Question

Find the average of all odd numbers up to $100$

• A. $30$
• B. $50$
• C. $4$
• D. $10$

Answer 1

Answer: (B)

$50$

Sum of odd numbers upto $100=1+3+5+7+9+....+93+95+97+99$.
Which can be grouped as $=(1+99)+(3+97)+(5+95)+(7+93)+.....$ upto $25$ times.
Since there is $50$ odd numbers they can be grouped into $25$ groups each group containing $2$ numbers.
So sum of numbers $100+100+100+100+....25$ times will be $100\times 25=2500$.
Average of odd numbers upto $100=$ (sum of the odd numbers upto $100$) / total number of odd numbers
$=\frac{2500}{50}=50$.