Question

# Pick a two digit number with distinct digits. Now, reverse the digits. Subtract the smaller number from the larger number. The difference thus obtained is always divisible by

A
3
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B
5
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C
7
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D
9
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Solution

## The correct options are A 3 D 9Let the two digit number be ab. ab=10a+b and its reverse will be 10b+a 10a+b - (10b+a) = 9a−9b We could also have 10b+a - (10a+b) = 9b−9a which would yield 9(a−b) or 9(b−a). In both the cases, the number thus obtained will be a multiple of 9 and thus will be divisible by 9. Since 3 is a factor of 9, the number obtained will be divisible by 3 as well.

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