The average of 29 numbers is 0. At most, how many of these numbers can be greater than 0?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 28
An average of 0 means the sum of the numbers is 0. Positive numbers can only be balanced by at least one negative number.
Sum of the 29 numbers \(=29\times0=0\)
If all 29 were greater than 0, their sum would be greater than 0, so at least one number must be 0 or negative
28 positive numbers are possible: for example, 28 numbers each equal to 1 and one number equal to \(-28\)
Check: \(28\times1+(-28)=0\), so the average is \(\displaystyle \frac{0}{29}=0\)
At most 28 of the numbers can be greater than 0.