Question : The average of three consecutive even numbers is A. If the next five even numbers are added, what is the average of these eight numbers?
Option 1: A + 3
Option 2: A + 4
Option 3: A + 5
Option 4: A + 7
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Correct Answer: A + 5
Solution :
Let $(x - 2)$, $x$, and $(x + 2)$ be the three consecutive even numbers.
Average = A = middle term = $x$
Let the next five consecutive even numbers added be $(x + 4), (x + 6), (x + 8), (x + 10)$ and $(x + 12)$
Then numbers are $(x - 2)$, $x$, $(x + 2)$, $(x + 4), (x + 6), (x + 8), (x + 10),$ and $(x + 12)$.
$\therefore$ Average = Average of two middle terms =$ \frac{(x + 4)+ (x + 6)}{2} =x+5 =A+5$
Hence, the correct answer is A + 5.
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