Question

If n is any odd number greater than 1, then $n(n^2 - 1)$ is

• A. divisible by 96 always
• B. divisible by 48 always
• C. divisible by 24 always
• D. None of these

Hint:

Three consecutive integers divisible by 3 and by at least one multiple of 4.

Answer 1

The Correct Option is B

$n(n^2-1) = n(n-1)(n+1)$ → product of 3 consecutive integers (odd, even, odd).
One multiple of 4 and another multiple of 2 → multiple of 8. Also multiple of 3 → $8 \times 3 = 24$. Since n is odd, even factors give extra multiple of 2 → $24 \times 2 = 48$.