GWD18-Q36急，请高手指点！

wo11111111

Q36:  
                    

If x and y are integers, is y an even integer?  A

      (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.

yang_jing_8

2y – x = x² – y² =>2y=x²+x – y²  =>2y=x(x+1)- y²      

Since 2y is even, x(x+1) --the product of 2 consecutive integer-- is even, then y²  must be even, so y is even.        

graysytl

2y – x = x² – y² =>y(y+2)=x(x+1)

y and y+2 must be both odd or both even

x(x+1) must be even....thus y is even

wo11111111

谢谢二位及时回答，这道题的重点是怎样化简，和x（x＋1）一定是偶数的应用！