Gmat Prep: function f

Hano · Posted: Mon Dec 03, 2007 8:46 pm Post subject: Gmat Prep: function f

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

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

Explanation would be appreciated.

mschling52 · Posted: Tue Dec 04, 2007 6:39 am Post subject:

I believe its A...p-1. If a number is prime, its only factors are 1 and itself. Therefore, if p is a prime, any number less p will not be a factor of p. So, each of the p-1 integers less than p will have no factor in common with p other than 1, which implies that f(p) = p-1.

As an example, consider the prime number 7. There are 6 integers less than 7, none of which share any of the factors of 7 except 1 so f(7) = 6