Question

If the average of 35 numbers is 22, the average of the first 17 numbers is 19, and the average of the last 17 numbers is 20, then the 18th number is

• A. 132
• B. 108
• C. 133
• D. 107

Answer 1

Answer:

D. 107

Solution: Given: The average of 35 numbers = 22 The average of first 17 numbers = 19 The average of the last 17 numbers = 20 Formula: Average = (Sum of all observations)/(Total number of all observations) Calculation: The sum of 35 numbers = 22 × 35 = 770 Sum of first 17 numbers = 17 × 19 = 323 Sum of last 17 numbers = 17 × 20 = 340 ∴ 18th number = 770 - (340 + 323) = 770 - 663 = 107 Alternate Method: nth Number = Sum of total number - (Sum of first (n - 1) + Sum of Last (n - 1)) ∴ 18th number = 770 - (340 + 323) = 770 - 663 = 107