Question

The digit from 0 to 9 which must be added to 2013 to make the resultant number divisible by 12 is

Answer 1

For a number to be divisible by $12$, it must be divisible by $3$ and $4$ both.

If last two digits of a number are divisible by 4, then the number is also divisible by 4.

Given number is $2013$
As we can add only 1 digit from 0-9 in the number.
For being divisible by 4, its last two digit can be 16 or 20 and this is possible only if we add 3 or 7 respectively.

We know: A number, whose sum of digits is a multple of 3, is divisible by 3.
$\Rightarrow 2016\to 2+0+1+6=9\Rightarrow 2020\to 2+0+2+0=4$
Here, 9 is a multiple of 3 but 4 is not a multiple of 3.
Hence, 2016 is completely divisible by 3.

We get that from 2013 to 2022, only 2016 is divisible by both 3 and 4 and hence by 12 also.

We need to add 3 in 2013 to make it equal to 2016.