sound easy, but I absolutely guarantee you that you'll make this mistake at least once, and probably many more times than that.)

Again, we're also considering information given in the question. Here, then, we know that x is positive, and that it is less than 8. If x is greater than 0 and less than 8, is it prime? Again, we don't know. It could be 3, which is prime, but it could be 4, which is not. Further, we don't know that x is an integer, which opens up the possibility that x is, say, 2.5. So, statement (2) is insufficient.

Putting the Statements Together

If both statements are insufficient on their own, we must consider both of them together. Here, we have all of the information available to us: x is positive, it is odd, and it is less than 8. The only possible values for x are 1, 3, 5, and 7.

Still, however, we don't have enough information. While 3, 5, and 7 are prime, 1 is not a prime. The statements, when taken together, are still insufficient.

The Choices

One thing that makes Data Sufficiency more manageable is that the choices never change: They are the same on every single DS item. Here they are:

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

(D) EACH statement ALONE is sufficient.

(E) Statements (1) and (2) TOGETHER are NOT sufficient.

(I wrote more about the choices, and some additional tricks you can use to navigate them, in this article.

In the question we just worked through, the correct choice was (E).

Data Sufficiency Strategies

I've written a few other articles on Data Sufficiency, but to keep things short, here are some pieces of advice to start with:

• Don't calculate except when necessary. You only need to know whether the statements are sufficient, not what the value of x is.
• Simplify everything. Often, the questions are needlessly complex, but if you spend a few seconds looking for what you really need to know, you can make the question much simpler.
• Don't pick numbers as your default strategy. (See: The Perils of Picking Numbers.)

When you're starting out, Data Sufficiency can seem very daunting, but keep practicing. By the time you take the test, you should be handling DS questions faster than Problem Solving items (because you don't have to calculate), and the format will be second nature.

About the author: Jeff Sackmann has written many GMAT preparation books, including the popular Total GMAT Math, Total GMAT Verbal, and GMAT 111. He has also created explanations for problems in The Official Guide, as well as 1,800 practice GMAT math questions.

• Data Sufficiency: more articles
• All articles at GMAT Hacks
• Search GMAT Hacks

Total GMAT Math The comprehensive guide to the GMAT Quant section. It's "far and away the best study material available," including over 300 realistic practice questions and more than 500 exercises! Click to read more.