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The function f is defined for all positive integers n by the [#permalink]
 29 Jan 2012, 16:53
Question Stats:
58% (02:01) correct
41% (01:50) wrong based on 7 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: 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?
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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.
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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Director
Status: Preparing for the 4th time -:(
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Re: The function f is defined for all positive integers n by the [#permalink]
29 Jan 2012, 17:05
Yes - crystal clear now. Thanks.
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Best Regards,
E.
MGMAT 1 --> 530
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Re: The function f is defined for all positive integers n by the [#permalink]
30 Jan 2012, 08:56
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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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 a prime number then f(p):
p-1
p-2
(p+1)/2
(p-1)/2
2
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GMAT Club team member
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[0], given: 829
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Re: The function f is defined for all positive integers n by the [#permalink]
04 Apr 2012, 10:14
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]
04 Apr 2012, 10:24
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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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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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?
_________________
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
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. NEW!!!
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. NEW!!!
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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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