To find the maximum possible number of positive integers among 25 integers whose average is zero, let's break down the problem step-by-step.

The average of 25 integers being zero means that the sum of these integers equals zero. Mathematically, this can be expressed as:

\frac{\text{Sum of integers}}{\text{Number of integers}} = 0\

This implies the sum of the integers is:

\text{Sum of integers} = 0

We want to maximize the number of positive integers while maintaining the condition that the sum is zero. Let's denote the number of positive integers as P and the number of negative integers as N. The equations become:

• P + N = 25
• The sum of all integers is zero, so \text{Sum of positive integers} + \text{Sum of negative integers} = 0
• If the positive integers are such that they are all 1 except one, then:
  P-1 \text{ integers are 1, and the remaining one integer can be large enough negative}.
• This single negative integer must balance the total sum to zero.

Suppose we have P = 24 positive integers, all being '1' (the smallest possible positive integer). The sum of these positive integers will be:

24 \times 1 = 24

The single negative integer must be -24 to make the total sum zero:

24 + (-24) = 0

Thus, the maximum number of positive integers possible is 24. This meets the condition that their average must be zero, and it balances the number of integers being 25.

Hence, the correct answer is 24.