If x is a positive integer

[NandishSS]

If x is a positive integer, f(x) is defined as the number of positive integers which are less than x and do not have a common factor with x other than 1. If x is prime, then f(x)=?

A. x−2
B. x−1
C. (x+1)/2
D. (x−1)/2
E. 2

OA:B

HI Experts,

Can you pls explain the question. Didn't get the question at all

Thanks
Nandish

[GMATGuruNY]

If x is a positive integer, f(x) is defined as the number of positive integers which are less than x and do not have a common factor with x other than 1. If x is prime, then f(x)=?

A. x−2
B. x−1
C. (x+1)/2
D. (x−1)/2
E. 2

Let x = 2.
f(2) = the number of positive integers that are less than 2 and that do not share a factor with 2 other than 1.
Only one positive integer satisfies the conditions in red: 1.
Thus:
f(2) = 1.

Now plug x=2 into the answers to see which yields the target value in blue.
Only B works:
x-1 = 2-1 = 1.

The correct answer is B.

[Scott@TargetTestPrep]

If x is a positive integer, f(x) is defined as the number of positive integers which are less than x and do not have a common factor with x other than 1. If x is prime, then f(x)=?

A. x−2
B. x−1
C. (x+1)/2
D. (x−1)/2
E. 2

We are given that f(x) is defined as the number of positive integers that are less than x and do not have a common factor with x other than 1. We also are given that x is a prime number and we must determine the value of f(x).

Since x can be any prime number, let's let x = 5. The positive integers less than 5 are 1, 2, 3, and 4. Note that those integers do not have a common factor with 5, other than 1. Thus, f(x) = 4.

Substituting 5 for x in our answer choices, we see that the only answer choice that equals 4 is B, x - 1.

Answer: B