※ 引述《oranger (从新出发)》之铭言： : 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. : Ans:A : 176. : If x and y are positive integers, is the product xy even? : (1) 5x - 4y is even. : (2) 6x + 7y is even. : Ans: D : 请大家帮忙解答了 谢谢!! : 我想请问大家在遇到像这种算奇数偶数的题目时， : 该怎麽解题 : 我每次只要碰到这种题目都会死的很难看 /_\ 好苦恼 167 由题目可知有两种情况:(i) xy = odd and z = even (ii) xy = even and z = odd (1) 考虑(i)，可得xz = odd，但z = even，故不可能得出xz = odd，矛盾 考虑(ii)，可得xz = even，又z = odd，则x必定为even ..........sufficient (2) 考虑(i)，可得 x = odd，代入(2)选项符合 考虑(ii)，x = odd or even代入(2)选项也符合，故无法确定......insufficient 176 (1) 4y = even，and we know 5x-4y = even，then 5x must be even since 5 is odd，so we get x is even therefore，xy is even..............sufficient (2) 6x = even，and we know 6x+7y = even，then 7y must be even since 7 is odd，so we get y is even therefore，xy is even..............sufficient --

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