Question

The average of five consecutive numbers is $n$. If the next two numbers are also included, the average will :

• A. remain the same
• B. increase by 1
• C. increase by 1.4
• D. increase by 2

Answer 1

The correct option is B increase by 1

let the five consecutive numbers be $x-2,x-1,x,x+1,x+2$

Given that the average of the numbers is $n$

Therefore, $n=\frac{(x-2)+(x-1)+x+(x+1)+(x+2)}{5}$

$⟹n=\frac{5x}{5}$

$⟹x=n$ -------(1)

The next two consecutive numbers are $x+3,x+4$

The the whole average is $\frac{(x-2)+(x-1)+x+(x+1)+(x+2)+(x+3)+(x+4)}{5+2}$

$=\frac{7x+7}{7}=x+1=n+1$ (from (1))

Therefore, the average increases by $1$