Question on division and remainder

Question

How to solve these type of questions?

Which of the following numbers must be added to $5678$ to give a remainder of $35$ when divided by $460$?(Options are)

A) 618
B) 955
C) 797
D) 980

This is an aptitude question.

Answer 1

The task is to solve $5678+n\equiv 35\ (\text{mod}\ 460)$.

If you don't have a calculator, I'd first note that you can subtract $4600$ from the $5678$ to get

$1078+n\equiv 35$

then subtract another $2\cdot460=920$:

$158+n\equiv 35$

For this to be true we need something like $158+n=495$. Solve to get $n=337$. This isn't an option so add another 460.