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

A. It shall increase by 1 B. It shall remain the same C. It shall increase by 1.4 D. It shall increase by 2 Answer: Option A
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Solution(By Apex Team)

Let the five consecutive numbers be z, z + 1, z + 3 and z + 4 Then, $\begin{aligned}&\Rightarrow\frac{z+(z+1)+(z+2)+(z+3)+(z+4)}{5}=x\\ &\Rightarrow5z+10=5x\\ &\Rightarrow z=\frac{5x-10}{5}\\ &\Rightarrow z=x-2\end{aligned}$ So, the numbers are x – 2, x – 1, x, x + 1, x + 2 $\begin{aligned}&\therefore\text{ Required mean }\\ &=\frac{(x-2)+(x-1)+x+(x+1)+(x+2)+(x+3)+(x+4)}{7}\\ &=\frac{7x+7}{7}\\ &=x+1\end{aligned}$

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