Step-by-step Solution:

Quick Solution

The easiest way to solve this is to use the most direct piece of information—Alan's age—to find the age of each brother one by one.

Step-by-Step Age Calculation

1. Find Carl's age: We are told, "Alan, who is 34, is two years younger than Carl."
   This means Carl must be two years older than Alan.
   Carl's Age = 34 + 2 = 36 years.
   
2. Find Bob's age: Next, "Bob is one year younger than Carl."
   Bob's Age = 36 - 1 = 35 years.
   
3. Find Dave's age: Finally, "Dave is two years older than Bob."
   Dave's Age = 35 + 2 = 37 years.
   

Comparing the Ages

Now we have the age of all four brothers:

• Alan: 34
• Bob: 35
• Carl: 36
• Dave: 37 (Oldest)

Final Answer: The oldest brother is Dave.