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

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

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29 Jan 2012, 15:53
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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

Guys - does this questions makes sense to anyone? I am struggling. Does it mean that:

F(n) is a list of positive integers. AM I right?

for e.g f(5) = 3,4.

[Reveal] Spoiler: OA

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Re: Function (f) [#permalink]

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29 Jan 2012, 15:59
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enigma123 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

Guys - does this questions makes sense to anyone? I am struggling. Does it mean that:

F(n) is a list of positive integers. AM I right?

for e.g f(5) = 3,4.

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.

Hope it's clear.
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Kudos [?]: 2970 [0], given: 217

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

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29 Jan 2012, 16:05
Yes - crystal clear now. Thanks.
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Re: The function f is defined for all positive integers n by the [#permalink]

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30 Jan 2012, 07:56
the answere is A, one just needs to read these kind of questions loud to themselves and there you have the answere!
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Re: The function f is defined for all positive integers n by the [#permalink]

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04 Apr 2012, 09:14
But it says no other factors in common with n other than 1, why do we have to include 1 then? I thought since 1 is a factor of 1 itself and p, we cannot include it.
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Re: The function f is defined for all positive integers n by the [#permalink]

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04 Apr 2012, 09:24
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BN1989 wrote:
But it says no other factors in common with n other than 1, why do we have to include 1 then? I thought since 1 is a factor of 1 itself and p, we cannot include it.

Each positive integer should have no factor common with n except 1.
1 also has only a single factor i.e. 1 common with p. So we do include 1.
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Re: Function (f) [#permalink]

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10 Feb 2013, 02:28
Bunuel wrote:
enigma123 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

Guys - does this questions makes sense to anyone? I am struggling. Does it mean that:

F(n) is a list of positive integers. AM I right?

for e.g f(5) = 3,4.

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.

Hope it's clear.

Thanks a lot,

can you also explain for the other option.
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Re: Function (f) [#permalink]

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10 Feb 2013, 02:30
FTG wrote:
Bunuel wrote:
enigma123 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

Guys - does this questions makes sense to anyone? I am struggling. Does it mean that:

F(n) is a list of positive integers. AM I right?

for e.g f(5) = 3,4.

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.

Hope it's clear.

Thanks a lot,

can you also explain for the other option.

What other option are you talking about?
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Re: Function (f) [#permalink]

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10 Feb 2013, 02:48
i read the question wrong & arrived to wrong answer. missed out the section less than n and has no positive factor in common with n other than 1 & got answer D. so no need to explain
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Re: The function f is defined for all positive integers n by the [#permalink]

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15 Jul 2014, 02:43
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Re: The function f is defined for all positive integers n by the [#permalink]

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11 Aug 2014, 20:57
Bunuel 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

Guys - does this questions makes sense to anyone? I am struggling. Does it mean that:

F(n) is a list of positive integers. AM I right?

for e.g f(5) = 3,4.

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.

Hope it's clear.[/quote]

Thanks a lot,

can you also explain for the other option.[/quote]

What other option are you talking about?[/quote]

Hi Bunuel,

This is concept of co-prime right? I mean 2 consecutive numbers has only as their factor in common. So from that sense we can select p-1 as the answer choice.
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Re: The function f is defined for all positive integers n by the [#permalink]

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06 Sep 2014, 21:29
CleanSlate wrote:
Bunuel wrote:
enigma123 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

Guys - does this questions makes sense to anyone? I am struggling. Does it mean that:

F(n) is a list of positive integers. AM I right?

for e.g f(5) = 3,4.

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.

Hope it's clear.

Thanks a lot,

can you also explain for the other option.

prime number will have no factor other than 1 & itself .
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Re: The function f is defined for all positive integers n by the [#permalink]

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19 Sep 2015, 22:07
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: The function f is defined for all positive integers n by the   [#permalink] 19 Sep 2015, 22:07
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# The function f is defined for all positive integers n by the

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