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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：
xy+z为奇数，y+xz为奇数，那么（xy+z）-（y+xz）=（x-1）（y-z）一定为偶数
则可能x-1为偶数，y-z为奇数，或x-1为奇数，y-z为偶数，或两者均为偶数，此时x-1的奇偶性不确定，故x的奇偶性不确定
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