10号上海,请教一道看似简单,中有玄机的题目

Rebeldom

Q36:
If x and y are integers, is y an even integer?
(1)      2y – x = x2 – y2
(2)      x is an odd integer.
    
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

flyincat

答案呢，选A不

ivymm0301

同意楼上
由条件1可以推出y(y+2)=x(x+1),因为x(x+1)一定是even，所以y(y+2)是even，由此推出y是even！

umichtongtong

答案是C
首先 如果只有A， 2y=（x+y)*(x-y)+x，x+y和x-y同奇偶，若x为偶，y可为奇或者偶，不充分
B单独显然不充分
若联合A，B，则若y为奇，2y=（x+y)*(x-y)+x 左边为偶，右边为奇，不可能，则y必然为偶。验证：2y=（x+y)*(x-y)+x左边为偶，右边也为偶。

umichtongtong

ivymm说得对 虚心学习~

chennyshu

我同意2楼选A？
LZ 有正确答案吗？

Rebeldom

正确答案是A,多谢各位指教