请教prep ds2 123题

hahaebcg0923

When positive integer n is divided by 3, the remainder is 2; and when positive integer t is divided by 5, the remainder is 3.  What is the remainder when the product nt is divided by 15 ?

 

(1) n - 2 is divisible by 5.

(2) t is divisible by 3.

   C

我记得有一个比较公式化的解法，不晓得有人知道吗???

或者有其它解法也行!!

我想好久呀~~弄不懂

yqqlmgsycl

Please see [原创]通项问题一招搞定 at http://forum.chasedream.com/dispbbs.asp?boardID=22&ID=51193&page=1

hjsh0204

以下是引用hahaebcg0923在2008-8-2 0:49:00的发言：

When positive integer n is divided by 3, the remainder is 2; and when positive integer t is divided by 5, the remainder is 3.  What is the remainder when the product nt is divided by 15 ?
                        

(1) n - 2 is divisible by 5.
                        

(2) t is divisible by 3.

来个旁门左道的解法，

n=3x+2, t=5y+3。

nt= (3x+2)(5y+3),

1）. n-2 is divisible by 5, ----->3x 是5的倍数，可以表示为15a

从而 nt=(15a+2)(5y+3)， 这个东西除以15的余数是2(5y+3)

由于y无法确认，所以余数不能确定!

2）. t is divisible by 3 -------> 5y is divisible by 3, 可以表示为15b

从而 nt= (3x+2)(15b+3)，这个东西除以15的余数是3(3x+2)

x 不能确定，余数也就不能确定！！

1，2）结合 . 2(5y+3)=2(15b+3),余数确定为6！答案是C.

    

不过我的方法很笨拙，并不适用于考场上的快速解题，希望NN们能分享自己的方法。怎么能在考场上快速解决这类问题？？

hang13

设n=3x+2,t=5y+3

nt=15xy+10y+9x+6

看10y+9x+6

由1 3x 被5整除 x=5a

由2 5y+3 被3整除 y=3b

nt=15xy+10y+9x+6=15xy+30b+45a+6

余数是6

[此贴子已经被作者于2009-3-21 16:45:58编辑过]