Find all School-related info fast with the new School-Specific MBA Forum

It is currently 18 Dec 2014, 14:24

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

For every positive even integer n, the function h(n) is

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Manager
Manager
avatar
Joined: 07 Jan 2008
Posts: 86
Followers: 2

Kudos [?]: 49 [1] , given: 1

For every positive even integer n, the function h(n) is [#permalink] New post 09 Feb 2008, 14:21
1
This post received
KUDOS
For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100)+1, then p is between

A. between 2 and 10
B. between 10 and 20
C. between 20 and 30
D. between 30 and 40
E. greater than 40
Expert Post
1 KUDOS received
CEO
CEO
User avatar
Joined: 17 Nov 2007
Posts: 3576
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 386

Kudos [?]: 1947 [1] , given: 359

GMAT ToolKit User Premium Member
Re: Prime numbers [#permalink] New post 09 Feb 2008, 14:28
1
This post received
KUDOS
Expert's post
E

h(100) contains all prime numbers between 2 and 47 inclusive. Obviously, these prime numbers cannot be factors of h(100)+1
_________________

HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | PrepGame

Director
Director
User avatar
Joined: 31 Mar 2007
Posts: 586
Location: Canada eh
Followers: 7

Kudos [?]: 39 [0], given: 0

Re: Prime numbers [#permalink] New post 11 Feb 2008, 04:49
I got this one today. E.

Right answer, but I'm not sure either.


What rule is +1 makes it the next prime.... some sieve algorithm?
SVP
SVP
avatar
Joined: 28 Dec 2005
Posts: 1586
Followers: 2

Kudos [?]: 78 [0], given: 2

Re: Prime numbers [#permalink] New post 11 Feb 2008, 08:58
yeah, what is the fundamental rule and concept we are looking for here ?
Director
Director
avatar
Joined: 01 Jan 2008
Posts: 629
Followers: 3

Kudos [?]: 136 [0], given: 1

Re: Prime numbers [#permalink] New post 11 Feb 2008, 09:19
pmenon wrote:
yeah, what is the fundamental rule and concept we are looking for here ?


n! + 1 doesn't have 2, 3, ... n as its factors.

generalize m*(n!) + 1 doesn't have 2, 3, ... n as its factors.

h(100) + 1 = 2^50*(50!)+ 1 doesn't have 2,3 ... 50 as its factors -> E
Director
Director
User avatar
Joined: 31 Mar 2007
Posts: 586
Location: Canada eh
Followers: 7

Kudos [?]: 39 [0], given: 0

Re: Prime numbers [#permalink] New post 11 Feb 2008, 16:19
So basically you guys aren't using any theorem per say, but just doing some testing/playing around? That's what I did too, but I still don't understand why that works. Argh
Expert Post
CEO
CEO
User avatar
Joined: 17 Nov 2007
Posts: 3576
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 386

Kudos [?]: 1947 [0], given: 359

GMAT ToolKit User Premium Member
Re: Prime numbers [#permalink] New post 11 Feb 2008, 22:41
Expert's post
StartupAddict wrote:
So basically you guys aren't using any theorem per say, but just doing some testing/playing around? That's what I did too, but I still don't understand why that works. Argh


only basic principles:

1. N=h(100) contains all prime numbers from 2 to 47. In other words, N is divisible by any prime number from set{2..47}.
2. M=h(100)+1. we can choose any prime number (p) from the set and write: M=p*s+1, where s is an integer.
3. M=p*s+1 means that M has reminder 1 for any prime numbers from the set.
4. Therefore, h(100)+1 is not divisible by prime number less or equal than 47.

Hope this help. :)
_________________

HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | PrepGame

SVP
SVP
avatar
Joined: 28 Dec 2005
Posts: 1586
Followers: 2

Kudos [?]: 78 [0], given: 2

Re: Prime numbers [#permalink] New post 12 Feb 2008, 17:47
walker wrote:
StartupAddict wrote:
So basically you guys aren't using any theorem per say, but just doing some testing/playing around? That's what I did too, but I still don't understand why that works. Argh


only basic principles:

1. N=h(100) contains all prime numbers from 2 to 47. In other words, N is divisible by any prime number from set{2..47}.
2. M=h(100)+1. we can choose any prime number (p) from the set and write: M=p*s+1, where s is an integer.
3. M=p*s+1 means that M has reminder 1 for any prime numbers from the set.
4. Therefore, h(100)+1 is not divisible by prime number less or equal than 47.

Hope this help. :)


how does N=h(100) contain all prime numbers from 2 to 47 ? h(100) is product of all even numbers from 2 to 100 ... and 2 is the only even prime.
Director
Director
avatar
Joined: 01 May 2007
Posts: 795
Followers: 1

Kudos [?]: 92 [0], given: 0

Re: Prime numbers [#permalink] New post 12 Feb 2008, 18:22
I got E as well...here is my thinking...


Unfortunately, I actually starting multiplying #s.

I made it 2 --> 10 instead of 100

which came to 3840 + 1. Basically, we need to be able to have a prime divisor of 3840 and 1. The only divisor of 1 is 1, and that is not prime. Hence only 1 and 3841 can be a factor...I believe 3841 is prime. Unfortunately, I needed to actually start multiplying #s in order to see what we needed here.

Is my reasoning right?


Also...if this said h(100) + 2 would the answer for p be 2?
Expert Post
CEO
CEO
User avatar
Joined: 17 Nov 2007
Posts: 3576
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 386

Kudos [?]: 1947 [0], given: 359

GMAT ToolKit User Premium Member
Re: Prime numbers [#permalink] New post 12 Feb 2008, 19:25
Expert's post
pmenon wrote:
how does N=h(100) contain all prime numbers from 2 to 47 ? h(100) is product of all even numbers from 2 to 100 ... and 2 is the only even prime.


N=h(100)=2*4*6*8....*98*100=2^50*1*2*3*4*5....*47*48*49*50.
_________________

HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | PrepGame

SVP
SVP
avatar
Joined: 28 Dec 2005
Posts: 1586
Followers: 2

Kudos [?]: 78 [0], given: 2

Re: Prime numbers [#permalink] New post 12 Feb 2008, 19:48
walker, can you dumb it down one more step for me please ?

N= h(100) = 2*4*6*8*...8*100 = 2*2^2*6*2^3 ...

where do you go from here ?
Expert Post
CEO
CEO
User avatar
Joined: 17 Nov 2007
Posts: 3576
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 386

Kudos [?]: 1947 [0], given: 359

GMAT ToolKit User Premium Member
Re: Prime numbers [#permalink] New post 12 Feb 2008, 19:59
Expert's post
pmenon wrote:
walker, can you dumb it down one more step for me please ?

N= h(100) = 2*4*6*8*...8*100 = 2*2^2*6*2^3 ...

where do you go from here ?


h(100) = 2*4*6*8*10*12...96*98*100
h(100) = 2*(2*2)*(2*3)*(2*4)*(2*5)*(2*6)...(2*48)*(2*49)*(2*50)
h(100) = 2^50*(2*3*4*5*6...48*49*50)
_________________

HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | PrepGame

Expert Post
1 KUDOS received
CEO
CEO
User avatar
Joined: 17 Nov 2007
Posts: 3576
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 386

Kudos [?]: 1947 [1] , given: 359

GMAT ToolKit User Premium Member
Re: Prime numbers [#permalink] New post 12 Feb 2008, 20:11
1
This post received
KUDOS
Expert's post
jimmyjamesdonkey wrote:
I got E as well...here is my thinking...


Unfortunately, I actually starting multiplying #s.

I made it 2 --> 10 instead of 100

which came to 3840 + 1. Basically, we need to be able to have a prime divisor of 3840 and 1. The only divisor of 1 is 1, and that is not prime. Hence only 1 and 3841 can be a factor...I believe 3841 is prime. Unfortunately, I needed to actually start multiplying #s in order to see what we needed here.

Is my reasoning right?

I guess it is an incorrect way. You are simply lucky with your answer :)
if you prove that h(10)+1 is a prime number, you cannot say that h(12)+1 is also a prime number.

By the way, 3841 is not a prime number: 3841=23*167.

jimmyjamesdonkey wrote:
Also...if this said h(100) + 2 would the answer for p be 2?

Agree.
_________________

HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | PrepGame

Director
Director
User avatar
Joined: 20 Aug 2007
Posts: 853
Location: Chicago
Schools: Chicago Booth 2011
Followers: 10

Kudos [?]: 83 [0], given: 1

Re: Prime numbers [#permalink] New post 13 Feb 2008, 06:37
walker wrote:
pmenon wrote:
walker, can you dumb it down one more step for me please ?

N= h(100) = 2*4*6*8*...8*100 = 2*2^2*6*2^3 ...

where do you go from here ?


h(100) = 2*4*6*8*10*12...96*98*100
h(100) = 2*(2*2)*(2*3)*(2*4)*(2*5)*(2*6)...(2*48)*(2*49)*(2*50)
h(100) = 2^50*(2*3*4*5*6...48*49*50)


That's some incredible number properties skills there. nice job.
Re: Prime numbers   [#permalink] 13 Feb 2008, 06:37
    Similar topics Author Replies Last post
Similar
Topics:
7 1) For every positive even integer n, function h(n) is g1m2a3t406 6 24 Nov 2006, 13:25
For every positive even integer, n, the function h(n) is ffgmat 1 22 May 2006, 03:56
For every positive even integer n, the function hn) is john2005 5 07 May 2006, 13:17
6 For every positive even integer n, the function h(n) is jlui4477 7 17 Apr 2006, 00:48
For every positive even integer n, the function h(n) is jodeci 1 01 Apr 2006, 21:31
Display posts from previous: Sort by

For every positive even integer n, the function h(n) is

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.