The average of nine consecutive even numbers is 24. What is the average of the smallest three of these 9 given numbers?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 18.
Let's assume nine consecutive even numbers are y, (y + 2), (y + 4), (y + 6), (y + 8), (y + 10) (y + 12) (y + 14) and (y + 16)
The average of nine consecutive even numbers is 24.
⇒ (y + (y + 2) + (y + 4) + (y + 6) + (y + 8) + (y + 10) + (y + 12) + (y + 14) + (y + 16))/9 = 24
⇒ y + (y + 2) + (y + 4) + (y + 6) + (y + 8) + (y + 10) + (y + 12) + (y + 14) + (y + 16) = 216
⇒ 9y + 72 = 216
⇒ y + 8 = 24
⇒ y = 24 - 8
⇒ y = 16
Average of the smallest three of these 9 given numbers = y + (y + 2) + (y + 4)
⇒ (3y + 6)/3
⇒ y + 2
⇒ 16 + 2 = 18