Chapter 11, Problem 9SAP

To determine

To find: the correct option for the given condition.

Answer to Problem 9SAP

The option A is correct.

Explanation of Solution

Given information:

The condition is given as “ $A$ is the average (arithmetic mean) of three consecutive positive even integers”.

Let three consecutive positive even integers are $x,x+2$ , and $x+4$ .

So,

  $\begin{array}{c}\frac{x+x+2+x+4}{3}=A\\ \frac{3x+6}{3}=A\\ x+2=A\end{array}$

As the average sum of the positive integers $x+2$ and the sum is divisible by 3. So, if divide the sum by 2 then minimum remainder should be 1.

Here x is the average number.

Therefore, the option A is correct.