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The function f is defined for all positive integers n by the [#permalink]
29 Jan 2012, 15:53

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Difficulty:

45% (medium)

Question Stats:

62% (01:52) correct
38% (01:10) wrong based on 197 sessions

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:

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.

I am stuck after this. Can someone please help?

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.

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

Re: The function f is defined for all positive integers n by the [#permalink]
04 Apr 2012, 09:24

Expert's post

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. _________________

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.

I am stuck after this. Can someone please help?

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.

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.

I am stuck after this. Can someone please help?

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.

Answer: A.

Hope it's clear.

Thanks a lot,

can you also explain for the other option.

What other option are you talking about? _________________

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

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

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Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

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

I am stuck after this. Can someone please help?

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.

Answer: A.

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.

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

I am stuck after this. Can someone please help?

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.

Answer: A.

Hope it's clear.

Thanks a lot,

can you also explain for the other option.

answer -A

prime number will have no factor other than 1 & itself .

gmatclubot

Re: The function f is defined for all positive integers n by the
[#permalink]
06 Sep 2014, 21:29

I couldn’t help myself but stay impressed. young leader who can now basically speak Chinese and handle things alone (I’m Korean Canadian by the way, so...