How Data Sufficiency Works
Data sufficiency problems are really weird—they were literally created for the GMAT, so if you’re new to the test, you’ve never seen math problems like this before. Even if you’ve been studying for a while, there’s a good chance you feel a little uncomfortable whenever a DS question pops up on the screen.
Why? Because you could completely mess up a DS question and still get to one of the 5 answer choices, having no idea that you messed something up. That’s a really uncomfortable feeling when taking a test! So let’s demystify the DS process.
What is Data Sufficiency?
The GMAT really isn’t a math test. These tests are actually trying to test us on our executive reasoning skills—that is, how well we make decisions and prioritize when faced with too many things to do in too short a length of time.
Data Sufficiency questions test our ability to (quickly) analyze a collective set of data and figure out which pieces are needed to do the job. Imagine your boss dumping a bunch of stuff on you and saying, “Hey, Sam is debating whether to raise the price on this product. Is this the right data to send to them to help them figure that out?” It’s crucial to notice what your boss actually asked you to do. She’s not actually asking you to do the calculations—Sam is going to do that. Instead, she’s just asking whether this data is what Sam will need to do those calculations.
That’s Data Sufficiency! And the beauty of DS is that you can get away with doing a lot less math than you have to do on standard Problem Solving problems—if you know what you’re doing on DS.
How does Data Sufficiency work?
First, you’re given what’s called the question stem. Here’s an example:
How old is Oliver?
The question stem can also provide information, such as:
If Oliver’s age is even, how old is Oliver?
So if they also told you, for example, that Oliver is either 13 or 14 years old, then you can conclude he must be 14, since you can only consider even numbers as possible values for Oliver’s age.
Next, the problem will provide two statements, such as:
(1) Oliver is 4 years older than Anh.
(2) Anh will be 11 years old in 5 years.
These statements are facts. From these facts, can you figure out how old Oliver is? Which facts do you need? The first statement, by itself, indicates a relationship between Oliver and Anh but doesn’t indicate how old Anh is, so that statement is not sufficient to answer the question.
The second statement, by itself, doesn’t help, because it doesn’t indicate anything about Oliver. Statement (2) is also not sufficient.
Put the two pieces of information together. In this case, using both statements 1 and 2 together is sufficient to answer the question, because you can figure out how old Oliver is. (And this situation corresponds to answer choice C on the GMAT.)
You don’t actually have to figure out how old Oliver is. You just have to know that you definitely could if you used both statements (1) and (2) together. In fact, it’s important to build this habit on DS: Only calculate as much as you have to calculate. Once you know that you can calculate a value, stop right there and choose your answer. Save that time to use elsewhere on the test.
There are 5 possible answers to Data Sufficiency questions:
(A) Statement 1 is sufficient to answer the question but statement 2 does not.
(B) Statement 2 is sufficient to answer the question but statement 1 does not.
(C) Neither statement works on its own, but together they are sufficient.
(D) Statement 1 works by itself and statement 2 works by itself.
(E) Nothing works. Even if I use both statements together, I still can’t answer the question.
Here’s an easier way to remember the five answer choices; we call this the twelve-ten mnemonic (memory aid):
1: only statement 1
2: only statement 2
T: together
E: either one
N: neither / nothing
Value vs. Yes/No on Data Sufficiency
All DS questions can be put into one of two broad categories: value questions or yes/no questions. The Oliver question, above, was an example of a value question: You were asked to find a specific value (Oliver’s age). If you can find one specific value, then that information is sufficient to answer the question. If, on the other hand, a statement gives you zero values or more than one value, then that statement is NOT sufficient.
But instead of asking how old Oliver is, a question might ask “Is Oliver 13 years old?” This is a Yes/No question. Imagine that Oliver is actually in his twenties. What’s the answer to that question? No. Is that answer sufficient? Yes!
That, in a nutshell, illustrates the weirdness of yes/no questions. A definitive NO answer to a question is a sufficient answer. Do I know how old Oliver is? Nope, I only know he’s in his twenties. But I wasn’t asked how old he is. The question asked whether Oliver is 13, and I know the answer to that: definitely not. Therefore, the information is sufficient to provide a definitive answer to the question.
If, on the other hand, someone said, “Oliver? Oh, he’s either 13 or 22,” now I would have a “maybe, maybe not” answer, or “sometimes yes, sometimes no.” That’s not sufficient to answer the question.
In short, a definitive Yes answer is sufficient and a definitive No answer is also sufficient. On the other hand, sometimes yes and sometimes no is NOT sufficient.
Finally, just a note. All questions, whether value or yes/no, have this in common:
– A definitive answer to the question (no ambiguity) is sufficient; the answer is always 3 or always Yes or always This One Thing.
– An “it might be this way or that way” answer is NOT sufficient. The answer is 3 or 14; the answer is Yes in this case but No in that case; the answer is It Depends. These are all examples of Not Sufficient answers.
What’s my overall Data Sufficiency strategy?
A new question pops up on the screen. Now what?
First, read the question stem (this is everything above the two statements labeled 1 and 2). Write down any facts, formulas, or info that you want in writing. Note whether you have a value or yes/no question.
Next, glance very briefly at the two statements, just long enough to notice the way in which the information is presented. Written out or pure math? With real numbers? Variables? Percentages or fractions? Fairly simple / straightforward, or more complicated? Do NOT actually do anything with the statements at this point. You’re just gathering information and getting oriented.
Do what’s been described so far for this problem, but then keep reading—don’t solve it all the way.
If x is a positive integer, is x less than 13 ?
(1) x is a multiple of 6.
(2) x < 17
Jot down the fact that x is a positive integer and that they’re asking whether it’s less than 13. Also jot down Y/N to indicate that this is a Yes/No question. The two statements provide pretty basic information—nothing to do yet.
Now, go back to the question stem. Can you figure out or infer anything from this information? Can you simplify or rephrase anything? Unless the question stem is extremely simple, you can probably do something with that information right now that will make your life easier once you get to the statements.
In this case, better articulate what the question really means. Since x must be a positive integer, it must be at least 1. If you can tell that x is in the range 1 to 12, inclusive, then the answer to the question “Is x < 13 ?" will be a definitive Yes. On the other hand, if x is 13 or greater, then the answer will be a definitive No. And if you can’t tell which grouping x falls into…then that information won’t be sufficient to answer the question.
So the real question Now you’re ready to tackle the statements. Usually, you’re going to start with statement 1. If statement (1) looks awful, though, of if statement (2) looks a lot easier than statement (1), then you can start with statement (2).
Let’s start with statement 1 on this one. Write AD on your scratch paper. Below that, write BCE. Now, evaluate statement 1:
In this case, statement 1 indicates that x is a multiple of 6. So x could be 6, in which case the answer to the question is Yes. But x could also be 60, in which case the answer to the question is No. A “sometimes Yes, sometimes No” situation is NOT sufficient, so cross off the top row of letters:
(If statement (1) had been sufficient, you’d cross off the bottom row instead.)
Next, evaluate statement 2. This is important: Completely ignore everything contained in statement 1. Just look at statement 2 all by itself. In this case, statement (2) indicates that x < 17. So x could be 5, in which case the answer is Yes, or x could be 14, in which case the answer is No. This statement is also NOT sufficient, so cross off answer (B):
(If statement (2) had been sufficient, you would have selected (B) as the correct answer.)
The next step is to evaluate statements 1 and 2 together. (Note: If you’ve already found an answer, you don’t have to do this; you only have to do this if you have crossed off answers A, B, and D, as has happened on this problem.)
Using the two statements together, x is a multiple of 6 and x is less than 17. In addition, the question stem indicated that x is positive. Given all of those constraints, x could equal either 6 or 12. So Yes, it is always the case that x < 13. The two statements together are sufficient to answer the question, so the correct answer is (C).
If the two statements together had NOT been sufficient, the answer would be (E).
How can the answer be sufficient when you don’t know whether x equals 6 or 12? The question didn’t ask what x was. The question asked only whether x was less then 13. On Data Sufficiency, it’s super important to understand whether the question is asking you for a value or whether it’s asking a Yes/No question—your answer will depend upon that distinction!
What if you want to start with statement 2 first? You can—the process is actually almost exactly the same, but you have to make one change at the start. In the AD/BCE answer grid, swap the A and the B to get the answer grid BD/ACE instead. Other than that, everything works exactly the same.
Go ahead and try the problem again, only this time start with the second statement and use the BD/ACE answer grid instead. You’ll get to the same answer in the end.
How do I get better at Data Sufficiency?
This article barely scratches the surface of DS. There are all kinds of great strategies out there—how to test numbers, how to prove insufficiency, how to use theory vs. real numbers, and so on. Any GMAT class or GMAT test-prep book will have strategies to help you learn how to get better and faster at DS.
Happy studying!