PREP DS 159题求助

nuno_qin

159.
                15957-!-item-!-187;#058&010660

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) n is not divisible by 2.

 

(2) n is not divisible by 3.

--------------------------------------------------------------------------------------------------------------------------------------------------------MingLiU","serif"; mso-highlight: yellow; mso-fareast-language: ZH-TW; mso-ascii-font-family: Tahoma; mso-hansi-font-family: Tahoma; mso-bidi-font-family: PMingLiU;">【答案】C

 

MingLiU","serif"; mso-highlight: yellow; mso-fareast-language: ZH-TW; mso-ascii-font-family: Tahoma; mso-hansi-font-family: Tahoma; mso-bidi-font-family: PMingLiU;">【思路】
                    =
                    

        (1) n = 3 , 5 , 7 ,9…… ,MingLiU","serif"; mso-highlight: yellow; mso-fareast-language: ZH-TW; mso-ascii-font-family: Tahoma; mso-hansi-font-family: Tahoma; mso-bidi-font-family: PMingLiU;">則r=8 , 1 ……,MingLiU","serif"; mso-highlight: yellow; mso-fareast-language: ZH-TW; mso-ascii-font-family: Tahoma; mso-hansi-font-family: Tahoma; mso-bidi-font-family: PMingLiU;">不充份

      (2)n=1 , 2 , 4,….,r=2 ,3………,MingLiU","serif"; mso-highlight: yellow; mso-fareast-language: ZH-TW; mso-ascii-font-family: Tahoma; mso-hansi-font-family: Tahoma; mso-bidi-font-family: PMingLiU;">不充份

 

 (1) + (2) MingLiU","serif"; mso-highlight: yellow; mso-fareast-language: ZH-TW; mso-ascii-font-family: Tahoma; mso-hansi-font-family: Tahoma; mso-bidi-font-family: PMingLiU;">不能被2 , 3MingLiU","serif"; mso-highlight: yellow; mso-fareast-language: ZH-TW; mso-ascii-font-family: Tahoma; mso-hansi-font-family: Tahoma; mso-bidi-font-family: PMingLiU;">整除 ,2 ,3 MingLiU","serif"; mso-highlight: yellow; mso-fareast-language: ZH-TW; mso-ascii-font-family: Tahoma; mso-hansi-font-family: Tahoma; mso-bidi-font-family: PMingLiU;">為 24 MingLiU","serif"; mso-highlight: yellow; mso-fareast-language: ZH-TW; mso-ascii-font-family: Tahoma; mso-hansi-font-family: Tahoma; mso-bidi-font-family: PMingLiU;">的公因數 ,MingLiU","serif"; mso-highlight: yellow; mso-fareast-language: ZH-TW; mso-ascii-font-family: Tahoma; mso-hansi-font-family: Tahoma; mso-bidi-font-family: PMingLiU;">所以n排除為24因數後,r=0

原来的解释是这样的，最后(1)+(2)看不懂，哪位大侠帮忙解释一下？  我认为是E……

yangli317

1+2的情況就是既不能被2也不能被3整除

如果n=5, r=4
       n=7,r=3

也不充分吧

yangli317

所以應該是E

pinpin117

二楼的举例不正确吧~~~~

“1+2的情況就是既不能被2也不能被3整除

如果n=5, r=4
       n=7,r=3

也不充分吧”

n=5, r=0.。。。带入计算4*6=24，所以除以24余数是0的。。。
n=7,r=0.。。。带入计算6*8=48，所以除以24余数是0的。。。

我认为选C。。。

alan722

这题。。好像讨论过无数次了

n+1,n-1都是偶数，两个连续的偶数，一定有个是4的倍数，相乘一定是8的倍数

连续三个自然数，一定有个是3的倍数，n不是，则n-1或n+1一定有个是

所以1+2推出一定是24的倍数，余数0，确定

选C

psn327

请问prep 的数学部分在哪里能下载阿？只找到了语法部分。有没有好心人能给个链接？