Question

Given a relation, \( n = 1 + x \) and \( x \) is a product of four consecutive integers. Then which of the following is true?

• A. n is an odd integer
• B. n is prime
• C. n is a perfect square
• D. None of these

Hint:

For problems involving products of consecutive integers, remember to check the divisibility properties of the resulting number.

Answer 1

The Correct Option is C

Since \( x \) is the product of four consecutive integers, \( x \) will always be divisible by 24. Therefore, \( n = 1 + x \) will always be odd. However, since \( n = 1 + x \) is a sum of 1 and a multiple of 24, \( n \) is not a perfect square, nor is it necessarily prime.