Virtual Gate Test Series: Numerical Ability - Number System

Question

If $N = 888 $ up to $100$ digits, what is the remainder when $N$ is divided by $625?$

1. 128
2. 138
3. 338
4. 388

Answer 1

$625 \times 16 = 10000$
i.e. anything which is multiple of 10000 will also be multiple of 625

$\underbrace{8888 \cdots 8}_{\text{100 times}} =\underbrace{8888 \cdots 8}_{\text{96 times}} \times 10000 +8888$

So to find reminder of $\underbrace{88888888888888\cdots 8}_{\text{100 times}}$, just find Reminder when 8888 is divided by 625

$8888 = 625 \times 14 + 138$
So, 138 is reminder.

Comments

o.O So for any such qn, we can use this method? If suppose the digits were not repeating, then also same method?