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Question
The sum of a two-digit number and the number obtained by reversing the digits is always divisible by ______.
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Solution
The sum of a two-digit number and the number obtained by reversing the digits is always divisible by 11.
Explanation:
Let ab be any two-digit number, then the number obtained by reversing its digits is ba.
Now, ab + ba = (10a + b) + (10b + a)
= 11a + 11b
= 11(a + b)
Hence, ab + ba is always divisible by 11 and (a + b).
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