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by 6983manish » Tue Mar 29, 2011 8:09 pm
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 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
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by rohu27 » Tue Mar 29, 2011 8:20 pm
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by Anurag@Gurome » Tue Mar 29, 2011 8:27 pm
6983manish 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 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
Since x is prime, then all positive numbers less than x will have no common factors with x, except 1. We can consider an example:
If x = 5, then numbers less than 7 which have no common factors with 7 are 1, 2, 3, 4, 5, 6, the count of these numbers = 6, which is 1 less than 7.
So, if x is prime, then f(x) = x - 1

The correct answer is B.
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by rohu27 » Tue Mar 29, 2011 8:43 pm
thanks Anurag, missed it completely.
Anurag@Gurome wrote:
6983manish 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 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
Since x is prime, then all positive numbers less than x will have no common factors with x, except 1. We can consider an example:
If x = 5, then numbers less than 7 which have no common factors with 7 are 1, 2, 3, 4, 5, 6, the count of these numbers = 6, which is 1 less than 7.
So, if x is prime, then f(x) = x - 1

The correct answer is B.
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by Anurag@Gurome » Tue Mar 29, 2011 8:44 pm
rohu27 wrote:thanks Anurag, missed it completely.
You are welcome.
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by GMATGuruNY » Wed Mar 30, 2011 3:30 am
6983manish 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 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 can plug in a prime number for x.

Let x=5.
f(5) = 1,2,3,4 = 4 integers. This is our target.

No we plug x=5 into the answers to see which yields our target of 4.

Only answer choice B works:
x-1 = 5-1 = 4.

The correct answer is B.
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