A Yes/No statement must force one answer
A statement is sufficient when it proves Yes for every value it permits or proves No for every value it permits. One example is not proof unless the statement restricts all possible cases.
← GMAT Course
DATA INSIGHTS · GMAT-DI-DSYN · DRAFT
Data Sufficiency: Yes-No Questions
Build the concept, interpret evidence, and apply it in a separate assessment pool.
Learn: Evidence and decisions
Use counterexamples to disprove sufficiency
If one allowed value answers Yes and another answers No, the statement is insufficient. Check the stated domain before choosing examples.
For Yes/No, one definite answer is enough
A statement is sufficient if it forces Yes or forces No. It does not need to determine a numerical value. To show insufficiency, produce admissible cases that lead to different answers.
Test independently before combining
Evaluate statement (1) by itself, then statement (2) by itself. Combine only when neither alone settles the requested decision.
Learning Objectives
- Classify each statement as sufficient or insufficient for a Yes/No question.
- Use counterexamples that produce both Yes and No to prove insufficiency.
- Combine statements only after evaluating them independently.
Prerequisite Knowledge
- Divisibility rules for integers.
- A Yes/No question is sufficient only if it forces the same answer for every allowed case.
Worked Examples
A definite No is sufficient
A warehouse has a positive whole number of crates. Can all crates be packed into groups of eight with none left over? Statement (1): the crate count is odd. Statement (2): the count is greater than twenty.
- Statement (1) forces No: every multiple of eight is even. You do not need the exact count.
- Statement (2) allows both a count that works and one that does not.
- Stop after establishing that the first statement alone answers the question and the second does not.
Conclusion: Statement (1) alone is sufficient. A guaranteed No is just as sufficient as a guaranteed Yes.
A statement may settle the decision without giving one value
Is x positive? (1) x²=9. (2) x>0.
- Test statement (1) alone. The possible values are 3 and −3, which give different answers to the question.
- Test statement (2) alone. It directly forces the answer Yes.
Conclusion: Statement (1) is insufficient; statement (2) alone is sufficient. Under the standard Data Sufficiency choices, the answer is (B).
A guaranteed property can answer a Yes/No question
Is integer n even? (1) n is divisible by 4. (2) n is divisible by 3.
- Divisibility by 4 guarantees that n is even, so statement (1) forces Yes.
- Divisibility by 3 alone allows both an odd multiple such as 3 and an even multiple such as 6.
Conclusion: Statement (1) alone is sufficient; statement (2) alone is not. The answer is (A).
Guided Practice: Try, then check
Work through each question on paper before opening its hint or explanation. This learning activity is separate from the scored Practice and Simulation pools.
Guided case: a definite No is enough
A retailer buys an item at a positive cost and later sells it. Is the selling price greater than the purchase cost? Evaluate each statement separately before combining them.
| (1) | The original selling price was 50% above cost. |
| (2) | The actual sale price was two thirds of the original selling price. |
Does the first statement alone answer the actual-sale question?
Show hint
The original price need not be the actual price.
Check reasoning
No. The actual price is unrestricted by the first statement. It could be above or below cost.
Does the second statement alone answer the question?
Show hint
Compare the original price with cost; their relationship is still unknown.
Check reasoning
No. With cost of sixty dollars, original prices of sixty and one hundred twenty dollars give actual prices of forty and eighty dollars, producing opposite answers.
Combine the statements. Is an exact cost necessary?
Show hint
Express each price as a multiple of cost.
Check reasoning
The actual price equals cost for every positive cost. The answer is always No, so both statements together are sufficient.
Sufficiency means one definite answer to the question. It does not mean the answer must be Yes or that the original cost must be known.
Think Like a GMAT Test-Taker
Restate the Yes/No target as a property that must always hold or always fail.
For insufficiency, find one allowed Yes case and one allowed No case.
Do not import a restriction from statement (1) into statement (2).
Common Traps
Assuming a statement guarantees the most familiar case.
Using only one example to claim sufficiency.
Carrying information between the two statements.