GWD math3-16又是不会...sos

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.

Answer: c

我选C,

如果(1),   (n-1) 和 (n+1) 都是偶数.

如果(2),   (n-1) 和 (n+1)里必有一个可被3 整除, 一个是 偶数

还是不太理解....

 (n-1) 和 (n+1)里必有一个可被3 整除, 一个是 偶数?为什么?

谢谢指教

假如條件(1)成立:

n=1, r=0

n=3, r=8

n=5, r=0

n=7, r=0

n=9, r=8

依此類推，r的出現必為8,0,0,8,0,0,8...則r有兩解

假如條件(1)and(2)成立，則r=0，所以答案是C

perfect!!!