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题库 / Prep2007E1-DS-167
If x, y, and z are integers and xy + z is an odd integer, is x an even integer?
(1) xy + xz is an even integer.
(2) y + xz is an odd integer.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
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Statement1：
因为xy+z为奇数，xy+xz为偶数，那么（xy+xz）-(xy+z)＝xz-z一定为奇数
xz-z＝Z(x-1)为奇数，那么z和x-1一定都为奇数，所以x只能为偶数。
Statement2代入特定数字来满足条件成立，看是否x 的值是否可被限定奇偶。
当x为1，y＝1，z为2满足statement2和题干
当x为2，y＝1，z＝1可满足statement2和题干
所以statement 2并不能决定x的奇偶性质。
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