Three pairs of numbers — Averages Aptitude Question
Three pairs of numbers: The average of 6 numbers is 3.95. The average of two of them is 3.4 and of another two is… Answer and worked solution on CodeKairo.
- Topic: Averages
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 90 seconds
Question
The average of 6 numbers is 3.95. The average of two of them is 3.4 and of another two is 3.85. What is the average of the remaining two?
Options
- 4.2
- 4.5
- 4.6
- 4.7
Show the answer and the worked solution
Correct answer: C. 4.6
Worked solution
- Total = 6 × 3.95 = 23.7.
- First pair = 6.8; second pair = 7.7; together 14.5.
- Remaining pair = 23.7 − 14.5 = 9.2, so their average is 9.2 ÷ 2 = 4.6.
Answer: 4.6.
The idea
Work in totals throughout and divide only at the very end. Averaging the pair averages happens to work here because every group has two numbers — it fails the moment the groups differ in size.
Shortcut. Measure from 3.95: the first pair is 2 × (−0.55) = −1.1 and the second 2 × (−0.1) = −0.2, so the last pair must make up +1.3, or +0.65 each: 4.6.
Common trap. "4.5" — close to the answer and a clean-looking figure, but it gives a total of 6.8 + 7.7 + 9.0 = 23.5, not 6 × 3.95 = 23.7.