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# Gmatprep function

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Intern
Joined: 19 Jan 2009
Posts: 18
Schools: Kellogg, Ross, Darden, Kelley, UNC

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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.

--== Message from GMAT Club Team ==--

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Intern
Joined: 19 May 2009
Posts: 5

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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! .
Intern
Joined: 19 Jan 2009
Posts: 18
Schools: Kellogg, Ross, Darden, Kelley, UNC

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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!

Take care
Manager
Joined: 14 May 2009
Posts: 189

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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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Manager
Joined: 04 Sep 2006
Posts: 113

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01 Jun 2009, 10:08
smallest prime factor of h(100)+1 is asked
Senior Manager
Joined: 16 Jan 2009
Posts: 349
Concentration: Technology, Marketing
GMAT 1: 700 Q50 V34
GPA: 3
WE: Sales (Telecommunications)

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01 Jun 2009, 11:27
I think I have seen this preblem before.
let me look around for the link.
_________________

Lahoosaher

Senior Manager
Joined: 16 Jan 2009
Posts: 349
Concentration: Technology, Marketing
GMAT 1: 700 Q50 V34
GPA: 3
WE: Sales (Telecommunications)

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01 Jun 2009, 11:33
http://gmatclub.com/forum/smallest-prim ... 76565.html

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

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Lahoosaher

Re: Gmatprep function   [#permalink] 01 Jun 2009, 11:33
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