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
6
7
8
The difference of the squares of two consecutive odd integers is divisible by which of the following integers ?
[A].
[B].
[C].
[D].
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.