The difference between the square of two consecutive odd integers is always divisible by :

A. 3

B. 6

C. 7

D. 8

Answer: Option D

Solution(By Examveda Team)

Let the two consecutive odd integers be (2m + 1) and (2m + 3)
Then, (2m + 3)² - (2m + 1)²
= [(2m + 3) + (2m + 1)] [(2m + 3) - (2m + 1)]
= (4m + 4) × 2
= 8m + 8
= 8(m + 1), which is always divisible by 8