Question

What is the sum of all two-digit numbers that give a remainder of $3$ when they are divided by $7$?

• A. $666$
• B. $676$
• C. $683$
• D. $777$

Answer 1

The correct option is B $676$

The two-digit number is of the form $7n+3$.
The first two-digit number will be for
$n=1$
i.e., $7\times 1+3=10$
The last two-digit number will be for
$n=13$
i.e., $7\times 13+3=94$
No. of terms $=$ Sum of all $13$ terms
$=\frac{13}{2}(10+94)=13\times 52=676$