The average of 11 numbers is 10.9. If the average of first six is 10.5 and…
2025
The average of 11 numbers is 10.9. If the average of first six is 10.5 and that of the last six is 11.4 the sixth number is?
- A.
11.4
- B.
11.5
- C.
11.0
- D.
11.3
Attempted by 71 students.
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Correct answer: B
Key idea: the sixth number is included in both the first six and the last six, so summing those two groups counts the sixth number twice.
Total sum of 11 numbers = 11 × 10.9 = 119.9
Sum of the first six = 6 × 10.5 = 63
Sum of the last six = 6 × 11.4 = 68.4
Because the sixth number is included in both partial sums: (sum of first six) + (sum of last six) = (total sum) + (sixth number).
Therefore sixth number = (63 + 68.4) − 119.9 = 11.5
Answer: 11.5