Two numbers discarded — Averages Aptitude Question
Two numbers discarded: The average of 50 numbers is 38. If the numbers 45 and 55 are discarded, what is the average… Answer and worked solution on CodeKairo.
- Topic: Averages
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 60 seconds
Question
The average of 50 numbers is 38. If the numbers 45 and 55 are discarded, what is the average of the rest?
Options
- 36.5
- 37
- 37.5
- 38
Show the answer and the worked solution
Correct answer: C. 37.5
Worked solution
- Total = 1,900.
- After discarding: 1,900 − 100 = 1,800 over 48 numbers.
- Average = 1,800 ÷ 48 = 37.5.
Answer: 37.5.
The idea
Both discarded numbers are above the average, so the average must fall — a quick check before computing. Work with totals, never with the averages directly.
Shortcut. At the average the two would total 76, but they total 100; removing that excess of 24 across the 48 numbers left drops the average by 0.5, to 37.5.
Common trap. "38" — assuming two numbers out of fifty cannot move the average; both lie above 38, so removing them must pull it down.