The difference between the squares of two consecutive odd

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

  1. 16
  2. 8
  3. 7
  4. 3

Answer

Let two consecutive odd integers be = 2k +1 and 2k +3, where k is any integer.

Now, (2k + 3)2 - (2k + 1)2 = (4k2 + 9 + 12k) - (4k2 + 1 + 4k) 

= 8k + 8 = 8(k + 1), which is a multiple of 8

So, the difference is always divisible by 8.

The correct option is B.