Discussion
The average of 4 consecutive even numbers is 27. The largest of these numbers will be
Answer: C
The largest number is 30.
Four consecutive even numbers are n, n + 2, n + 4 and n + 6. Their average is the mean of the middle two, n + 3, so
\[ n + 3 = 27 \quad\Rightarrow\quad n = 24 \]
The numbers are 24, 26, 28 and 30, whose sum 108 divided by 4 is 27. The largest is 30. 28 is the third number, and 32 and 36 would push the average above 27.
Shortcut: for an even number of consecutive even numbers, the average lies midway between the two middle terms, so 26 and 28 surround 27, and the list ends two steps later at 30.
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