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:

The function f is defined for all positive integers n by the following [#permalink]

Show Tags

29 Sep 2009, 11:12

1

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

45% (medium)

Question Stats:

56% (02:04) correct
44% (01:35) wrong based on 80 sessions

HideShow timer Statistics

The function f is defined for all positive integers n by the following rule. f(n) is the number of positive integers each of which is less than n and has no positive factor in common with n other than 1. If p is any prime, number then f(p)=

Re: The function f is defined for all positive integers n by the following [#permalink]

Show Tags

29 Sep 2009, 12:01

manojgmat wrote:

The function f is defined for all +ve integers n by the following rule: f(n) is the number of +ve intergers each of which is less than n and has no +ve factor in common with n other than 1. if p is any prime number then f(p) =

a. p-1 b. p-2 c. (p+1)/2 d. (p-1)/2 e. 2

we need to solve it by picking numbers, i picked 5, 7 , 11 and 23 , all satisfies P-1 , hence A. Because since N is prime , it is divisible only by itself and 1, so there will be no common positive factors other than 1 for all +ve integers less than N. hence P-1

Re: The function f is defined for all positive integers n by the following [#permalink]

Show Tags

30 Sep 2009, 20:48

Since p is prime, by definition it only has as its +ve factors {P,1}. Therefore nothing below N will ever share a common factor with it aside from 1. Answer will always be p-1

Re: The function f is defined for all positive integers n by the following [#permalink]

Show Tags

26 Dec 2014, 13:43

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

The function f is defined for all positive integers n by the following rule. f(n) is the number of positive integers each of which is less than n and has no positive factor in common with n other than 1. If p is any prime, number then f(p)=

A. p-1 B. p-2 C. (p+1)/2 D. (p-1)/2 E. 2

If not the wording the question wouldn't be as tough as it is now. The GMAT often hides some simple concept in complicated way of delivering it.

This question for instance basically asks: how many positive integers are less than given prime number p which have no common factor with p except 1.

Well as p is a prime, all positive numbers less than p have no common factors with p (except common factor 1). So there would be p-1 such numbers (as we are looking number of integers less than p).

For example: if p=7 how many numbers are less than 7 having no common factors with 7: 1, 2, 3, 4, 5, 6 --> 7-1=6.

Happy New Year everyone! Before I get started on this post, and well, restarted on this blog in general, I wanted to mention something. For the past several months...

It’s quickly approaching two years since I last wrote anything on this blog. A lot has happened since then. When I last posted, I had just gotten back from...

Happy 2017! Here is another update, 7 months later. With this pace I might add only one more post before the end of the GSB! However, I promised that...

The words of John O’Donohue ring in my head every time I reflect on the transformative, euphoric, life-changing, demanding, emotional, and great year that 2016 was! The fourth to...