The average of eight consecutive odd numbers is 28. The sum of the smallest and the largest number is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 56.
Let the first odd number as (n - 7)
Other consecutive odd numbers would be (n - 5), (n - 3), (n - 1), (n + 1), (n + 3), (n + 5), and (n + 7)
Sum = (n - 7) + (n - 5) + (n - 3) + (n -1) + (n + 1) + (n + 3) + (n + 5) + (n + 7) = 8n
We know that,
Average = Sum of observations/Number of observations
Thus,
The average of eight consecutive odd numbers = 8n/8
⇒ 8n/8 = 28
⇒ n = 28
Largest odd number = n + 7 = 28 + 7 = 35
Smallest odd number = n - 7 = 28 - 7 = 21
Hence, the sum of the largest and smallest odd numbers = 35 + 21 = 56