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# The function f is defined for all positive integers n by the following

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The function f is defined for all positive integers n by the following [#permalink]

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29 Sep 2009, 12:12
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Question Stats:

56% (02:04) correct 44% (01:35) wrong based on 80 sessions

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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)=

A. p-1
B. p-2
C. (p+1)/2
D. (p-1)/2
E. 2

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-function-f-is-defined-for-all-positive-integers-n-by-the-126738.html
[Reveal] Spoiler: OA
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Re: The function f is defined for all positive integers n by the following [#permalink]

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29 Sep 2009, 13:01
manojgmat wrote:
The function f is defined for all +ve integers n by the following rule: f(n) is the number of +ve intergers each of which is less than n and has no +ve factor in common with n other than 1. if p is any prime number then f(p) =

a. p-1
b. p-2
c. (p+1)/2
d. (p-1)/2
e. 2

we need to solve it by picking numbers, i picked 5, 7 , 11 and 23 , all satisfies P-1 , hence A. Because since N is prime , it is divisible only by itself and 1, so there will be no common positive factors other than 1 for all +ve integers less than N. hence P-1
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Re: The function f is defined for all positive integers n by the following [#permalink]

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30 Sep 2009, 21:48
Since p is prime, by definition it only has as its +ve factors {P,1}. Therefore nothing below N will ever share a common factor with it aside from 1. Answer will always be p-1
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Re: The function f is defined for all positive integers n by the following [#permalink]

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02 May 2011, 23:28
for 2 , it is 1
for 3, 1,2 hence 2
for 5, 1,2,3,4 hence 4
for 7, 1,2,3,4,5,6 hence 6

thus p-1
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Re: The function f is defined for all positive integers n by the following [#permalink]

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26 Dec 2014, 14:43
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Re: The function f is defined for all positive integers n by the following [#permalink]

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27 Dec 2014, 03:34
Expert's post
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manojgmat 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 prime, number then f(p)=

A. p-1
B. p-2
C. (p+1)/2
D. (p-1)/2
E. 2

If not the wording the question wouldn't be as tough as it is now. The GMAT often hides some simple concept in complicated way of delivering it.

This question for instance basically asks: how many positive integers are less than given prime number p which have no common factor with p except 1.

Well as p is a prime, all positive numbers less than p have no common factors with p (except common factor 1). So there would be p-1 such numbers (as we are looking number of integers less than p).

For example: if p=7 how many numbers are less than 7 having no common factors with 7: 1, 2, 3, 4, 5, 6 --> 7-1=6.

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-function-f-is-defined-for-all-positive-integers-n-by-the-126738.html
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Re: The function f is defined for all positive integers n by the following   [#permalink] 27 Dec 2014, 03:34
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