Question

Difference of squares of two odd integers is always divisible by ?

• A. 3
• B. 5
• C. 16
• D. 8

Answer 1

Answer: (D)

8

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

Difference$={(2k+3)}^2-{(2k+1)}^2$

$=4k^2+9+12k-4k^2-1-4k=8k$

Hence, the difference is always divisible by $8$.