In a GMAT Data Sufficiency question asking for the unique value of a variable x, if Statem… — GMAT

In a GMAT Data Sufficiency question asking for the unique value of a variable $x$ , if Statement (1) alone limits the possible values of $x$ to the set $\{2, 5\}$ and Statement (2) alone limits the possible values of $x$ to the set $\{5, 8\}$ , then the two statements combined are sufficient to answer the question.

Answer: Answer

Answer

True. Combining two consistent Data Sufficiency statements yields a solution set equal to the intersection of their individual solution sets. The intersection of

\{2, 5\}

and

\{5, 8\}

\{5\}

, which uniquely identifies

x

and is therefore sufficient.

The statement is true because taking the intersection of the two solution sets

\{2, 5\}

and

\{5, 8\}

leaves only the single value

x = 5

, satisfying the GMAT Data Sufficiency requirement for a unique value.

Step-by-Step Solution

Evaluate Statement (1) alone

Statement (1) yields

x \in \{2, 5\}

, which contains two possible values and is insufficient on its own.

A Value Data Sufficiency question requires a single unique numerical value for sufficiency.

Evaluate Statement (2) alone independently

Statement (2) yields

x \in \{5, 8\}

, which contains two possible values and is insufficient on its own.

Statement (2) must be evaluated without carrying over any constraints from Statement (1).

Combine Statement (1) and Statement (2)

The combined solution set is

\{2, 5\} \cap \{5, 8\} = \{5\}

Combining statements requires identifying values that satisfy both statements simultaneously.

Determine sufficiency of the combined solution set

Since

x = 5

is the only value in the combined set, the statements together provide a single unique answer.

A single unique result satisfies the criterion for Data Sufficiency.

Key Concept

Statement Combination and Solution Set Intersection

Question

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Step-by-Step Solution

Key Concept

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