Single correct option
The average of 11 numbers is 50. The average of the first six is 49 and the average of the last six is 52. What is the sixth number?
- A. 50
- B. 54
- C. 56
- D. 58
Show answer and solution
Answer: (C) 56
Sum of all 11 numbers = 11 × 50 = 550.
Sum of the first six = 6 × 49 = 294, and sum of the last six = 6 × 52 = 312.
The 6th number falls in both groups, so it is counted twice: 294 + 312 = 606 = 550 + (6th number).
Sixth number = 606 − 550 = 56.
Tip: When two overlapping groups share exactly one term, that term = (sum of group 1 + sum of group 2) − total.
Sum of the first six = 6 × 49 = 294, and sum of the last six = 6 × 52 = 312.
The 6th number falls in both groups, so it is counted twice: 294 + 312 = 606 = 550 + (6th number).
Sixth number = 606 − 550 = 56.
Tip: When two overlapping groups share exactly one term, that term = (sum of group 1 + sum of group 2) − total.
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