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题目
the reflection of a positive integer is obtained by reversing its digits.for ex.321 is the reflection of 123.the difference between a five-digit integer and its reflection must be divisible by which of the following?
A.2 B.4 C.5 D.6 E.9
头疼死了.

提问时间:2021-03-27

答案
一个正整数的倒影就是把它的各位数字颠倒过来,例如123的倒影是321.一个5位正整数和它的倒影的差一定能被下列哪个数整除?
设原数A为10000a+1000b+100c+10d+e
则它的倒影B为10000e+1000d+100c+10b+a
A-B=9999a+990b-990d-9999e
=9(1111a+110b-110d-1111e)
能被9整除,选E
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