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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 \(f(x) = ?\)

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 \(f(x) = ?\)

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.

the number of numbers below three that do not have a any factor apart from 1 is 2 since 1 has a factor of 1 itself, it doenst count. therefore, \(f(x3)\) = 1

f(2) = 0 = 0 numbers f(3) = 2 = 1 number f(5) = 2,3,4 = 3 numbers f(7) = 2,3,4,5,6 = 5 numbers f(x) = x-2 numbers if Ans is b then f(2) = 1 = 1 numbers f(3) = 2 = 2 number f(5) = 4 = 4 numbers f(7) = 6 = 6 numbers f(x) = x-1 numbers all numbers other then 1 is having comman factor 2 with x and it is given that x is do not have common factor with f(x)
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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) = ?

factors below 7 = 6,5,4,3,2, and 1 "6" has no common factor with "7" except digit "1" "5" has no common factor with "7" except digit "1" "4" has no common factor with "7" except digit "1" etc, etc

By the same token, do we also say "1" has no common factor with "7" except itself?
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KUDOS me if you feel my contribution has helped you.

bipolar u're forgetting 1. u need to count 1 as well. hence f(2) = 1 f(3) = 1,2 -> 2 f(4) = 1,2,3 -> 3

i got this exact question on the gmatprep and answer is x-1.

Agree that answer is B. A can't be answer because if we put 2 which is a prime number in place of X in option 1, we get 0, which is not a positive integer. All other options give fraction if we put prime numbers to check. Last option can't be for the obvious reasons. So, only option that satisfies the given condition is option B, which satisfies the condition for all the prime number. I don't agree with few people that we need to count 1 because anyhow 1 is not a prime number and in question it is clearly mentioned that x is a prime number.

all are positive integers and less than x ( including 1 ) and not multiples of x (naturally) .. x is prime . I.E this means f(x) = all integers from 0 to x not inclusive . This will be x-1
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If x is a positive integer, f(x) is defined [#permalink]

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12 Aug 2013, 23:06

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)=?