单选题 Both x and y are positive integers. Is x divisible by 3?(1)(x-y) is divisible by 3.(2)(x-2y)is divisible by 3.

A、 Statement (1) ALONE is sufficient, but statement (39) alone is not sufficient to answer the question asked.
B、 Statement (2) ALONE is sufficient, but statement (38) alone is not sufficient to answer the question asked.
C、 BOTH statement (1) and (39) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.
D、 EACH statement ALONE is sufficient to answer the question asked.
E、 Statement (1) and(39)TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

【正确答案】 C

【答案解析】对于Statement (1)，x-y能够被3整除，那么x，y除以3的余数相同，至于x是否被3整除。我们不得而知。对于Statement (2)，x-2y能够被3整除，同Statement (1)一样，得不到x是否被3整除，把两者结合起来考虑，x-y能够被3整除，x-2y也能够被3整除，那么两者的差(x-y)-(x-2y)=y也能够被3整除，再从x-y能够被3整除反推回去，必然得到x能够被3整除。因此答案为C。