CAT 1996 — QA Question 10
If n is any odd number greater than 1, then n(n2 – 1) is
Answer & solution
Correct answer: divisible by 24 always
- A
divisible by 96 always
- B
divisible by 48 always
divisible by 24 always
- D
None of these
n(n2 – 1) = (n – 1)n(n + 1). If you observe, this is the product of three consecutive integers with middle one
being an odd integer. Since there are two consecutive even numbers, one of them will be a multiple of 4 and the other one will be multiple of 2. Hence, the product will be a multiple of 8. Also since they are three consecutive integers, one of them will definitely be a multiple of 3.
Hence, this product will always be divisible by (3 × 8)= 24.
Hint: Students, please note if a number is divisible by 96, it will also be divisible by 48 and 24. Similarly, if a number is divisible by 48, it is will always divisible by 24. Since there cannot be more than one right answers, we can safely eliminate options (a) and (b).