The average of five consecutive numbers is x. If the next two numbers are included, how shall the average vary?

Answer: Option A

Let the five consecutive numbers be z, z + 1, z + 3 and z + 4
Then,
$$\Rightarrow \frac{z+\left(z+1\right)+\left(z+2\right)+\left(z+3\right)+\left(z+4\right)}{5}=x$$
$$\begin{array}{rl}& \Rightarrow 5z+10=5x\\ & \Rightarrow z=\frac{5x-10}{5}\\ & \Rightarrow z=x-2\end{array}$$
So, the numbers are x - 2, x - 1, x, x + 1, x + 2
∴ Required mean
$$=\frac{\left(x-2\right)+\left(x-1\right)+x+\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+\left(x+4\right)}{7}$$
$$\begin{array}{rl}& =\frac{7x+7}{7}\\ & =x+1\end{array}$$