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OG11 Question 153


 
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cliou21
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PostPosted: Fri May 09, 2008 2:33 pm    Post subject: OG11 Question 153 Reply with quote
Can someone please explain this better then the OG?

153. Does the integer k have a factor p such that 1>p>k?
(1) k>4!
(2) 13! + 2 <= k <= 13! + 13

I understand that (1) is not sufficient.
With (2), how can you be sure that k is not a prime number between 13!+2 and 13! + 13?

Thanks!
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gabriel
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PostPosted: Tue May 13, 2008 12:56 pm    Post subject: Re: OG11 Question 153 Reply with quote
cliou21 wrote:
Can someone please explain this better then the OG?

153. Does the integer k have a factor p such that 1>p>k?
(1) k>4!
(2) 13! + 2 <= k <= 13! + 13

I understand that (1) is not sufficient.
With (2), how can you be sure that k is not a prime number between 13!+2 and 13! + 13?

Thanks!


K will never be a prime number if it is an integer between 13!+2 and 13!+13. Here is why. 13! (= 1*2*3*...*12*13) is a multiple of every number between 1 and 13 i.e every number between 1 and 13 is a factor of 13!. If there is a number of the type 13!+a and if "a" is contained in 13! (By that I mean it is one of the integer between 1 and 13,) then "a" will be a factor of 13!+a. In the above question "a" assumes values between 2 and 13, all of which are a part of 13!. Hence the integers between 13!+2 and 13!+13 are not prime. Let me know if you have any doubts.

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cliou21
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PostPosted: Wed May 14, 2008 12:24 pm    Post subject: Reply with quote
Thanks! This helps alot! Very Happy
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