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

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

[A].

3

[B].

6

[C].

7

[D].

8

Answer: Option D

Explanation:

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.