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Zorluk: ZorValue vs. Yes/No Data Sufficiency Decision Logic

In a GMAT Data Sufficiency 'Yes/No' question asking whether a2>b2a^2 > b^2, a statement establishing that a+b=0a + b = 0 (where a≠0a \neq 0) is sufficient to answer the question.

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The statement is True. In Yes/No Data Sufficiency, proving that a target condition is conclusively false constitutes a definitive 'No' answer, which makes the statement sufficient.
In Data Sufficiency Yes/No decision logic, sufficiency is attained whenever a statement leads to a single, unambiguous answer—either always 'Yes' or always 'No'. Here, a+b=0a + b = 0 forces a2=b2a^2 = b^2, meaning a2>b2a^2 > b^2 is never true. Thus, the statement provides a definitive 'No' answer to the question, making it sufficient. Therefore, the assertion is correct (True).

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1
Identify the target question type and sufficiency condition.
The target is a Yes/No Data Sufficiency question: 'Is a2>b2a^2 > b^2?' Sufficiency requires either a definitive 'Yes' in all cases or a definitive 'No' in all cases.
Establishing decision logic boundaries is required before evaluating statement sufficiency.
2
Rephrase the given statement algebraically.
The statement gives a+b=0  ⟹  a=−ba + b = 0 \implies a = -b (with a≠0a \neq 0).
Expressing one variable in terms of another allows direct substitution into the target inequality.
3
Substitute the expression into the target inequality a2>b2a^2 > b^2.
(−b)2>b2  ⟹  b2>b2(-b)^2 > b^2 \implies b^2 > b^2, which simplifies to 0>00 > 0. This statement is universally false for any non-zero real number bb.
Evaluating the target inequality under the given constraint tests whether the outcome is deterministic.
4
Apply Data Sufficiency decision logic to the result.
Since a2>b2a^2 > b^2 is false for all allowable values, the answer to the question 'Is a2>b2a^2 > b^2?' is a definitive 'No'. A definitive 'No' answer means the statement is sufficient.
In GMAT DS logic, both a definitive 'Yes' and a definitive 'No' satisfy the requirement for sufficiency.

Anahtar Kavram

Definitive No Sufficiency Rule in Yes/No Data Sufficiency
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Konular

Value vs. Yes/No Data Sufficiency Decision Logic

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