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Gmatprep function

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Intern
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Gmatprep function [#permalink]

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New post 20 May 2009, 11:28
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Can someone explain?

The function should result in 100! + 1, which is odd. But I can't move further.
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Re: Gmatprep function [#permalink]

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New post 22 May 2009, 09:57
Quote:
Can someone explain?

The function should result in 100! + 1, which is odd. But I can't move further.


You made a small mistake: h(n) is DIFFERENT than n!

Please note that h(n) is defined as the multiplication of the EVEN integers for 2 to n

so h(6)= 2*4*6 = 2^4 * 3

and h(100)=2*4*6*...*100

obviously h(100)+1 can not be divided for any non trivial factor of h(100) and this includes of course any prime number P from 1 to 50 which appears in h(100) at least as 2*P, for example 17 appears as factor in 34 and 68 in h(n). From that follows the right answer you showed.

Just for fun it would have been the same answer if h(n)=n! .

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Re: Gmatprep function [#permalink]

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New post 24 May 2009, 23:26
Thanx Jorge, excellent explanation. I already spot my error after posting, however it didn't make much difference because I was lacking the concept to solve this problem.

Let me just fix up a small error on your side:

so h(6)= 2*4*6 = 2^3 * 3!
because 2*4*6 = 2*2(2)*2(3) = 2^3*3! :wink:

Take care

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Re: Gmatprep function [#permalink]

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New post 25 May 2009, 23:52
\(h(100) + 1 = 2(4)(6)(8)...(98)(100) + 1
= 2(1*2*3*...*49*50) + 1\)

Stare at it really hard... it's in the quotient remainder form. Anytime a number can be written as \(Q + R\) where \(0<=R<=Q\) and \(R & Q are coprime\) (ie they have no common factors in common) then that number is NOT divisible by Q or any factor of Q.

Hence the largest prime factor has to be bigger than 50, and conversely, 40.

Final Answer, \(E\).
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Re: Gmatprep function [#permalink]

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New post 01 Jun 2009, 10:08
smallest prime factor of h(100)+1 is asked

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Re: Gmatprep function [#permalink]

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New post 01 Jun 2009, 11:27
I think I have seen this preblem before.
let me look around for the link.
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Re: Gmatprep function [#permalink]

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New post 01 Jun 2009, 11:33
smallest-prime-factor-76565.html
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Re: Gmatprep function   [#permalink] 01 Jun 2009, 11:33
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