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题库 / GMATAdvanced-DS-64
If x and y are integers, is xy+1 divisible by 3?
(1)When x is divided by 3, the remainder is 1.
(2)When y is divided by 9, the remainder is 8.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
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求余时分母的加减法和乘法可以直接拆开；
x=3m+1，y=9n+8，其中m，n是整数。
把这两个式子代入xy+1可得：
xy+1=(3m+1)(9n+8)+1
=27mn+24m+9n+84-1
=3(9mn4-8m+3n+3)
因此xy+1能被3整除，所以(1)+(2)充分。