In a GMAT Data Sufficiency question asking for the specific numerical values of two variab… — GMAT

In a GMAT Data Sufficiency question asking for the specific numerical values of two variables $x$ and $y$ , if Statement (1) provides the equation $2x + 3y = 12$ and Statement (2) provides the equation $4x + 6y = 24$ , combining both statements is sufficient to determine unique values for $x$ and $y$ .

Answer: Answer

Answer

The statement is False.

The correct answer is False because Statement (2) is a scalar multiple of Statement (1). Linearly dependent equations do not reduce the number of unknown variables or narrow down the solution set to a single unique pair

(x, y)

. Therefore, combining both statements does not yield sufficient information to answer the question stem.

Step-by-Step Solution

Analyze Statement (1) equation

Statement (1) provides

2x + 3y = 12

, which defines a line with infinitely many valid coordinate pairs

(x, y)

A single linear equation in two variables has infinitely many solutions.

Analyze Statement (2) equation and test for linear independence

Dividing Statement (2),

4x + 6y = 24

, by

2

yields

2x + 3y = 12

, which is identical to Statement (1).

Linearly dependent equations provide redundant data and do not provide a distinct second constraint.

Evaluate the combination of Statement (1) and Statement (2)

Combining both statements produces no new information beyond

2x + 3y = 12

, leaving infinitely many solution pairs.

Determining unique values for two variables requires two linearly independent equations. Because these statements are dependent, combining them remains insufficient.

Key Concept

Linear Independence in Statement Combination

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Answer

Step-by-Step Solution

Key Concept

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