GWD 30-13

[小小白]

If x + y is an integer, is y an integer?
(1) x – y is an integer.
(2) x + 2y is an 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.

答案是B,不解. 懇請各位高手賜教!!

[Yimmiwan]

Statement (1) x - y is an integer
set x = 2.5, y = 1.5
x + y = 4, satisfy original condition
x - y = 1, satisfy statement (1)
but y is not an integer, statement (1) not sufficient
(I assume you already know y can also be integer)

Statement (2) x + 2y is an integer
in order to satisfy statement (2)
x & y both must be integer because no fraction would work
ex. x = 2.3, y = 1.7
x + y = 4, satisfy original condition
x + 2y = 5.7, not satisfy statement (2)
If you try other fractions it won't work either
so y is an integer, statement (2) sufficient

[小小白]

I get it .Thanks very much!!