请教一道数学题

crystal9006 · 发表于 2010-11-19 20:25:14

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)    2 is not a factor of n.
(2)    3 is not a factor of n.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Answer: C
这题遇到了好多遍我是用具体数据代入做的请教各位高手，严谨的应该怎么分析呀？
谢谢啦~~

kevin0214 · 发表于 2010-11-19 21:09:54

n不是2的倍数，n+1,n-1是两个连续的偶数，大于2的两个连续偶数中必定有一个是4的倍数，所以他们的和必定是8的倍数

n不是3的倍数，n+1,n-1必定有一个是3的倍数

所以……得证

seyouji · 发表于 2010-11-19 22:03:43

只用公式不说话，呵呵。

（1）2 is not a factor of n.=》n=2x-1 or 2x+1=>2x*(2x+2)=24k+r
(2) 3 is not a factor of n.=>n=3x-1 or 3x+1=>3x*(3x+2)=24k+r
(1)+(2)=>n=6x-1 or 6x+1=>6x*(6x+-2)=24k+r (x is odd,so 3x+-1 is even, r=0)

crystal9006 · 发表于 2010-11-28 21:56:38

多谢~~！

请教一道数学题

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