In a GMAT Data Sufficiency problem asking for the unique value of an integer x, Statement … — GMAT

In a GMAT Data Sufficiency problem asking for the unique value of an integer $x$ , Statement (1) establishes that $x \in \{3, 7\}$ and Statement (2) establishes that $|x - 5| = 2$ . Evaluating both statements together provides sufficient information to determine a unique value for $x$ .

Answer: Answer

Answer

The statement is False. Combining both statements yields the intersection set {3, 7}, which still contains two possible values for x and therefore does not uniquely determine x.

The statement is false because solving Statement (2)'s absolute value equation

|x - 5| = 2

produces

x = 7

x = 3

, which is identical to the candidate set given by Statement (1). Combining two identical solution sets leaves the candidate set as

\{3, 7\}

, which does not yield a single unique value for

x

Step-by-Step Solution

Evaluate Statement (1) solution set

Statement (1) restricts

x

to the set

\{3, 7\}

Statement (1) explicitly provides two candidate values for

x

Evaluate Statement (2) solution set independently

Statement (2) yields

|x - 5| = 2 \implies x = 7

x = 3

. The solution set is

\{3, 7\}

Solving the absolute value equation yields the two roots 3 and 7 without using any information from Statement (1).

Combine Statement (1) and Statement (2)

The intersection of the two solution sets is

\{3, 7\} \cap \{3, 7\} = \{3, 7\}

When combining statements in Data Sufficiency, valid values must satisfy both statements simultaneously.

Determine sufficiency of the combined statements

Since

x

can still be either 3 or 7, a single unique value is not determined. The combined statements are insufficient.

A Value Data Sufficiency question requires a single, unique numerical value to be considered sufficient.

Key Concept

Statement Combination and Redundancy in Data Sufficiency

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