If n is a positive integer and r is the remainder when (n - 1)(n + 1) is divided by 24, what is the value of r ?

(1) n is not divisible by 2.
(2) n is not divisible by 3.


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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考题讲解

自然数里，三个数内肯定能有一个数能被三整除~N不能被3整除，那N-1或者N+1肯定可以被三整除；同理，自然数的两个数内有一个数能被2整除，如果N又不能被2整除，那N-1和N+1肯定都能被2整除。如果N-1能被2整除，那N+1肯定可以被4整除（因为里面又多了一个2了），因此，(N-1)(N+1)肯定可以被2*3*4整除。

因此，答案为(C)。

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Prep2007E1-DS
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