这道数学题不会做：（

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.

请高手赐教

代数法。

C

由（1），n是奇数，n=3，与，n=5带入试验，r不同，则（1）单独不成立；

由（2），n不是3的倍数，n=2,n=4带入实验，r不同，则（2）单独不成立；

（1）和（2）两个条件联合：

n是奇数，则(n-1)(n+1)是相邻的两个偶数积，是8的倍数（简单易证）

n不是3的倍数，则(n-1)与(n+1)之一必是3的倍数（简单易证）

联合是24的倍数

1+2 可知n=6k+1或6k-1，k>=0

则 (n-1)(n+1)=6k(6k-2)=12k(3k-1)或6k(6k+2)=12k(3k+1)

(3k-1)和(3k+1)都是偶数，故(n-1)(n+1)必能整除24

这题我考试遇到了，选c没问题的，考试的时候代数法就可以了，因为有时候会没有思路嘛

http://www.beatthegmat.com/gmat-prep-remainder-question-t16996.html

(1) says that n is odd. Thus n-1 and n+1 are both even. In fact, one of them must be divisible by 4, because every second even number is divisible by 4. So from (1) we know that (n-1)(n+1) is divisible by 8.

(2) says that n is not divisible by 3. Notice that n-1, n, and n+1 are three consecutive integers. If you have any three consecutive integers, exactly one of them must be divisible by 3. So if n is not divisible by 3, either n-1 or n+1 is.

Using both (1) and (2) together, we know (n-1)(n+1) is divisible by both 3 and 8, and therefore by 24.
看多題目GWD的数学题目都可以在这个上边找到.