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I have got some confusing answers from my friends. So I needed to be sure.
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This is a flawed question. On the GMAT, two data sufficiency statements always provide TRUE information and these statements NEVER contradict each other or the stem.
The question asks whether k < 0.
(1) gives 1 < k, which is sufficient to give a NO answer to the question. (2) gives k < 0 or 0 < k < 1, which is not sufficient to answer the question.
Now, technically the answer should be A, as Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
But even though the formal answer to the question is A, this is not a realistic GMAT question, as: on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other. (1) says that k^2 < k^3 but (2) says that k^2 > k^3, so the statements clearly contradict each other.