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The difference of the squares of two consecutive odd integers is divisible by which of the following integers?

Correct Answer: 8

Explanation:

Let the two consecutive odd integers be (2 n + 1) and (2 n + 3). Then,

(2n + 3)2 - (2n + 1)2 = (2n + 3 + 2n + 1) (2n + 3 - 2n - 1)


     = (4n + 4) x 2


     = 8(n + 1), which is divisible by 8.


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