In a GMAT Data Sufficiency 'Yes/No' question regarding whether a real variable x is positi… — GMAT

In a GMAT Data Sufficiency 'Yes/No' question regarding whether a real variable $x$ is positive, a statement establishing that $x^2 - 4x + 3 = 0$ is sufficient, whereas in a 'Value' question asking for the exact numerical value of $x$ , the exact same statement is insufficient.

Answer: Answer

Answer

The statement is True.

The statement accurately reflects GMAT Data Sufficiency decision rules: a 'Yes/No' question requires only that all possible cases produce a uniform 'Yes' or uniform 'No' answer (which occurs here since both

x=1

and

x=3

are positive), while a 'Value' question strictly requires a single unique value (which fails here due to having two solutions).

Step-by-Step Solution

Analyze the mathematical implications of the given statement.

Solving

x^2 - 4x + 3 = 0

yields

(x-1)(x-3) = 0

, so

x = 1

x = 3

Determine the exact solution set allowed by the statement.

Evaluate sufficiency for a 'Yes/No' Data Sufficiency question stem.

Since both

x = 1

and

x = 3

are strictly greater than

0

, the answer to 'Is

x > 0

?' is unconditionally 'Yes'. Thus, the statement is sufficient.

In 'Yes/No' DS logic, any statement that yields a definitive, consistent 'Yes' (or a definitive, consistent 'No') is sufficient.

Evaluate sufficiency for a 'Value' Data Sufficiency question stem.

Since

x

can be either

1

3

, a single unique value for

x

cannot be determined. Thus, the statement is insufficient.

In 'Value' DS logic, a statement is sufficient if and only if it leads to exactly one numerical value.

Compare the conclusions with the given assertion.

The assertion correctly identifies that the statement is sufficient for 'Yes/No' logic and insufficient for 'Value' logic.

Confirm total alignment between the assertion and GMAT DS decision logic.

Key Concept

Value vs. Yes/No Data Sufficiency Decision Logic

Question

Answer

Step-by-Step Solution

Key Concept

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