SOLUTION: On a square gameboard this is divided into n rows of n squares each, k of these squares lie along the boundary of the gameboard. Which of the following is a possible value of k?

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Question 393640: On a square gameboard this is divided into n rows of n squares each, k of these squares lie along the boundary of the gameboard. Which of the following is a possible value of k?
A. 10 B. 25 C. 34 D. 42 E. 52
Answer by robertb(5830) About Me  (Show Source):
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k must have the form k+=+n%5E2+-+%28n-2%29%5E2+=+n%5E2+-+n%5E2+%2B+4n+-+4++=4n-4+=+4%28n-1%29. Hence k must be divisible by 4. The answer is E, because 52 is the only number divisible by 4.