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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 9

Let the two digit number be ab.
ab=10a+b and
its reverse will be 10b+a

10a+b - (10b+a) = 9a9b

We could also have
10b+a - (10a+b) = 9b9a

which would yield 9(ab) or 9(ba).

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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