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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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因为xy+1能否被3整除，不但取决于x的值，而且还取决于y的值，所以(1)和(2)单独都很明显不充分；根据(1)+(2)可得：
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。
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