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

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

[A].

3

[B].

4

[C].

6

[D].

7

Answer: Option B

Explanation:

Let the two consecutive even integers be 2n and (2n + 2). Then,

(2n + 2)2 = (2n + 2 + 2n)(2n + 2 – 2n)

     = 2(4n + 2)

     = 4(2n + 1), which is divisible by 4.