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

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Manager
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The function f is defined for all positive integers n by the [#permalink]  06 May 2006, 13:24
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 is any prime number then f(p) =

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

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Re: Function F - from Gmatprep [#permalink]  06 May 2006, 15:47
i guess i did this one earlier.............................................

a. f(p) = p-1
Manager
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This was posted earlier.

http://www.gmatclub.com/phpbb/viewtopic.php?t=28928
_________________

Thanks,
Zooroopa

Manager
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I'm confused with the answer given in the other link it seems to be wrong

BUT according to GMATPREP the answer is A and not B ... so professor is correct .

Last edited by ipc302 on 06 May 2006, 16:58, edited 1 time in total.
VP
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Its B

f(p) = {2,3,4....(n-1)}
Manager
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i agree with what u have mentioned , but the question is whether to take 1 in the answer or not .

It seems that GMATPREP has taken 1 in account so the answer is P-1 .

I'm confused not for this question but what to do during the real test if i encounter one of this kind
VP
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ipc302 wrote:
i agree with what u have mentioned , but the question is whether to take 1 in the answer or not .

It seems that GMATPREP has taken 1 in account so the answer is P-1 .

I'm confused not for this question but what to do during the real test if i encounter one of this kind

i donot see any reason for p-2 as answer because it isnot mentioned that 1 has to be excluded. 1 is treated as a positive common factor factor not as an integer that is to be excluded. so we should include 1 as well.

therefore, it is p-1.

ipc302 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 is any prime number then f(p) =

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

Manager
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Professor ,

Thanks for the response . I agree with you and in exam if i encounter such situation i will do the same .
Senior Manager
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Re: Function F - from Gmatprep [#permalink]  12 May 2006, 00:48
Professor wrote:
i guess i did this one earlier.............................................

a. f(p) = p-1

'cuase I do not know how to solve such kind of questions? Thank you.
Senior Manager
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Re: Function F - from Gmatprep [#permalink]  13 May 2006, 07:36
M8 wrote:
Professor wrote:
i guess i did this one earlier.............................................

a. f(p) = p-1

'cuase I do not know how to solve such kind of questions? Thank you.

Director
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Hi M8

Here f(n) is a the number of positive integers each of which is less than n and has no positive factor in common with n other than 1.

So f(4) = 2 as the integers which share no common positive factor (other than 1) with 4 are 3 and 1

And f(9) = 6 as the integers which share no common positive factor (other than 1) with 9 are {8,7,5,4,2,1}

The question asks, if p is a prime number, what is f(p)?

So, lets take a prime # as example.

f(7) = 6 because the set is {6,5,4,3,2,1} as none of these numbers have any common factor with 7 besides 1.

Same if you check with any prime number like 11, 13, you will get the same result.

Hence f(p) is = p-1

Hope I didn't confuse you more

Last edited by gmatmba on 13 May 2006, 08:45, edited 1 time in total.
Senior Manager
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Thanks gmatmba for your kind explanation, I got it now.
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Re: Function F - from Gmatprep [#permalink]  13 May 2006, 10:24
M8 wrote:
M8 wrote:
Professor wrote:
i guess i did this one earlier.............................................
a. f(p) = p-1
'cuase I do not know how to solve such kind of questions? Thank you.

M8, sorry i didn't notice your posts.

lets go by example. say 7 is a prime integer. 7 has 1 and 7 as its +ve factors. f (p) = 6, 5, 4, 3, 2, and 1, altogather 6 integers = p-1 = 7-1. it canot be 0 and -ves cuz the question clearly says that any +ve integers.

therefore, f(p) = p-1.

hope it works..
Re: Function F - from Gmatprep   [#permalink] 13 May 2006, 10:24
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