Correct Answer:
D. 28
This problem requires finding three consecutive even natural numbers that sum to 78. Consecutive even natural numbers are integers that follow each other, differing by 2 (e.g., 2, 4, 6). Natural numbers are positive integers. Let the smallest even natural number be x. The next two consecutive even numbers will be x + 2 and x + 4.
Setting up the equation for their sum: x + (x + 2) + (x + 4) = 78. Simplifying, we get 3x + 6 = 78. Subtracting 6 from both sides gives 3x = 72. Dividing by 3, we find x = 24. Thus, the three numbers are 24, 26, and 28. Their sum is 24 + 26 + 28 = 78, confirming the solution. The greatest number among them is 28, making option D correct.
The other options are incorrect because they do not satisfy the conditions:
- A: 22 - If 22 were the greatest, the sequence would be 18, 20, 22, summing to 60 (too low).
- B: 24 - If 24 were the greatest, the sequence would be 20, 22, 24, summing to 66 (too low). 24 is the smallest number in the correct sequence.
- C: 26 - If 26 were the greatest, the sequence would be 22, 24, 26, summing to 72 (too low). 26 is the middle number in the correct sequence.