2. 外语
  3. When a certain number is divided by 7, the remainder is 0. If the remainder is not 0 when the number is divided by 14, then the

When a certain number is divided by 7, the remainder is 0. If the remainder is not 0 when the number is divided by 14, then the

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问题 When a certain number is divided by 7, the remainder is 0. If the remainder is not 0 when the number is divided by 14, then the remainder must be ?
选项 A、1
B、2
C、4
D、6
E、7
答案E
解析 某数被7除时余数为0，若被14除时余数不为0，那么余数一定是
解：本题的正确答案为(E)。该数是7的倍数，可分两种情况：(1)该数是7的奇数倍，可写成：7n=7×(2k+1)=14k+7，其中n=2k+1； (2)该数是7的偶数倍，可写成：7n=7×2k=14k，其中n=2k；由以上可知，当该数不能被14整除时，其余数一定是7。
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