求助确认一Prep数学题答案

BeyondGS · 发表于 2009-12-7 20:13:21

昨天做模考碰到这道DS

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.

貌似之前就没搞懂，就做错了，对答案的时候不知道是不是眼花看错答案了，应该是C吧？怎么答案给的A？望指教。

zscsl · 发表于 2009-12-7 20:19:10

我顶一下。。。我也不会做。。。我会选E哟。。。呵呵。。。我数学爆烂。。。

neversight · 发表于 2009-12-7 22:33:04

我也觉得选C，带个数字看看好了。有时候不会做就带数字，排除呗

juange1014 · 发表于 2009-12-10 15:59:19

Answer is C.

1) n is not divisible by 2=> n=2k+1=> (n+1)(n-1)=2k*(2k+2)=4k*(k+1) =>not sure whether divisible by 24

2) n is not divisible by 3=> n=3k'+1 or 3k'+2 => (n+1)(n-1)=3k'(3k'+2) or (3k'+3)(3k'+1)=3(k'+1)(3k'+1) also not sure whether divisible by 24

1)&2) together, we could know that (n+1)(n-1) is at least divisible both by 4 & 3, also, k>=1, k'>=1, then (n+1)(n-1) divisible by 24 (at least one of k or k+1 will be even number, therefore have a factor of 2)

求助确认一Prep数学题答案

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