GMAT Data Sufficiency

What a Data Sufficiency question asks

Data Sufficiency (DS) is one of five GMAT Data Insights question types. A question gives a problem followed by two statements. Your task is to decide whether the information is enough to answer the problem. You do not have to find the requested number if you can prove that the statements determine exactly one answer.

This distinction changes how you work. In a normal problem, you solve for x. In DS, you ask whether the information pins down x. A statement that narrows x to one value is sufficient. A statement that narrows it to many possible values is not. For a yes-or-no question, sufficient information must force the answer to be yes in every allowed case or no in every allowed case.

The most common DS mistake is treating one example as proof. If a statement permits x = 2 and x = 5, finding one value that satisfies the condition does not show the answer is fixed. A single counterexample can prove insufficiency when it produces a different outcome, but sufficiency requires a logical argument covering all permitted cases.

Use a four-step method

1. Read the question and identify exactly what must be determined. Note restrictions such as integer, positive, distinct or nonzero.
2. Test statement one by itself. Ignore statement two. Decide whether statement one alone forces a unique value or a definite yes/no answer.
3. Reset and test statement two by itself. Do not carry a conclusion from statement one into this step.
4. If neither statement alone is sufficient, combine them and decide whether both together settle the question.

The answer choices encode the sufficiency pattern. Learn the choice mapping used by official GMAT practice so you can select the corresponding option quickly. The core logic remains the same: statement one alone, statement two alone, or both together. Do not begin by solving both statements simultaneously; that makes it easy to assume one statement while evaluating the other.

Translate the question precisely

Before testing statements, rewrite the target in plain language. 'What is x?' needs one exact value. 'Is x positive?' needs a fixed yes or no. 'Is n even?' is a parity decision. 'What is the remainder when n is divided by 5?' needs a unique remainder, not a unique value of n.

Restrictions in the question matter. If x is an integer, x squared equals 9 allows x = 3 or x = -3. If x is positive, it allows only 3. If x is a positive integer, a statement that x is greater than 2 may still permit many values. Do not assume a value is positive or integral unless the question or a statement says so.

For yes-or-no questions, test both outcomes. If a statement allows one case where the answer is yes and another where it is no, it is insufficient. For example, knowing that x is an integer does not answer whether x is positive. A sufficient statement could be x > 0, which forces yes, or x < 0, which forces no.

Test one statement at a time

When statement one says x + 5 = 12 and the question asks for x, it is sufficient because x = 7. Statement two might say x is a positive integer, which is not sufficient alone. Since statement one already determines x, the combined information is also sufficient, but you do not need to combine them to reach the choice pattern.

If a statement contains an equation with two variables, ask whether it determines the requested quantity. The equation x + y = 10 does not determine x alone because several pairs work. But if the question asks whether x + y equals 10, the statement is sufficient because it directly answers yes. Sufficiency always depends on the question, not the amount of math in the statement.

Reset completely between statements. If statement one gives x = 4, do not use x = 4 while evaluating statement two. Many questions are designed so each statement alone leaves multiple possibilities but both together settle the target. Keeping the statements separate prevents accidental use of information that is not available in that step.

Use cases and counterexamples

For a statement that appears insufficient, try to produce two allowed cases with different answers to the question. That is a clean proof of insufficiency. If the question asks for x and the statement permits x = 2 or x = 8, the target is not unique. If the question asks whether x is greater than 5, those two cases produce different yes/no answers, so the statement is insufficient.

Choose cases that respect every condition. If the statement says x is a positive integer, x = 0 is not a valid counterexample. If it says x and y are distinct, do not use equal values. A counterexample outside the permitted domain proves nothing.

For sufficiency, move beyond examples. If the question asks whether a positive integer n is divisible by 3 and a statement says n = 3k for an integer k, that is sufficient by definition. Trying n = 3 and n = 6 illustrates the rule but does not replace the proof. A short algebraic argument is often more reliable than a list of test values.

Original worked examples

One statement determines a value

Question: What is integer n? Statement one: 3n - 4 = 17. Statement two: n is positive. Statement one is sufficient because 3n = 21 and n = 7. Statement two is insufficient because many positive integers are possible. The answer pattern is statement one alone.

A distractor might claim both statements are needed because statement two confirms that n is positive. It is not needed: statement one already gives one exact value. Another mistake is to find n = 7, then evaluate statement two using that value. That improperly combines the statements in the second step.

A yes-or-no target

Question: Is integer k even? Statement one: k squared is even. Statement two: k is a multiple of 4. Statement one is sufficient because an integer with an even square must itself be even. Statement two is sufficient because every multiple of 4 is even. Each statement alone answers yes, so either one is enough.

A common wrong approach is to test only k = 2 and k = 4, then conclude the answer is yes. Here the logic is what proves sufficiency. If statement one had instead said k squared is 36, the statement would be insufficient because k could equal 6 or -6, although both are even. If the question asked for k itself, those two values would be different answers.

Combine statements after separate tests

Question: Is x greater than y? Statement one: x + y = 12. Statement two: x - y = 4. Statement one alone is insufficient; (x,y) could be (7,5) or (5,7), giving different answers. Statement two alone is sufficient because x - y = 4 directly implies x is greater than y. Therefore the question is answered by statement two alone.

This example shows why an equation with two variables is not automatically insufficient. The first equation leaves the comparison open, while the second states the difference's sign. The requested relation can be determined without finding each variable. A candidate who solves both equations before testing each statement may get the right result but use an inefficient and error-prone process.

Statement that appears specific but is not enough

Question: What is the remainder when positive integer m is divided by 5? Statement one: m is divisible by 2. Statement two: m is between 10 and 14, inclusive. Statement one allows many remainders. Statement two allows m = 10, 11, 12, 13 or 14, with remainders 0 through 4. Neither alone is sufficient. Together, the even choices are 10, 12 and 14, with remainders 0, 2 and 4, so even the combination is insufficient.

The range in statement two looks narrow, but it does not determine a unique remainder. Listing the allowed values is an efficient way to test it. A common distractor assumes that 'between 10 and 14' means 12, when the statement includes every integer in the range.

Common DS traps

• Using statement one while evaluating statement two, or vice versa.
• Assuming values are positive, integer or distinct when the question does not impose that restriction.
• Treating one example as proof of sufficiency.
• Solving for more information than the question asks for.
• Forgetting that a yes-or-no question can be sufficient even when variables are not uniquely determined.
• Overlooking a denominator that could be zero or a boundary value that changes the result.
• Spending several minutes on algebra when a counterexample would establish insufficiency.

Be especially careful with squares, absolute values, inequalities and ratios. If x squared equals 16, x may be 4 or -4 unless a restriction removes one value. If a ratio is 2:3, the quantities can be 2 and 3 or 20 and 30; the ratio does not set their scale. If x is at least 5, it can equal 5, so a strict inequality conclusion may not follow.

Timing strategy

Data Insights gives 45 minutes for 20 questions, so the average is 2 minutes and 15 seconds. Some DS questions resolve quickly; others need casework. Start by formalizing the target, because that can prevent unnecessary solving. If a statement is clearly insufficient, write two valid cases and move on. If a statement seems sufficient, state the reason every permitted case gives the same answer.

Use scratch work to label the steps: Q, S1, S2, Both. This simple structure helps prevent information leakage between tests. Keep algebra compact and write domain restrictions beside the equation. If you have spent too long expanding expressions, pause and ask whether a unique answer is actually needed.

At the end of practice, note which error type occurred: missed restriction, weak counterexample, accidental combination, or unnecessary calculation. Then choose a new DS problem that tests the same issue. A review note such as 'check negative roots when squaring' is more useful than copying a solution.

How to practice Data Sufficiency

Begin with untimed questions and explain why each statement does or does not determine the answer. Once the logic is consistent, add time limits and mix DS with other DI formats. Mixing matters because the live section does not announce that the next problem is a sufficiency problem; you have to recognize its structure.

For every insufficient statement, save a counterexample pair. For every sufficient statement, save the proof in one sentence. Review these notes after a delay and solve fresh questions. Do not memorize the five answer choices as a pattern detached from reasoning. The reliable skill is testing determinacy.

Data Sufficiency is one piece of the 20-question Data Insights section, alongside multi-source, table, graphics and two-part questions. The section has an on-screen calculator, but DS often rewards algebraic structure and logical testing more than arithmetic. Treat the calculator as optional support, not as the central method.