Problem:

The average of 20 numbers is zero. Of them, how many of them may be greater than zero, at the most?

Solution:

To solve this problem, let's consider the given information:
- There are 20 numbers in total.
- The average of these numbers is zero.

Understanding the Average:
The average of a set of numbers is calculated by summing all the numbers and dividing the sum by the total count of numbers. In this case, since the average is zero, it means that the sum of the 20 numbers is also zero.

Exploring Possible Scenarios:
To find out the maximum number of positive numbers among the 20 numbers, let's consider different scenarios.

Scenario 1: No positive numbers:
If all the numbers are negative or zero, the sum of the numbers will be negative or zero. But since the average is zero, this scenario is not possible.

Scenario 2: Only one positive number:
If there is only one positive number, the rest of the numbers must be negative in order to maintain the average as zero. Let's say the positive number is 'x'. The sum of the other 19 numbers will be -x, which cancels out the positive contribution of 'x'. Therefore, only one positive number is possible.

Scenario 3: More than one positive number:
If there are more than one positive numbers, the sum of the numbers will be positive. However, since the average is zero, it contradicts the given information. Therefore, more than one positive number is not possible.

Conclusion:
Based on the above analysis, the maximum number of numbers that may be greater than zero is 1. Thus, the correct answer is option (D) 19.