### 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

### 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}

A. 20
B. 21
C. 28
D. 32

A. 18
B. 20
C. 24
D. 30

A. 10 years
B. 10.5 years
C. 11 years
D. 12 years