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Is x² - 4x + 3 > 0? (1) x > 3 (2) x < 1

GMAT · 2022 · Quantitative
Question:
Is x² - 4x + 3 > 0? (1) x > 3 (2) x < 1

Options

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
(D) EACH statement ALONE is sufficient
(E) Statements (1) and (2) TOGETHER are NOT sufficient
Answer: (D) EACH statement ALONE is sufficient

Explanation:
Factor: x² - 4x + 3 = (x - 1)(x - 3). This is positive when x < 1 or x > 3. Statement (1): x > 3 means the expression is positive. Sufficient. Statement (2): x < 1 means the expression is positive. Sufficient.

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