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

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Manager
Joined: 17 Jan 2006
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The function f is defined for all positive integers n by the [#permalink]  28 Apr 2006, 22:05
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

OA to follow
VP
Joined: 06 Jun 2004
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Location: CA
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I'll take a shot at this and take B

All prime numbers have 7 integers less than itself and have no common factor with the prime other than 1

2 ==> 1 (1 is less than 2 but it has a common factor with 2) so 2-2 = 0

3 ==> 1, 2 (only 2 is less than 3 that have no common factor with 3 other than 1) so 3 - 2 = 1

5 ==> 1, 2, 3, 4 (only 2, 3, 4 are less than 5 that have no common factor with 5 other than 1) so 5-2 = 3
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Don't be afraid to take a flying leap of faith.. If you risk nothing, than you gain nothing...

VP
Joined: 29 Apr 2003
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Agreed with B!

f(P)= number of items in the set {2,3,4,....(n-1)}
Manager
Joined: 09 Apr 2006
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Does the expression 'other than 1' means we ought to exclude 1?

Can this expression also mean the numbers are co prime to each other, in which case 1 is an acceptable common factor between n and any number less than it?

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Thanks,
Zooroopa

Manager
Joined: 13 Dec 2005
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Dinesh are you sure of the OA ? I got this question from gmatprep and the offical answer is A and not B .

Director
Joined: 24 Oct 2005
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I've seen this q before and the OA is A, though I get B.
can someone pls explain how it can be A?
Manager
Joined: 23 Jan 2006
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the number 1 has no positive factor in common with n other than 1.
so A it is.

Tricky. I thought B first too...
Director
Joined: 24 Oct 2005
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kook44 wrote:
the number 1 has no positive factor in common with n other than 1.
so A it is.

Tricky. I thought B first too...

Oh yes, thar's it !! Tricky question.
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