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Question

The sum of a two digit number and the number obtained by reversing the digits is always divisible by _________ .


Solution

Lets $$xy$$ is a two digit number.
From the question, we have to check for $$xy+yx$$
$$xy+yx=10x+y+10y+x=11x+11y=11(x+y)$$
So, this number is always divisible by $$11$$
Hence the sum of a two digit number and the number obtained by reversing the digit is always divisible by $$11$$.

Mathematics

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