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Question

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


Options:
A .  3
B .  6
C .  7
D .  8
Answer: Option D

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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