• Award-winning private GMAT tutoring
Register now and save up to $200 Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

## Integers

tagged by: BTGmoderatorRO

This topic has 1 expert reply and 0 member replies
BTGmoderatorRO Moderator
Joined
30 Aug 2017
Posted:
770 messages
Followed by:
6 members

#### Integers

Wed Dec 13, 2017 6:32 pm
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 number then f(p) =

(a) p-1

(b) p-2

(c) $$\frac{p+1}{2}$$

(d) $$\frac{p-1}{2}$$

(e) 2

OA is A

Can an Expert give me the mathematical approach to solve this question? Thanks in anticipation

### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
Joined
23 Jun 2013
Posted:
9594 messages
Followed by:
482 members
2867
GMAT Score:
800
Wed Dec 13, 2017 7:25 pm
Hi Roland2rule,

To start, this question has a 'typo' in it - P must be a PRIME number (NOT "any number").

We're told that 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. We're asked for the value of f(P) if P is a PRIME number. This question can be solved by TESTing VALUES.

IF.... P = 5
then the positive integers that are LESS than 5 and have NO factors in common with 5 (other than the number 1) are 1, 2, 3 and 4.
Thus, the f(5) = 4, so we're looking for an answer that equals 4 when we plug P=5 into the answer choices. There's only one answer that matches.

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

### Top First Responders*

1 GMATGuruNY 108 first replies
2 Brent@GMATPrepNow 41 first replies
3 Rich.C@EMPOWERgma... 35 first replies
4 Jay@ManhattanReview 25 first replies
5 Scott@TargetTestPrep 11 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 GMATGuruNY

The Princeton Review Teacher

154 posts
2 Brent@GMATPrepNow

GMAT Prep Now Teacher

129 posts
3 Scott@TargetTestPrep

Target Test Prep

103 posts
4 Rich.C@EMPOWERgma...

EMPOWERgmat

81 posts
5 Max@Math Revolution

Math Revolution

80 posts
See More Top Beat The GMAT Experts