GmatPrep?? (function)

The key to the problem is decoding the language here:

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.

and understanding what a prime number is. Start with an example- what is f(2)? f(2) is the number of positive integers less than 2 (there's only one of those- 1) which have no divisor in common with 2 besides 1. Does 1 have no divisor in common with 2 besides 1? Yes, of course. So f(2) = 1. You could now just plug p=2 into each answer choice to find that p-1 must be correct.

In general, if p is prime, then p has no positive divisors besides 1 and p. So p cannot share a divisor besides 1 with any number less than p. That is, all p-1 positive integers (1, 2, 3, ..., p-2, p-1) less than p cannot share a divisor larger than 1 with p, and will all be counted by f(p). So the answer is p-1.