If x is a real number, is x equal to 3?
(1) x³ = 9x
(2) x² = 3x
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Data InsightsData Sufficiency
Free GMAT Data Sufficiency Practice Question
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Answer & Explanation
Correct answer
E
Never divide an equation by a variable that could be zero; factor instead.
(1) alone: x³ = 9x becomes x³ − 9x = 0, so x(x² − 9) = 0, giving x = 0, x = 3, or x = −3. That includes a yes (x = 3) and a no (x = 0), so it is insufficient. (2) alone: x² = 3x becomes x² − 3x = 0, so x(x − 3) = 0, giving x = 0 or x = 3, again a yes and a no: insufficient. Together: the common solutions of both equations are the values in {0, 3, −3} that also lie in {0, 3}, namely x = 0 and x = 3. Since x could still be 0 (answer no) or 3 (answer yes), even both statements together do not settle the question.
The trap is the strong pull to cancel x and read x = 3 from each statement; the overlooked root x = 0 survives both equations and is exactly why the answer is not (C). Answer: (E).