Correct Answer - Option 3 : 100
Given:
Average of 9 consecutive integers is 50.
Concepts used:
Average = (Sum of all observations)/(Number of observations)
Calculation:
Let first intger be x.
So, nine consecutive numbers are x, (x + 1), (x + 2), (x + 3), (x + 4), (x + 5), (x + 6), (x + 7) and (x + 8)
Sum of 9 consecutive integers = x + (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5) + (x + 6) + (x + 7) + (x + 8) = 9x + 36
Average = Sum of all observations/Number of observations
⇒ 50 = (9x + 36)/9
⇒ x + 4 = 50
⇒ x = 50 – 4 = 46
Smallest integer = x = 46
Largest integer = x + 8 = 46 + 8 = 54
Sum of largest and smallest integers = 46 + 54 = 100
∴ The sum of largest and smallest integers is 100.