William picks a three digit number and subtract it from the same number after reversing order of its digits. If this difference is divided by 11, find the remainder.
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Step by Step Explanation:
- Let the number be xyz, where x, y and z are the digits of the number. Hence, the number xyz can be written as 100x+10y+z .
- When we reverse it , the number would be zyx which is equal to 100z+10y+x .
- When we subtract these two numbers , we get 99x-99z or 99z-99x , which is 99(x-z) or 99(z-x).
- This is a multiple of 9,11,99 . So the remainder when divided by 11 is always 0 .