GMAT Book Excerpt Exclusive! Data Sufficiency 101

The GMAT invented its own type of math problem, Data Sufficiency (DS), that tests how you think logically about mathematical concepts. DS problems are a cross between math and logic. Imagine that your boss just dumped a bunch of papers on your desk, saying, “I’m wondering whether we should raise the price on this product. Can you answer that question from this data? If so, which pieces do we need to prove whether we should or should not raise the price?” What would you do?

Your boss has asked a specific question: Should you raise the price? You have to decide which pieces of information will allow you to answer that question—or, possibly, that you don’t have enough information to answer the question at all.

This kind of logical reasoning is exactly what you use when you answer DS questions.

How Data Sufficiency Works

You will certainly need to know math in order to answer Data Sufficiency questions, but you also need to know how DS works in the first place. And you need to know certain strategies that will help you to work through DS problems efficiently and effectively.

Consider this question: How old is Farai?

Obviously, you can’t answer that question right now—you have no information about Farai or Farai’s age. Imagine that you’re also told a fact: Farai is 10 years older than Dmitry.

But you don’t know anything about Dmitry’s age either! The GMAT would say that this fact—Farai is 10 years older than Dmitry—is not sufficient (i.e., not enough) to answer the question. If you do know this fact, though, then what additional information would allow you to be able to answer the question?

Well, if you knew how old Dmitry was, then you could figure out how old Farai was. For example, if Dmitry is 10, then Farai would have to be 20.

So if you know both that Farai is 10 years older than Dmitry and that Dmitry is 10 years old, then you have sufficient (i.e., enough) information to answer the question: How old is Farai?

Every DS problem has the same basic form. It will ask you a question. It will provide you with some facts. And it will ask you to figure out what combination of facts is sufficient to answer the question.

Take a look at another example, in full DS form:

The Question Stem always contains the Question you need to answer. It may also contain Additional Info (also known as givens) that you can use to help answer the question.

Below the question stem, the two Statements provide additional facts or given information—and you are specifically asked to determine what combination of those two statements would be sufficient to answer the question.

The Answer Choices describe various combinations of the two statements: For example, statement (1) is sufficient, but statement (2) is not. Note that the answer choices don’t contain any possible ages for Farai. DS questions aren’t asking you to solve; they’re asking whether you can solve. (By the way: No need to try to figure out what all of those answer choices mean right now; you’ll learn as you work through this chapter.)

DS questions look strange but you can think of them as deconstructed Problem Solving (PS) questions—the “regular” type of multiple-choice math problem. Compare the DS-format problem shown earlier to the PS-format problem below:

Samantha is 4 years younger than Dmitry, and Samantha will be 11 years old in 5 years. If Farai is twice as old as Dmitry, how old is Farai?

The two questions contain exactly the same information; that information is just presented in a different order. The PS form puts all of the givens as well as the question into the question stem. The DS problem moves some of the givens down to statement (1) and statement (2).

As is true for the given information in PS problems, the DS statements are always true. In addition, the two statements won’t contradict each other. In the same way that a PS question wouldn’t tell you that x > 0 and x < 0 (that’s impossible!), the two DS statements won’t do that either.

In the PS format, you would need to calculate Farai’s age. In the DS format, you typically will not need to solve all the way to the end; you only need to go far enough to know whether Farai’s age can be calculated. Since every DS problem works in this same way, it is critical to learn how to work through all DS questions using a systematic, consistent process. Take a look at how this plays out:

If Farai is twice as old as Dmitry, how old is Farai?

Samantha is 4 years younger than Dmitry.
Samantha will be 11 years old in 5 years.
Statement (1) ALONE is sufficient, but statement (2) is NOT sufficient.
Statement (2) ALONE is sufficient, but statement (1) is NOT sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.

The goal: Figure out which pieces of information would allow you to answer the question (How old is Farai?).

Your first task is to understand what the problem is saying and jot down the information in math form. Draw a T on your page to help keep the information organized; write information from the question stem above the horizontal line. Make sure to include a question mark to indicate the question itself (later, you’ll learn why this is important):

Hmm. Reflect for a moment. If they tell you Dmitry’s age, then you could just plug it into the given equation to find Farai’s age. Remember that!

Take a look at the first statement. Also, write down off to the right of your scratch paper, above the line (you’ll learn what this is as you work through this chapter):

Samantha is 4 years younger than Dmitry.

Translate the first statement and jot down the information below the horizontal line, to the left of the T. (Not confident about how to translate that statement into math? Use Manhattan Prep’s GMAT Foundations of Math to practice translating.)

The first statement doesn’t allow you to solve for either Samantha or Dmitry’s real age. Statement (1), then, is not sufficient. Cross off the top row of answers, (A) and (D).

Why? Here’s the text for answers (A) and (D):

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

(D) EACH statement ALONE is sufficient.

These two answers indicate that statement (1) is sufficient to answer the question. But statement (1) is not sufficient to find Farai’s age, so both (A) and (D) are wrong.

The five answer choices will always appear in the order shown for the above problem, so any time you decide that statement (1) is not sufficient, you will always cross off answers (A) and (D) at the same time. That’s why the answer grid groups these two answers together on the top row.

Next, consider statement (2), but wait! First, forget what statement (1) told you. Because of the way the DS answers are constructed, you must evaluate the two statements separately before you look at them together. So here’s just statement (2) by itself:

In your T diagram, write the information about statement (2) below the horizontal line and to the right. It’s useful to separate the information this way in order to help remember that statement (2) is separate from statement (1) and has to be considered completely by itself first. (You’ll always organize the information in this way: The question stem goes above the T, statement (1) goes below and to the left of the T, and statement (2) goes below and to the right.)

Back to statement (2). This one allows you to figure out how old Samantha is now, but alone the info doesn’t connect back to Farai or Dmitry. By itself, statement (2) is not sufficient. Of the remaining answers (BCE), answer (B) says that statement (2) is sufficient by itself. This isn’t the case, so cross off answer (B).

When you’ve evaluated each statement by itself and haven’t found sufficient information, you must look at the two statements together. Statement (2) allows you to figure out Samantha’s age. Statement (1) allows you to calculate Dmitry’s age if you know Samantha’s age. Finally, the question stem allows you to calculate Farai’s age if you know Dmitry’s age!

As soon as you can tell that you can find Farai’s age, write an S with a circle around it to indicate sufficient. Don’t actually calculate Farai’s age; you only need to know that you can calculate it. Save that time and mental energy for other things on the test.

The correct answer is (C): Both statements together are sufficient to answer the question but neither statement alone is sufficient.

The Answer ChoicesThe five Data Sufficiency answer choices will always be exactly the same (and presented in the same order), so you won’t even need to read them on the real test. By then, you’ll have done enough DS problems to have them memorized. (In fact, to help you memorize, this book won’t even show the DS answer choices in end-of-chapter problem sets.)

Here are the five answers written in an easier way to understand:

Statement (1) does allow you to answer the question, but statement (2) does not.
Statement (2) does allow you to answer the question, but statement (1) does not.
Neither statement works on its own, but you can use them together to answer the question.
Statement (1) works by itself and statement (2) works by itself.
Nothing works. Even if you use both statements together, you still can’t answer the question.

Answer (C) specifically says that neither statement works on its own. For this reason, you are required to look at each statement by itself first and decide that neither one works alone before you are allowed to evaluate the two statements together.

Here’s an even shorter way to remember the five answer choices, the “12-TEN” mnemonic (memory aid):

As you practice DS over the next couple of weeks, make an effort to memorize the five answers. If you do a couple of practice DS problems every day in that time frame, you’ll likely memorize the answers without conscious effort—and you’ll solidify the DS lessons you’re learning right now.

Speaking of solidifying the lessons you’re learning, set a timer for two minutes and try this problem:

What is the value of 20% of x ?

30 is one-half of x.
x is 0.25 of 240.

Statement (1) ALONE is sufficient, but statement (2) is NOT sufficient.
Statement (2) ALONE is sufficient, but statement (1) is NOT sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.

Ready? What did you get? (If you got stuck and didn’t get to an answer, pick one anyway. That’s what you’ll have to do on the real test, so you might as well practice that now.)

Start with the question stem: What is 20% of x ? Pause. Your first goal is to understand the significance of the question. This is DS—you don’t have to find the actual value. What would you need to know in order to be confident that you could calculate that value?

If you can find a single value for x, then you can find 20% of that value, so the real question is a bit simpler: What is x ?

Congratulations! You’ve just rephrased a DS question. Rephrasing a question allows you to get right down to the heart of the question—and save yourself time and mental energy as you solve.

Now, you can dive into the statements with a simpler plan: Will this statement allow you to find a single value for x ? Jot down your answer grid and look at the first statement:

1. 30 is one-half of x.

Some people may be able to evaluate this statement without writing anything down. Others will want to jot it down in “real math” terms—as an equation, not a sentence.

Statement (1) is a linear equation with just one variable. This equation can indeed be solved for a single value of x, so this statement is sufficient to answer the question. Which row should you cross off in the grid, AD or BCE?

Think of statement (1) as associated with answer choice (A). If statement (1) is sufficient, then answer (A) needs to stay in the mix; cross off the bottom row, BCE.

What’s next? Pause and try to remind yourself before you keep reading.

Now, forget about statement (1) and take a look at statement (2):

2. x is 0.25 of 240.

If you feel confident that this statement will also translate into a linear equation with just one variable, then you may choose not to write anything down. If you’re not sure, though, write it down to confirm.

This equation will also allow you to solve for a single value for x, so statement (2) is sufficient to answer the question.

Since statement (2) is also sufficient, cross off answer (A) and circle answer (D): Either statement alone is sufficient to answer the question. Do actually take the time to do this on your scratch paper before you select your answer on screen. It won’t take you more than a second and this action will help to minimize careless mistakes on the test.

Here’s a summary of the answer choice process when starting with statement (1):

{That’s it for our excerpt! We hope you learned something. If you like what you’ve read, you can find the rest of this chapter—and a lot more!—in Manhattan Prep’s GMAT All the Quant book. If you’re looking for other free lessons and practice problems, sign up for a free Starter Kit syllabus on our site.}

Stacey Koprince is a Manhattan Prep instructor based in Montreal, Canada and Los Angeles, California. Stacey has been teaching the GMAT, EA, GRE, and LSAT for more than 15 years and is one of the most well-known instructors in the industry. Stacey loves to teach and is absolutely fascinated by standardized tests.