Bunuel wrote:
Is x^3 an odd integer?
(1) \(3\sqrt{x}\) is an odd integer.
(2) x is an odd integer.
Question Stem Analysis:We need to determine whether x^3 is an integer. No other information is provided in the question stem.
Statement One Analysis:\(\Rightarrow 3\sqrt{x}\) is an odd integer.
If \(\sqrt{x}\) is an integer, then both x and x^3 must be an odd integer and the answer to the question is yes. The danger here is to overlook the fact that \(3\sqrt{x}\) can be an odd integer even when neither \(\sqrt{x}\) nor x is an integer (for instance, if x = 1/9 or 4/9 or 25/9, etc.). In this case, x^3 will not be an odd integer and the answer to the question will be no. Since we have more than one possible answers, statement one alone is not sufficient.
Eliminate answer choices A and D.
Statement Two Alone:\(\Rightarrow\) x is an odd integer.
If x is an odd integer, then not only x^3 will also be an integer, but also x^3 will not contain any factors of 2 (because x does not contain any factors of 2) and consequently, it will be an odd integer. Statement two alone is sufficient.
Answer: B