Question

Ajay multiplied $484$ by a certain number to get the result $3823a$. Find the value of $a$.

Answer 1

$3823a$ is divisible by $484$, hence $484$ is a factor of $3823a$.

$4,11$ are factors of $484$.

Hence, $3823a$ is divisible by both $4$ and $11$.

To be divisible by $4$, the last two digits have to be divisible by $4$.

So, $a$ can take two values $2$ and $6$.

However, $38232$ is not divisible by $11$ but $38236$ is divisible by 11.

Hence, $6$ is the correct choice.