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# If N is a positive integer, is N! divisible by 14 ? 1. (N +

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If N is a positive integer, is N! divisible by 14 ? 1. (N + [#permalink]  29 Oct 2007, 13:41
If N is a positive integer, is N! divisible by 14 ?

1. (N + 1)! is divisible by 15
2. (N + 2)! is divisible by 16

whats a good approach / intuitive way of solving these type of problems?
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Re: N! [#permalink]  29 Oct 2007, 14:15
beckee529 wrote:
If N is a positive integer, is N! divisible by 14 ?

1. (N + 1)! is divisible by 15
2. (N + 2)! is divisible by 16

whats a good approach / intuitive way of solving these type of problems?

Let me try this one. We have to prove yes/no with this question.

Hint: Use the knowlege of Prime number. In the question stem, N must be at least more than or equal to number 7. so N!/(7x2) is an integer.

1. (N + 1)!/15 = a positive integer

To prove YES, Can N be a number that allow both N!/14 and (N+1)!/15 be integer numbers? The answer is YES!
- Ex. N = 14
To prove NO, Can N be a number that allow (N+1)!/15 be an interger but does not do so with N!/14.
- Ex. N = 4

You have both "YES" and "NO". Therefore, INSUFF

2. (N + 2)!/16 = a positive integer

To prove YES, Pick N = 14
To prove NO, Pick N = 4 (again)

You have both "YES" and "NO". Therefore, INSUFF

1. & 2.)
N can be a number >=7
N can still be a number <7
INSUFF

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Re: N! [#permalink]  29 Oct 2007, 14:35
beckee529 wrote:
If N is a positive integer, is N! divisible by 14 ?

1. (N + 1)! is divisible by 15
2. (N + 2)! is divisible by 16

whats a good approach / intuitive way of solving these type of problems?

1: N >= 4.
2: N >= 4.

so same E.
Re: N!   [#permalink] 29 Oct 2007, 14:35
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