Question

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

• A. 8
• B. 7
• C. 6
• D. 3

Answer 1

The correct option is A 8

Let the two consecutive odd integers be $(2x+1)$ and $(2x+3)$
$\therefore (2x+3{)}^2-(2x+1{)}^2=4x^2+12x+9-4x^2-4x-1$
$=8x+8=8(x+1)$
Hence, the difference is divisible by $8$