Question

The sum of all two digit numbers each of which leaves remainder $3$ when divided by $5$ is

• A. $952$
• B. $999$
• C. $1064$
• D. $1120$

Answer 1

The correct option is B $999$

Two digit numbers which leaves remainder $3$ when divide by $5$ are$13,18,----98$

From the formed AP, first term $a=13$, common difference $d=5$ and $a_n=98$

using general term of an AP form

$a_n=a+(n-1)d$

$98=13+(n-1)5$

$85=(n-1)5$

$17+1=n$

$\therefore n=18$

In total we have 18 such numbers

So, $S_{18}=\frac{18}{2}(2\times 13+17\times 5)=999$