Question

The average of four consecutive even numbers is $27$. The largest of these numbers is?

Answer 1

Let $x-2,x,x+2,x+4$ be the four consecutive even numbers.

Given that the average of four consecutive even numbers is $27$.

We know that,

$Average=\frac{totalsum}{totalnumbers}$

$\begin{array}{rcl}& \Rightarrow & 27=\frac{\left(x-2\right)+\left(x\right)+\left(x+2\right)+\left(x+4\right)}{4}\\ & \Rightarrow & 27\times 4=x-2+x+x+2+x+4\\ & \Rightarrow & 108=4x+4\\ & \Rightarrow & 180=4\left(x+1\right)\\ & \Rightarrow & \frac{108}{4}=x+1\\ & \Rightarrow & 27=x+1\\ & \Rightarrow & x=27-1=26\\ & & \end{array}$

Thus, the four consecutive numbers are,

$\begin{array}{rcl}x-2& =& 26-2=24\\ x& =& 26\\ x+2& =& 26+2=28\\ x+4& =& 26+4=30\end{array}$

Hence, the largest of these numbers is $30.$