Question

What is the average (arithmetic mean) of all numbers multiples of $6$ from $6$ to $510$ inclusive?

• A. $516$
• B. $258$
• C. $1530$
• D. $252$
• E. $1510$

Answer 1

The correct option is B $258$

The average $A$ of all multiples of $6$ from $6$ to $510$ is given by

$A=\frac{S}{n}$

where $S=6+12+...+510$ and $n$ is the number of multiples from $6$ to $510$.

$S=\frac{1}{2}n(6+510)$

For $n=1$, $A$ is given by:

$\left(\frac{1}{2}\right)(6+510)=\left(\frac{1}{2}\right)\left(516\right)=258$

Hence, the average is $258$.