Four consecutive even integers have an average of 27. What is the greatest of these four even numbers?

Introduction / Context:
This problem checks understanding of averages and evenly spaced numbers. For consecutive even integers, values are equally spaced by 2, so the mean equals the midpoint of the set, and endpoints can be rebuilt from that midpoint systematically.

Given Data / Assumptions:

• Four consecutive even integers.
• Average (arithmetic mean) = 27.
• We must find the greatest of the four.

Concept / Approach:
If the smallest even integer is x, the set is x, x + 2, x + 4, x + 6. The average of equally spaced terms equals the average of the first and last term, or equivalently x + 3. Setting x + 3 = 27 gives x directly; the greatest term is x + 6.

Step-by-Step Solution:

Verification / Alternative check:
Numbers are 24, 26, 28, 30. Their mean is (24 + 30)/2 = 27, consistent with the given average.

Why Other Options Are Wrong:

• 28, 26, 32: Do not match the computed greatest value.
• None of these: A correct option (30) exists.

Common Pitfalls:
Using odd increments or treating 27 as a member of the set (it cannot be, since all terms are even).

Final Answer:
30