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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

For every positive even integer n, the function h(n) is [#permalink]

Show Tags

09 Feb 2008, 15:21

1

This post received KUDOS

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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

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

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.

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.

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?

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?