Which answer choices should you use?
Data Sufficiency is part of Data Insights on the current GMAT. GMAC describes it as a decision task: identify the relevant information and determine whether it is enough to solve the problem. The question does not always require you to calculate a numeric value.
The answer choices below are paraphrased for learning purposes. Learn the logic before memorizing the letters. They resemble those on other sufficiency tests, but you should practice the answer choices and English prompts used on your exam.
| Choice | Decision |
|---|---|
| A | Statement 1 alone is sufficient; statement 2 alone is not. |
| B | Statement 2 alone is sufficient; statement 1 alone is not. |
| C | The statements together are sufficient; neither statement alone is sufficient. |
| D | Each statement alone is sufficient. |
| E | Even together, they are not sufficient. |
Why must you reset the information between the two tests?
The main question applies to both statements. However, what you learned from statement 1 does not carry over when you test statement 2 alone. If you tend to carry a previous condition forward mentally, make two columns in your scratch work.
For a value question, look for two different values that fit. For a yes/no question, look for one yes case and one no case. Two different values that both produce “yes” do not prove insufficiency: the answer to the question itself must change.
Is x positive? (1) x² = 36. (2) x > −2.
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The solution, step by step
C — the two statements together are sufficient; neither alone is sufficient.
The method in action
- With statement 1 alone, x can be 6 or −6: both yes and no are possible. With statement 2 alone, x can be 1 or −1: both answers are still possible.
- Together, x = −6 is ruled out by x > −2. That leaves x = 6, so the answer is yes. You could not use x² = 36 while testing statement 2 alone.
- A and B assign sufficiency to an ambiguous statement; D says each is sufficient; E overlooks that combining them rules out the negative case.
Can a “no” answer be sufficient?
Yes. “Sufficient” does not mean that the property in question is true. It means you can determine the answer. This distinction keeps you from treating a proven “no” as a lack of information.
Is the integer n divisible by 3? (1) n leaves a remainder of 1 when divided by 3. (2) n is even.
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The solution, step by step
A — statement 1 alone is sufficient.
The method in action
- Statement 1 establishes a no: n = 3k + 1 cannot be divisible by 3.
- With statement 2 alone, n = 6 gives yes and n = 8 gives no. Evenness does not determine divisibility by 3.
- B reverses the statements; C overlooks that statement 1 is already sufficient; D incorrectly says statement 2 is sufficient; E confuses a negative answer with insufficiency.
The pitfall
One matching example never proves uniqueness
Finding one value that works shows only that it is possible. To establish sufficiency, you must show that every allowed value leads to the same answer. A few trials may suggest a rule; a factorization, bound, or logical condition must justify it.
Do not add an unstated assumption: real does not mean integer, and a variable is not necessarily positive. In English, “positive” means strictly greater than zero. These restrictions change which counterexamples are possible.
How can you tell whether each statement is sufficient on its own?
Even after establishing that the first statement is sufficient, test the second independently to distinguish A from D. Stopping after the first success leads to an incorrect choice.
What is the value of x? (1) 3x + 2 = 17. (2) x is the positive square root of 25.
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The solution, step by step
D — each statement alone is sufficient.
The method in action
- Statement 1 gives 3x = 15, then x = 5. Statement 2 also gives x = 5 because it specifies the positive square root.
- A or B overlooks a sufficient statement; C unnecessarily requires combining them; E contradicts both determinations.
- Their agreement confirms the result is consistent, but choice D rests on two separate lines of reasoning.
Key takeaways
- Test statement 1 alone, then statement 2 alone with the given information.
- Look for two different answers, not just two values.
- Combine the statements only after establishing that each is insufficient on its own.