Single correct option
The average of 11 numbers is 50. The average of the first six numbers is 49 and the average of the last six numbers 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.
Sum of the last six = 6 × 52 = 312.
The sixth number is in both groups, so it is counted twice when the two sums are added:
294 + 312 = 550 + (6th number), so the 6th number = 606 − 550 = 56.
Tip: whenever two overlapping groups cover everything, the overlap = (sum of the groups) − (total).
Sum of the first six = 6 × 49 = 294.
Sum of the last six = 6 × 52 = 312.
The sixth number is in both groups, so it is counted twice when the two sums are added:
294 + 312 = 550 + (6th number), so the 6th number = 606 − 550 = 56.
Tip: whenever two overlapping groups cover everything, the overlap = (sum of the groups) − (total).
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