When the even integer n is divided by 7, the remainder is 5, then what is the re

游客2024-01-12 43

问题 When the even integer n is divided by 7, the remainder is 5, then what is the remainder when n is divided by 14?

选项 A、5
B、10
C、6
D、12
E、it can not be calculated according to the information above

答案 D

解析 n被7除余数为5，那么n可以表示为n=7k+5，由于n是偶数，因此k必然为奇数，假设k=2m+1，那么n可以写为n=14m+12，所以n被14除余数为12。有些考生认为是不能够计算。其实是忽略了n是偶数这一个环节。因为在n为奇数的情况下n=7k+5，那么k必然为偶数，7k必能够被14整除，那么7k+5除以14，余数为5。

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