Nancy's roll number is a two digit number. Her friend Donna's roll number has the same digits as Nancy's roll number, but with digits interchanged. If they add their roll number, and divide the sum by 11. Find the remainder of this division.



Step by Step Explanation:
  1. Let Nancy's roll number be xy . Another way of depicting this is 10x + y .
  2. So the roll number of Donna will be yx . Another way of depicting it is 10y + x .
  3. So the sum of their roll numbers would be 11x + 11y or 11(x+y),which is a multiple of 11.
  4. So the remainder will always be 0 when divided by 11.

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