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题库 / Prep2007E2-DS-73
If n is a positive integer, is n3 - n divisible by 4 ?
(1) n = 2k + 1, where k is an integer.
(2) n2 + n is divisible by 6.
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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这道题中 先拆解题目
原式=n(n2-1)
条件1：n=2k+1,将n带入(n2-1)n=4(...)，所以可以被4整除
条件2：继续拆分=n(n+1)(n-1), 题目给出n(n+1),假设=6x。所以代入得出6x(n-1)，由于不能确定x(n-1)与3的关系 所以不充分
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