In a GMAT Data Sufficiency Yes/No question asking whether x > 0, if Statement (1) implies … — GMAT

In a GMAT Data Sufficiency Yes/No question asking whether $x > 0$ , if Statement (1) implies $x^3 - x = 0$ and Statement (2) implies $x^2 - 1 = 0$ , then combining both statements is sufficient to answer the question because combining them narrows the set of possible values of $x$ to a smaller set than either statement alone.

Answer: Answer

Answer

False

The correct evaluation is False. In GMAT Data Sufficiency Yes/No questions, combining statements is sufficient only if every remaining value in the combined solution set yields the exact same answer (either all 'Yes' or all 'No'). Here, the combined set

\{-1, 1\}

contains

x = -1

(which yields 'No') and

x = 1

(which yields 'Yes'), so the combined statements remain insufficient.

Step-by-Step Solution

Analyze Statement (1) independently.

Solving

x^3 - x = 0

yields

x(x - 1)(x + 1) = 0

, so

x \in \{-1, 0, 1\}

. Testing these values against the question 'Is

x > 0

?':

x = -1

gives No,

x = 0

gives No, and

x = 1

gives Yes. Because both Yes and No are possible, Statement (1) alone is insufficient.

Each statement must first be evaluated independently by checking if all allowed values yield a uniform answer.

Analyze Statement (2) independently.

Solving

x^2 - 1 = 0

yields

x \in \{-1, 1\}

. Testing these values:

x = -1

gives No and

x = 1

gives Yes. Because both Yes and No are possible, Statement (2) alone is insufficient.

Statement (2) must be evaluated strictly without carrying over any information or restrictions from Statement (1).

Evaluate the combined statement information.

Taking the intersection of the solution sets from both statements gives

\{-1, 0, 1\} \cap \{-1, 1\} = \{-1, 1\}

Combining statements requires finding all values that satisfy both Statement (1) and Statement (2) simultaneously.

Determine sufficiency of the combined set for a Yes/No question.

Within the combined set

\{-1, 1\}

x = -1

yields 'No' (

x \ngtr 0

) while

x = 1

yields 'Yes' (

x > 0

). Since a definitive Yes or No answer cannot be reached, the statements together remain insufficient.

For a Yes/No Data Sufficiency question, sufficiency requires that EVERY value in the combined solution set leads to the exact same answer.

Key Concept

Data Sufficiency Statement Combination for Yes/No Questions

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