If m and n are positive integers and (m - n) is an even number, then (m² - n² ) will always be divisible by :

A. 4

B. 6

C. 8

D. 12

Answer: Option A

Solution(By Examveda Team)

Note : In such type of questions assume any values which satisfy the question condition
(i) Let m = 3,   n = 1
m - n = 3 - 1 = 2 (Even)
m² - n² = (3)² - (1)² = 8
(ii) Let m = 4,   n = 2
m - n = 4 - 2 = 2 (Even)
m² - n² = 16 - 4 = 12
(iii) Let m = 5,   n = 3
m - n = 5 - 3 = 2 (Even)
m² - n² = 25 - 9 = 16
H.C.F. of 8, 12, 16 = 4
So, the number is divisible by 4