# GMAT Yes/No Data Sufficiency: Prove a Verdict | topin

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## Judge the verdict rather than the number of possible values

GMAC describes Data Sufficiency as identifying relevant information and determining when enough data are available. The examples here are original reasoning exercises. The [Data Sufficiency overview](/gmat/data-insights/data-sufficiency) explains the five response combinations; this article concentrates on proving a yes/no verdict across the allowed cases.

A numerical variable may take several values while a yes/no question still has a single answer. If the question asks whether x is positive and the statement establishes x > 10, many values remain, but all give yes. Demanding an exact value of x would judge a harder problem than the one asked.

Likewise, if the statement establishes x ≤ 0, every allowed value gives no. The question has been answered. “No” is not evidence of insufficiency; a mixture of yes and no is. Write the target as a verdict so you do not accidentally begin solving for a precise quantity.

To disprove sufficiency, produce two allowed cases with opposite verdicts. To prove it, explain why no opposite-verdict case can satisfy the condition. Testing many friendly examples without finding a counterexample is weaker than identifying the condition that forces the answer.

## Original example: when both statements force no

Question: for a real number x, is x greater than 5? Statement 1: x ≤ 3\. Statement 2: x² = 4\. Statement 1 allows many x values, but every one is at most three, so it gives a definite no. It is sufficient by itself.

Statement 2 allows x = 2 or x = −2\. Both are not greater than five, so it also gives a definite no. Each statement alone is sufficient: choose the response corresponding to that outcome, conventionally D. The negative root must be considered, but it does not change the verdict here.

Contrast a different question using the same statement 2: is x positive? Now x = 2 gives yes and x = −2 gives no. Statement 2 is insufficient for that target. The information has not changed, but the question has. Sufficiency belongs to a statement-question pair, not to an equation in isolation.

This is why memorising “two roots means insufficient” is unreliable. Two roots are insufficient for a unique-value target, but can be sufficient for a yes/no target if both lie on the same side of the condition. Keep the target visible while considering the domain.

## Original example: each alone fails but together works

Question: x is a real number. Is x positive? Statement 1: x² = 9\. Statement 2: x > −1\. For statement 1, x = 3 gives yes and x = −3 gives no. Those two cases prove insufficiency. Do not silently assume the positive root.

For statement 2 alone, x = 2 gives yes and x = −0.5 gives no. Both satisfy x > −1\. Statement 2 is insufficient. You must not carry x² = 9 into this separate test, because that would contaminate the judgment of statement 2 alone.

Together, the possible roots from statement 1 are 3 and −3, and statement 2 excludes −3\. Only x = 3 remains, giving yes. Both together are sufficient while neither alone is: the conventional C response. The conclusion follows from intersecting the permitted cases.

__Original case record for “is x positive?”__
| Information tested  | Yes case | No case            | Sufficiency         |
| ------------------- | -------- | ------------------ | ------------------- |
| Statement 1: x² = 9 | 3        | −3                 | Insufficient alone  |
| Statement 2: x > −1 | 2        | −0.5               | Insufficient alone  |
| Both statements     | 3        | No allowed no case | Sufficient together |

## Use the stated domain to choose valid counterexamples

Question: is x² greater than x? For real x, the difference is x(x − 1). It is positive when x < 0 or x > 1, zero at 0 and 1, and negative between 0 and 1\. Those regions give you a compact map for later statements.

If a statement says x is positive, x = 2 gives yes while x = 0.5 gives no, so it is insufficient. If the question instead specifies x is an integer greater than one, the answer is always yes without needing a unique value. The domain removes the fractional counterexample.

Do not use x = 0 to refute a statement requiring a positive x, or x = 0.5 when the prompt requires an integer. A counterexample is useful only if it satisfies every condition in the information being tested. List the conditions beside the candidate values before judging the verdict.

The broader [number and rate examples](/articles/gmat-rates-work-units) also require explicit assumptions. In sufficiency, an invented assumption can be especially damaging because it removes cases that should remain possible. Do not assume money, measurements or variables are integers unless the prompt makes that restriction.

Original boundary question: for a real x, is x at least 1? Statement 1 says x > 0\. Statement 2 says x² = 1\. Statement 1 allows x = 0.5 and x = 2, so it is insufficient. Statement 2 allows −1 and 1, giving opposite verdicts, so it is insufficient. Together only x = 1 survives, and the inclusive “at least” gives yes. The combined response is C.

Change the target to “is x greater than 1?” while leaving those statements. Each alone remains insufficient, but together x = 1 now gives no. The combined response remains C because the verdict is still unique. The answer to the underlying question changed; the sufficiency classification did not. This is a useful check against equating a no verdict with failure.

Before trying a boundary value, copy the inequality accurately. In the two versions above, one word changes whether equality qualifies. When reviewing a wrong answer, record the target and verdict separately so you can see whether you misunderstood the question or correctly answered it but selected the wrong sufficiency combination.

## Recognise when combined information still allows both answers

Original question: a shop’s revenue increased. Did its profit increase? Statement 1: revenue rose from £100,000 to £120,000\. Statement 2: costs increased by £10,000\. With statement 1 alone, costs might rise by £5,000 or £30,000, producing different profit effects. It is insufficient.

Statement 2 alone does not specify the revenue change. Revenue might rise £5,000 or £20,000 while costs rise £10,000, again giving different answers. Together, revenue rises £20,000 and costs rise £10,000, so profit rises £10,000 under the stated revenue-minus-cost model. This pair is sufficient together.

Change statement 2 to “costs increased by more than £10,000”. Together, costs could rise £15,000, producing higher profit, or £25,000, producing lower profit. Both fit the new condition. The combined information is now insufficient, corresponding to E. A bound is not necessarily an exact amount.

The difference between the two versions is one qualifier. A familiar business story should not lead you to overlook it. Our [percentage-base guide](/articles/gmat-percent-change-reverse-percentages) explains how to calculate the figures, but sufficiency asks whether the available relationship determines the verdict across all allowed cases.

## Use a case record rather than an open-ended search

For each statement alone, write S or I and a brief reason. If insufficient, record one yes case and one no case. If sufficient, record the condition that forces the verdict. Then combine only when the individual outcomes require it. This keeps your scratch work aligned with the response combinations.

When searching for cases, try meaningful boundaries: zero, one, a negative, a fraction between zero and one, or an exact inequality endpoint when allowed. These are candidate tests, not a ritual to perform on every question. Select cases from the actual domain and the expression’s structure.

On review, ask whether the failure came from contamination, an unstated domain restriction, treating no as insufficient or confusing a unique value with a unique verdict. Repair that cause on a fresh question. Repeating the same roots example after memorising it does not establish that the habit transfers.

topin’s [free full-length GMAT mock](/gmat/practice-test), marked on the official scale, can check whether the method remains efficient among other DI tasks. If you bookmark a sufficiency item, note the exact case you still need to test. The [review strategy](/articles/gmat-review-edit-strategy) prioritises those concrete checks over restarting every uncertain solution.

For a final response check, read your two individual S/I labels and combined verdict before selecting the answer combination. This catches a correct logical solution entered under the wrong letter.

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## FAQs

Is a definite no sufficient in Data Sufficiency?

Yes. If every allowed case gives no, the yes/no question is answered.

Do multiple possible values always mean insufficient?

No. Different values can give the same verdict. The target may not require a unique value.

How do I prove a statement is insufficient?

Find a permitted yes case and a permitted no case that both satisfy that statement and the original question conditions.

Can I use statement 1 while testing statement 2 alone?

No. Test statement 2 with the original conditions only, then combine when appropriate.

Why is my fractional counterexample sometimes invalid?

If the prompt requires an integer, a fraction is outside the allowed domain and cannot refute sufficiency.

## Sources (checked 5 October 2026)

* [mba.com: official Data Sufficiency purpose (checked 5 October 2026)](https://www.mba.com/exams/gmat-exam/about/exam-content)

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