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
4
6
7
The difference of the squares of two consecutive even integers is divisible by which of the following integers ?
[A].
[B].
[C].
[D].
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.