1951 AMC 12 第 19 题

Question

将一个三位数重复书写一次，组成一个六位数，例如

256{,}256

、

678{,}678

等。任何这种形式的数都一定能被下列哪个数整除？

A six-place number is formed by repeating a three-place number; for example,

256{,}256,

or

678{,}678,

etc. Any number of this form is always exactly divisible by:

仅

7

7

only

仅

11

11

only

仅

13

13

only

101

1001

用

N

表示被重复的三位数

Represent the repeated three-digit block by

N

这个六位数为

1000N+N

The six-digit number is

1000N+N

若被重复的三位数为

N

，则这个六位数为

1000N+N=1001N\text{。}

因此，它一定能被

1001

整除。

因此，正确答案是 E。

If the repeated block is

N,

then the six-place number is

1000N+N=1001N.

It is therefore always divisible by

1001.

Thus, the correct answer is E.

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