Single correct option
The average of 11 numbers is 50. The average of the first six of them is 49 and that 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 first six = 294; sum of last six = 312. The sixth number is counted in both groups, so
294 + 312 = 550 + (sixth number) ⇒ sixth number = 606 − 550 = 56.
Tip: Whenever two overlapping groups cover the whole set, (sum of group 1 + sum of group 2) − total = the overlap.
Sum of first six = 294; sum of last six = 312. The sixth number is counted in both groups, so
294 + 312 = 550 + (sixth number) ⇒ sixth number = 606 − 550 = 56.
Tip: Whenever two overlapping groups cover the whole set, (sum of group 1 + sum of group 2) − total = the overlap.
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