How many can be positive — Averages Aptitude Question
How many can be positive: The average of 20 numbers is zero. At most how many of them may be greater than zero? Answer and worked solution on CodeKairo.
- Topic: Averages
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 60 seconds
Question
The average of 20 numbers is zero. At most how many of them may be greater than zero?
Options
- 0
- 1
- 19
- 20
Show the answer and the worked solution
Correct answer: C. 19
Worked solution
- An average of zero means the total is zero.
- If 19 numbers are positive, a single sufficiently large negative number can balance them.
- All 20 cannot be positive, so the maximum is 19.
Answer: 19.
The idea
'At most' questions ask for the extreme case that is still possible. One negative number of any size can offset any number of positives, so only one must be sacrificed.
Shortcut. Take 19 ones and a single −19: the total is 0 with 19 positives. All 20 positive would force a positive total.
Common trap. "20" — counting zeros as positive: all 20 numbers can be 0, but zero is not greater than zero.