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Function and factors - question

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Intern
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Function and factors - question [#permalink]

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New post 01 Aug 2009, 17:36
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I got this question during a practice exam which i took this morning. Its from the GMAT Prep exam so there was no explanation given in the answer sheet. I don't quite understand the answer and wanted to share it with the group to get an explanation.

For every positive even integer n, function F(n) describes the product of all even integers from 2 to n. if p is the smallest prime factor of f(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

[Reveal] Spoiler:
Answer is E, but why?


thanks

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Intern
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Re: Function and factors - question [#permalink]

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New post 02 Aug 2009, 00:49
snipertrader wrote:
I got A.


yes so did i but the GMAT Prep gives the answer as E.

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Re: Function and factors - question [#permalink]

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New post 03 Aug 2009, 10:45
Hello ppl,

I just did the same question too.

But, i didn't know how to do it at all, so I guessed E.

Anyone mind showing me the workings to get answer A?

Maybe, we can work the answer backwards.

Thanks.

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Senior Manager
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Re: Function and factors - question [#permalink]

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New post 03 Aug 2009, 17:44
saw this problem days ago here, explaination is that two adjacent numbers are relatively prime (is this the term?) to each other, for example: 6, 7 dont share any prime factors...15 16 dont share ... etc.

so since f(100) = 2^50*(1*2*3.....*48*49*50), which includes all prime factors smaller than 50, therefore, f(100) + 1's smallest prime factor has to be larger than 50 (because f(100) and f(100)+1 are relatively prime to each other, thus answer is E

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Re: Function and factors - question [#permalink]

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New post 03 Aug 2009, 20:28
wow...how can one solve this problem in 2-3 mins :roll:

Is there any ref material for relative primes?
_________________

If you have made mistakes, there is always another chance for you. You may have a fresh start any moment you choose, for this thing we call "failure" is not the falling down, but the staying down.

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Re: Function and factors - question   [#permalink] 03 Aug 2009, 20:28
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