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When a certain number is divided by 7, the remainder is 0. If the remainder is n
When a certain number is divided by 7, the remainder is 0. If the remainder is n
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2024-01-12
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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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