求教GWD数学3-16

FGHYU19912301

Q16:
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.

如题，请教怎么做啊？

Vickyliu

1) 2 is not a factor of n. So n is odd. n=1, r =0; n=3, r=8. Insufficient
2) 3 is not a factor of n. So either (n-1) or (n+1) has a factor of 3. n=1, r=0; n=4, r= 15. Insufficient.

1) and 2). So n is odd and n is not a factor of 3. If so, 1) both n-1 and n+1 are even; 2) one of them has a factor of 4; 3) one of them has a factor of 3. So n=2*4*3*m = 24*m. r=0. Sufficient.

CC

angelsgx

这个是不是选E呀？？

这样做的:

第一个条件说n不能被2整除，假设n=3或n=5，得到的余数不一样，所以不能确定r;

第二个条件说n不能被3整除，假设n=2或n=4，得到的余数不一样，所以也不能确定r。

angelsgx

等一下，看看两个一起的情况哈

angelsgx

不好意思呀，选C，一起的时候就可以了，余数都是0

FGHYU19912301

thax~~~~