The difference of the squares of two consecutive even integers is divisible by which of the following integers ?
3
4
6
7
Explanation:
Let the two consecutive even integers be 2$n $ and $\left(2 n + 2\right) $. Then,
$\left(2n + 2\right)$2 = $\left(2 n + 2 + 2 n\right )$$\left(2 n + 2 - 2 n \right)$
= 2$\left(4 n + 2\right) $
= 4$\left(2 n + 1\right)$, which is divisible by 4.