GMATDemiGod wrote:
Bunuel wrote:
sagarsabnis wrote:
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) =?
1) x-2
2) x-1
3) (x+1)/2
4) (x-1)/2
5) 2
Please can some one explain this?
The confusing moment in this question is its wording. Basically question is: how many positive integers are less than given prime number x which has no common factor with x except 1.
Well as x is a prime, all positive numbers less than x have no common factors with x (except common factor 1). So there would be x-1 such numbers (as we are looking number of integers less than x).
If we consider x=7 how many numbers are less than 7 having no common factors with 7: 1, 2, 3, 4, 5, 6 --> 7-1=6.
Answer: B.
I understand the logic, but I cannot figure out why x-2 doesn't work for this question.
It's easy to understand when you pick numbers.
For example, the question asks how many numbers there are bellow the X.
If we have a prime number, so the quantity of integers bellow the prime number is the answer.
Lets get the prime number 5.
How many numbers bellow 5 we have?
1,2,3,4 (none of them have a common factor with 5, besides 1, so this quantity of numbers will be your answer)
It means X-1.
If you get X-2 then the quantity would be 3, which is wrong.