If x and y are integers and xy3 is a positive odd integer, which of the following must be true?

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问题 If x and y are integers and xy³ is a positive odd integer, which of the following must be true?

选项 A、x+y is even.
B、xy is positive.
C、x²y is positive.

答案A,B

解析条件：xy³是正奇数，可以拆解xy³＞0，且xy³是奇数。由xy³＞0，可以得出x和y³同号(同为正数或同为负数)，又y³与y同号，则x和y同号，那么B选项xy是正数，正确。因为x²＞0，那么y＞0时，x²y＞0；y＜0时，x²y＜0，不一定是正数，因此不选C选项x²y。又由xy³是奇数，得到x×y×y×y是奇数，那么x和y都是奇数。那么A选项x+y是偶数(奇数+奇数=偶数)，正确。所以答案选A和B。

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本试题收录于： GRE QUANTITATIVE题库GRE分类

GRE QUANTITATIVE

GRE

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If x and y are integers and xy3 is a positive odd integer, which of the following must be true?

GRE QUANTITATIVE

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