In a GMAT Data Sufficiency question asking whether the real number x is positive, a statem… — GMAT

In a GMAT Data Sufficiency question asking whether the real number $x$ is positive, a statement that uniquely restricts $x$ to the set $\{-3, -1\}$ is sufficient to answer the question.

Answer: Answer

Answer

True. In Yes/No Data Sufficiency questions, a statement is sufficient if it determines a conclusive 'Yes' or 'No'. Because all possible values of

x

(

-3

and

-1

) produce a definitive 'No' to whether

x

is positive, the statement is sufficient.

The statement is true because in a Yes/No Data Sufficiency framework, sufficiency requires only a single definitive answer ('Yes' or 'No'). Since all candidate values in the set

\{-3, -1\}

are strictly negative, the question 'Is

x

positive?' receives a definitive 'No' answer in every case.

Step-by-Step Solution

Identify the decision structure of the question stem.

The target question stem asks 'Is

x > 0

?', which is a Yes/No Data Sufficiency structure.

Determining whether a question stem requires a single numerical value (Value structure) or a definitive binary answer (Yes/No structure) dictates the criteria for sufficiency.

Evaluate the answer to the stem under all permissible values from the statement.

x = -3

x > 0

is False ('No'). If

x = -1

x > 0

is False ('No').

Check if every allowed case produces the exact same binary outcome.

Apply Data Sufficiency criteria for Yes/No questions.

Because every permissible value leads to a single, unambiguous answer of 'No', the statement provides sufficient information.

A definitive 'No' establishes sufficiency just as effectively as a definitive 'Yes'.

Key Concept

Value vs. Yes/No Data Sufficiency Decision Logic

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