ChaseDream

标题: 请教TTmath3中的一道数学题 [打印本页]

作者: GSQQ 时间: 2010-4-11 10:10
标题: 请教TTmath3中的一道数学题
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

请教这题的思路和解法~

作者: cindytim 时间: 2010-4-11 11:41
先把24分解=3 x 8
(1) 2不是n的因數, n=2k+1, (n-1)(n+1) = (2k)(2k+2) ==> 連續偶數乘積可被8整除, 連續偶數一定某個被2整除,某個被4整除
(2) 3不是n的因數 n=3y+1, (n-1)(n+1)=(3y)(3y+2) 或是 n=3y+2, (n-1)(n+1)=(3y+1(3y+3) ==> 可被3整除.

(1)+(2)
兩個條件合起來, 可同時被8與3整除的數..除以24..餘數為0.

作者: GSQQ 时间: 2010-4-12 20:18
谢谢，解释的真详细，我明白了~

欢迎光临 ChaseDream (https://forum.chasedream.com/)