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

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Solution

The correct options are
A 3
D 9
Let the two digit number be ab.
$a b = 10 a + b$ and
its reverse will be $10 b + a$

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

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

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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