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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] New post 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.

I am stuck after this. Can someone please help?
[Reveal] Spoiler: OA

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Re: Function (f) [#permalink] New post 29 Jan 2012, 15:59
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Expert's post
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.
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Re: The function f is defined for all positive integers n by the [#permalink] New post 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] New post 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] New post 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] New post 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.
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Re: Function (f) [#permalink] New post 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.

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.
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Re: Function (f) [#permalink] New post 10 Feb 2013, 02:30
Expert's post
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.

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?
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Function (f) [#permalink] New post 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] New post 15 Jul 2014, 02:43
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Re: The function f is defined for all positive integers n by the [#permalink] New post 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] 11 Aug 2014, 20:57
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