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LetNbe a positive integer not equal to 1. Then none of the numbers 2, 3,...., N is a divisor of (N! - 1). Thus, we can conclude that
  • a)
    (N - 1) is a prime number
  • b)
    At least one of the numbers N + 1 N + 2,... ,N  - 2 is a divisor of (N! - 1)
  • c)
    The smallest number between N and N! which is a divisor of (N! + 1), is a prime number
  • d)
    None of the foregoing statement is necessarily correct
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
LetNbe a positive integer not equal to 1. Then none of the numbers 2, ...
Eliminate the options.
For example, option (1) can be eliminated by assuming N = 2
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Most Upvoted Answer
LetNbe a positive integer not equal to 1. Then none of the numbers 2, ...
Given information
- N is a positive integer not equal to 1
- None of the numbers 2, 3,...., N is a divisor of (N!- 1)

Explanation
- N!-1 is not divisible by any integer from 2 to N
- This means that N!-1 is either a prime number or a product of multiple prime numbers greater than N
- However, we cannot conclude that N-1 is a prime number because there are counterexamples such as N=4 where 3 is not a prime but satisfies the given condition
- Similarly, we cannot conclude that any of the numbers N-1, N-2, ..., 2 is a divisor of N!-1 because there are counterexamples such as N=5 where none of these numbers divide 5!-1
- Finally, we cannot conclude that the smallest number between N and N! which is a divisor of N!-1 is a prime number because there are counterexamples such as N=6 where 5 divides 6!-1 but is not a prime

Conclusion
- None of the options (a), (b), or (c) can be concluded based on the given information
- Therefore, the correct answer is option (d)
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LetNbe a positive integer not equal to 1. Then none of the numbers 2, 3,...., N is a divisor of (N!- 1). Thus, we can conclude thata)(N- 1) is a prime numberb)At least one of the numbers N + 1 N + 2,... ,N- 2 is a divisor of (N!- 1)c)The smallest number between N and N! which is a divisor of (N!+ 1), is a prime numberd)None of the foregoing statement is necessarily correctCorrect answer is option 'D'. Can you explain this answer?
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LetNbe a positive integer not equal to 1. Then none of the numbers 2, 3,...., N is a divisor of (N!- 1). Thus, we can conclude thata)(N- 1) is a prime numberb)At least one of the numbers N + 1 N + 2,... ,N- 2 is a divisor of (N!- 1)c)The smallest number between N and N! which is a divisor of (N!+ 1), is a prime numberd)None of the foregoing statement is necessarily correctCorrect answer is option 'D'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about LetNbe a positive integer not equal to 1. Then none of the numbers 2, 3,...., N is a divisor of (N!- 1). Thus, we can conclude thata)(N- 1) is a prime numberb)At least one of the numbers N + 1 N + 2,... ,N- 2 is a divisor of (N!- 1)c)The smallest number between N and N! which is a divisor of (N!+ 1), is a prime numberd)None of the foregoing statement is necessarily correctCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for LetNbe a positive integer not equal to 1. Then none of the numbers 2, 3,...., N is a divisor of (N!- 1). Thus, we can conclude thata)(N- 1) is a prime numberb)At least one of the numbers N + 1 N + 2,... ,N- 2 is a divisor of (N!- 1)c)The smallest number between N and N! which is a divisor of (N!+ 1), is a prime numberd)None of the foregoing statement is necessarily correctCorrect answer is option 'D'. Can you explain this answer?.
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