Question
The difference of the squares of two consecutive odd integers is divisible by which of the following integers ?
Answer: Option D
= 8(n + 1), which is divisible by 8
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Let the two consecutive odd integers be (2n + 1) and (2n + 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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