Question

Take any two digit number three times to make a $6-digit$ number. Is it divisible by $3$?

Answer 1

Let a number be $ab$
Now, as described above 6-digit number is $ababab$
Now, $ababab=ab\ast 10101$
And $10101$ is divisible by $3$ as $1+0+1+0+1=3$
Therefore, $ababab$ is divisible by $3$