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题库 / Prep2007E2-DS-162
If n is a positive integer and r is the remainder when n2 - 1 is divided by 8, what is the value of r ?
(1) n is odd.
(2) n is not divisible by 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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n^2-1=(n+1)（n-1）
条件一：n是奇数，设n=2a+1，则n^2-1=(n+1)（n-1）=2a（2a+2）=4a（a+1）；a和a+1是两个连续整数，一定有个因子2，因此4a（a+1）=8*？，充分；
条件二：n不能被8除，n里面不含有因子2和4，所以n^2也不能被8除，n^2-1不好判断，不充分；
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