Question:
Given a relation, \( n = 1 + x \) and \( x \) is a product of four consecutive integers. Then which of the following is true?
Given a relation, \( n = 1 + x \) and \( x \) is a product of four consecutive integers. Then which of the following is true?
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For problems involving products of consecutive integers, remember to check the divisibility properties of the resulting number.
Updated On: Mar 23, 2026
- n is an odd integer
- n is prime
- n is a perfect square
- None of these
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The Correct Option is C
Solution and Explanation
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.
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