In a GMAT Data Sufficiency 'Value' question asking for the numerical value of the expressi… — GMAT

In a GMAT Data Sufficiency 'Value' question asking for the numerical value of the expression $xy$ , a statement that permits $x$ to be either $2$ or $-2$ while establishing that $y = \frac{8}{x}$ is insufficient to answer the question because $x$ itself is not uniquely determined.

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False. In Data Sufficiency 'Value' questions, sufficiency depends solely on whether the target expression can be uniquely determined. Because

xy = 8

under all permitted conditions, the statement is sufficient regardless of whether

x

has multiple values.

The claim presented in the stem is false. In GMAT Data Sufficiency 'Value' questions, a statement is sufficient if it yields a single, unambiguous numerical value for the requested target expression. It is not necessary for individual variables within the expression to be uniquely determined. Given

y = \frac{8}{x}

, multiplying both sides by

x

yields

xy = 8

. Whether

x = 2

x = -2

, the product

xy

remains constant at

8

. Thus, the statement is sufficient to answer the question, rendering the claim of insufficiency false.

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Identify the precise target of the question stem.

The target quantity is the expression

xy

, not the individual variable

x

y

Evaluating Data Sufficiency requires focusing on the target expression as a single entity.

Test all cases allowed by the statement.

Case 1: If

x = 2

, then

y = \frac{8}{2} = 4

, so

xy = (2)(4) = 8

.
Case 2: If

x = -2

, then

y = \frac{8}{-2} = -4

, so

xy = (-2)(-4) = 8

Both permissible values of

x

must be tested alongside their corresponding

y

values.

Determine sufficiency based on target uniqueness.

Both cases yield the exact same value (

xy = 8

). The statement provides a unique numerical answer to the question.

Because the value of the target expression is uniquely determined, the statement is sufficient, making the claim in the stem false.

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Target Expression Uniqueness vs. Variable Uniqueness in Value Questions

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