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楼主
发表于 2012-4-15 06:39:17 | 只看该作者 回帖奖励 |倒序浏览 |阅读模式
N=a+b+c=XYZ, abc连续,xyz连续,问N除以5的余数
(1)a除以5余1  

(2)x除以5余1



(提供者ID:PsycheCC原文:余数题 N=a+b+c=XYZ, abc连续,xyz连续,问N除以5的余数
(1)a除以5余1  (2)x除以5余1

思路:因为a+b+c=XYZ,abc连续,所以必有xyz=3b,则xyz肯定是3的倍数,当(1)a除以5余1时,a的尾数可能为1或者6,这时b的尾数为2或者7,则xyz的尾数为6或者4,则xyz除以5的余数为1,可以求到(2)x除以5余1,则x可能为1或者6,此时可以算出xyz为123或者678,此时xyz除以5的余数为3。选D
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xyz的尾数为6或者4,则xyz除以5的余数为1,为什么? 234/5, 余数就等于4... NOT 1..
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沙发
 楼主| 发表于 2012-4-16 05:02:58 | 只看该作者
求助??
板凳
发表于 2012-4-16 05:52:20 | 只看该作者
That's how I think :
first consider (1) . Let's set a =5x+1 according to the question. Because a.b .c are Consecutive numbers。 b=5x+2  c=5x+3
Add a.b and c together ,we get N, which is 15x+6 . When N is divided by 5 , the reminder  is always 1 .

Consider(2) because XYC is a three-digit number ,and X divided by 5 has a reminder of 1. The only possible number of X either 1 or 6 . 123 and 678  both have a reminder of 3 .

Hence, both are sufficient (D).
地板
发表于 2012-4-16 05:53:54 | 只看该作者
1. a, b, c 的尾数可以为1,2,3或者6,7,8. 相加之和均为6。所以N除5的余数是12. x,y,z 的尾数也同样是1,2,3或者6,7,8. 相乘尾数也是6。所以N除5的余数是1
5#
 楼主| 发表于 2012-4-16 09:35:58 | 只看该作者
That's how I think :
first consider (1) . Let's set a =5x+1 according to the question. Because a.b .c are Consecutive numbers。 b=5x+2  c=5x+3
Add a.b and c together ,we get N, which is 15x+6 . When N is divided by 5 , the reminder  is always 1 .

Consider(2) because XYC is a three-digit number ,and X divided by 5 has a reminder of 1. The only possible number of X either 1 or 6 . 123 and 678  both have a reminder of 3 .

Hence, both are sufficient (D).
-- by 会员 sailing198961 (2012/4/16 5:52:20)



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