Data sufficiency: how the question works

A different kind of question

Data Sufficiency is one of the question types in the GMAT Data Insights section, which has 20 questions in 45 minutes and an on-screen calculator. A data sufficiency question does not ask you to find an answer. It asks whether you could find one with the information given.

Each question has a question stem and two numbered statements:

What is the value of $x$?

(1) $3x + 2y = 12$

(2) $x - y = -1$

Your job is to decide whether statement (1) alone, statement (2) alone, both together, or neither even together, gives enough information to answer the stem. In this course the five answer choices are always worded the same way and come in the same order:

Choice	Meaning
A	Statement (1) alone is sufficient, but statement (2) alone is not.
B	Statement (2) alone is sufficient, but statement (1) alone is not.
C	Both statements together are sufficient, but neither alone is.
D	Each statement alone is sufficient.
E	Statements (1) and (2) together are not sufficient.

Learn these once so you never reread them under time pressure.

What "sufficient" means

A statement is sufficient when it leads to exactly one answer to the stem. For a value question ("What is $x$?"), that means exactly one possible value. It does not matter whether the value is large, ugly or negative, only that there is one of it. If two or more values remain possible, the statement is not sufficient.

This changes how you work. You do not need the value itself, only proof that it is pinned down. If you can see that a linear equation in one unknown has a single solution, stop: you know it is sufficient without solving it.

The routine

Work in a fixed order, and keep the statements apart until the last step.

1. Read the stem and decide what would answer it. "What is $a + b$?" needs the sum, not $a$ and $b$ separately. Rewrite the stem in its simplest form if you can.
2. Statement (1) alone. Forget statement (2) exists. Is there exactly one answer?
3. Statement (2) alone. Now forget statement (1). Is there exactly one answer?
4. Together, only if neither alone worked. Combine both and ask again.

The order of steps 2 and 3 cuts the choices quickly:

• If (1) alone is sufficient, the answer is A or D. Statement (2) decides between them.
• If (1) alone is not sufficient, the answer is B, C or E. If (2) alone is sufficient, it is B; if not, combine to choose between C and E.

You may start with whichever statement looks easier; just keep track of which choices remain.

Proving "not sufficient" with two cases

To show a statement is not sufficient, find two different situations that both satisfy the statement and give different answers to the stem. For "What is $x$?" with $3x + 2y = 12$: $x = 0, y = 6$ and $x = 2, y = 3$ both satisfy it, with different values of $x$. Two cases settle it; you do not need a general argument.

To show a statement is sufficient, you need a reason that covers every case, such as "this is one linear equation in one unknown" or "the remainder is fixed by the form $12m + 5$".

Counting equations, carefully

A useful rule of thumb: to find $n$ unknowns you usually need $n$ independent linear equations. It is only a rule of thumb. It fails when:

• the two equations are really one equation (one is a multiple of the other);
• the stem asks for a combination such as $a + b$, which one equation can give;
• an equation is not linear, so it can have two solutions ($x^2 = 9$);
• the unknowns must be integers, which can leave a single solution to one equation.

The next two lessons return to the last three. For now: when two equations appear, check that they are genuinely different before you call the pair sufficient.

The statements describe one situation

Treat both statements as true facts about the same situation. A well-built data sufficiency question, including every one in this course, is written so that at least one case satisfies both statements at once. When you combine them, you are looking for exactly those cases. If your work suggests that no case satisfies both, take that as a sign of a slip and recheck.