Final answer:
The youngest brother is 1964 years old.
Step-by-step explanation:
In this question, we are given that three brothers were all born on New Year's Day in consecutive even years, and the sum of these years is 5898. We need to find the age of the youngest brother.
Let's denote the year of the youngest brother as x. Since the brothers are born on consecutive even years, the middle brother would be x + 2 years old, and the oldest brother would be x + 4 years old.
According to the given information, the sum of these three years is 5898, so we can set up the equation x + (x+2) + (x+4) = 5898. Simplifying the equation, we get 3x + 6 = 5898.
By subtracting 6 from both sides, we have 3x = 5892. Dividing both sides by 3, we find x = 1964.
Therefore, the youngest brother is 1964 years old.