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Problem I faced in Problem Solving (GMAT Prep Test)

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by Rezinka » Sun Oct 17, 2010 9:46 pm
For every positive integer n, the function h(n) is defined to be the product of all even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100) + 1, then p is :
A) between 2 and 10
B) between 10 and 20
C) between 20 and 30
D) between 30 and 40
E) greater than 40

Please provide the answer with explanation.
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Source: — Problem Solving |

by kvcpk » Sun Oct 17, 2010 10:14 pm
This question is discussed many times on this forum. PLease search for explanations.
Here is one link: https://www.beatthegmat.com/gmat-prep-nu ... hlight=100
"Once you start working on something,
don't be afraid of failure and don't abandon it.
People who work sincerely are the happiest."
Chanakya quotes (Indian politician, strategist and writer, 350 BC-275BC)
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by Rezinka » Sun Oct 17, 2010 10:20 pm
Thanks.. SOrry I missed it..
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by fskilnik@GMATH » Mon Oct 18, 2010 3:28 am
Hi Rezinka!

This is a beautiful problem, indeed.

Let us start by the question:

> is it 2 the prime we are looking for?

Nope. It´s easy to see that h(100) is even, therefore h(100)+1 is odd, therefore not divisible by 2, correct ?

> is it 3 the prime we are looking for?

Nope... it´s easy to see that h(100) is divisible by 3 (6 is a factor present at h(100)), therefore h(100)+1 is not divisible by 3, correct?

> is it 5?

Nope. h(100) is divisible by 5 (10 is a factor present at h(100), therefore...

Well, what can we infer from this reasoning?

Note that all prime numbers that are less than 50 will be factors of h(100), because twice each of them will be present as a factor of h(100), therefore...

Best Regards,
Fábio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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by Rezinka » Mon Oct 18, 2010 3:36 am
Yeah..
Thank you so much..
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by fskilnik@GMATH » Mon Oct 18, 2010 3:38 am
Rezinka wrote:Yeah..
Thank you so much..
My pleasure, Rezinka!

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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