GMATPrep function question

[allenkt]

This was one of the first questions I had on the GMATPrep and it threw me for a loop.

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

I know the answer is (a) and knowing that I can see how to backsolve it. But without knowing the answer, how do I solve this?

[Neo2000]

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.

You are basically looking for all Co-Primes less than the number n

Definition :"Two numbers which have a highest common factor of 1 are called co-prime numbers"