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# Function and factors - question

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Intern
Joined: 08 Nov 2008
Posts: 4
Schools: MIT Sloan, Columbia, Cornell, Michigan
Function and factors - question [#permalink]

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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:

thanks
Intern
Joined: 08 Nov 2008
Posts: 4
Schools: MIT Sloan, Columbia, Cornell, Michigan
Re: Function and factors - question [#permalink]

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02 Aug 2009, 00:49
I got A.

yes so did i but the GMAT Prep gives the answer as E.
Intern
Joined: 01 May 2009
Posts: 41
Re: Function and factors - question [#permalink]

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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.
Senior Manager
Joined: 17 Jul 2009
Posts: 281
Concentration: Nonprofit, Strategy
GPA: 3.42
WE: Engineering (Computer Hardware)
Re: Function and factors - question [#permalink]

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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
Senior Manager
Affiliations: ACA, CPA
Joined: 26 Apr 2009
Posts: 428
Location: Vagabond
Schools: BC
WE 1: Big4, Audit
WE 2: Banking
Re: Function and factors - question [#permalink]

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

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.

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