5 and it's remainder 3!

Number Theory Level 1

What is the sum of all the $2$ digit numbers which leaves a remainder of $3$ when divided by $5$ ?

Note: $2$ digit numbers don't include numbers from $0$ to $9$ .

2 solutions

A Former Brilliant Member
May 27, 2020

The numbers described in the problem are $13,18,23,28,...,98$ . There are $18$ terms in all, whose sum is

$\dfrac{18}{2}(13+98)=9\times 111=\boxed {999}$ .

They r in AP right?

Soham Nimale - 1 year ago

Yes, they are in AP

Mahdi Raza - 1 year ago

Mahdi Raza
Jun 1, 2020

The numbers are: $13, 18, \ldots 93, 98$
Each term of the AP is the form $8 + 5n$ . The total numbers are 18
They form an A.P. whose sum is: $\dfrac{n}{2}(a+l) \implies \dfrac{18}{2}(13 + 98) = \boxed{999}$