The middle number of eleven — Averages Aptitude Question
The middle number of eleven: The average of 11 numbers is 10.9. If the average of the first six is 10.5 and of the… Answer and worked solution on CodeKairo.
- Topic: Averages
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 90 seconds
Question
The average of 11 numbers is 10.9. If the average of the first six is 10.5 and of the last six is 11.4, what is the sixth number?
Options
- 10.3
- 11.0
- 11.5
- 12.0
Show the answer and the worked solution
Correct answer: C. 11.5
Worked solution
- First six = 63.0; last six = 68.4; sum = 131.4.
- All eleven = 11 × 10.9 = 119.9.
- Sixth number = 131.4 − 119.9 = 11.5.
Answer: 11.5.
The idea
The same overlap rule with decimals. Keep one decimal place throughout rather than rounding early.
Shortcut. Measure from 10.9: the first six are −0.4 each (−2.4) and the last six +0.5 each (+3.0), so the double-counted sixth is 10.9 + 0.6 = 11.5.
Common trap. "11.0" — averaging the two group averages, (10.5 + 11.4) ÷ 2 ≈ 10.95, and rounding; the sixth number is the overlap, not a mean.