The function f is defined for all

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The function f is defined for all

by BTGmoderatorLU » Mon Oct 16, 2017 10:39 am
The function f is defined for all positive integers n by the following rule: 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. If p is any number then f(p) =

(a) p-1

(b) p-2

(c) (p+1)/2

(d) (p−1)/2

(e) 2

The OA is A.

Can any expert explain this PS question please? I don't have it clear. Thanks.

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by EconomistGMATTutor » Mon Oct 16, 2017 12:40 pm
The function f is defined for all positive integers n by the following rule: 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. If p is any number then f(p) =

(a) p-1

(b) p-2

(c) (p+1)/2

(d) (p-1)/2

(e) 2

The OA is A.

Can any expert explain this PS question please? I don't have it clear. Thanks.
Hi LUANDATO,
Let's take a look at your question.
The question statement should be like:
The function f is defined for all positive integers n by the following rule: 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. If p is any prime number then f(p) = ?

The function is defined as:
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

If p is a prime number let's say 5,
f(p) will contain the number of positive integers less than 5,
It means f(p) will contain 4 positive integers less than 5 i.e. {1, 2, 3, 4}
We can see that all of these four numbers have only factor in common with 5 i.e. 1. No factor other than 1 is common between these four numbers and 5.

Therefore, f(p) = p - 1
If p = 5, f(p) will contain 4 positive integers. i.e. f(p) = 5-1 = 4
Similarly, if p = 11, f(p) will contain 10 positive integers. i.e. f(p) = 11 - 1 = 10

Therefore, Option A is correct.

Hope this helps.
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by Scott@TargetTestPrep » Fri Nov 22, 2019 11:26 am
BTGmoderatorLU wrote:The function f is defined for all positive integers n by the following rule: 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. If p is any number then f(p) =

(a) p-1

(b) p-2

(c) (p+1)/2

(d) (p−1)/2

(e) 2

The OA is A.

Can any expert explain this PS question please? I don't have it clear. Thanks.
We can see that, in other words, f(n) is the number of positive integers less than n that are relatively prime to n. If p is a prime, then any positive integer less than p will be relatively prime to p. For example, if p = 7, then f(7) = 6 since 1, 2, 3, 4, 5, and 6 are all relatively prime to 7. Therefore, f(p) = p - 1.

Answer: A

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by [email protected] » Sat Nov 23, 2019 9:38 am
Hi All,

This question is meant to ask: "If P is a prime number, then f(P)= ?" This question can be solved by TESTing VALUES.

Let's TEST N=7. The f(7) = all the positive integers less than 7 that have no factor in common with 7 except for 1.

THAT list is 1, 2, 3, 4, 5, 6 = 6 terms.

Thus, we're looking for an answer that equals 6 when we plug N=7 into it. There's only one answer that matches...

Final Answer: A

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