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When the even integer n is divided by 7, the remainder is 5, then what is the re
When the even integer n is divided by 7, the remainder is 5, then what is the re
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2024-01-13
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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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