The average of 10 numbers is 0. Of them, how many can be smaller than zero, at…
2024
The average of 10 numbers is 0. Of them, how many can be smaller than zero, at most?
- A.
0
- B.
1
- C.
9
- D.
10
Attempted by 123 students.
Show answer & explanation
Correct answer: C
Answer: 9
Key idea: the sum of all ten numbers must be 0 because the average is 0.
Suppose nine numbers are smaller than zero. Let their sum be -S where S > 0.
To make the total sum zero, the tenth number must be +S. Then (-S) + S = 0, so the average is 0.
This shows nine numbers can indeed be smaller than zero while the average is 0.
You cannot have all ten numbers smaller than zero, because then the sum would be negative and the average would not be 0.
Example: nine numbers -1 (sum = -9) and one number 9 gives total 0 and average 0.