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Zorluk: OrtaStatement Independence Evaluation and Statement Combination

In a GMAT Data Sufficiency question asking for the specific numerical values of two variables xx and yy, if Statement (1) provides the equation 2x+3y=122x + 3y = 12 and Statement (2) provides the equation 4x+6y=244x + 6y = 24, combining both statements is sufficient to determine unique values for xx and yy.

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

Adım Adım Çözüm

1
Analyze Statement (1) equation
Statement (1) provides 2x+3y=122x + 3y = 12, which defines a line with infinitely many valid coordinate pairs (x,y)(x, y).
A single linear equation in two variables has infinitely many solutions.
2
Analyze Statement (2) equation and test for linear independence
Dividing Statement (2), 4x+6y=244x + 6y = 24, by 22 yields 2x+3y=122x + 3y = 12, which is identical to Statement (1).
Linearly dependent equations provide redundant data and do not provide a distinct second constraint.
3
Evaluate the combination of Statement (1) and Statement (2)
Combining both statements produces no new information beyond 2x+3y=122x + 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.

Anahtar Kavram

Linear Independence in Statement Combination
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Konular

Statement Independence Evaluation and Statement Combination

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