Number properties

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rnaah: Junior | Next Rank: 30 Posts; Posts: 24; Joined: Thu Jul 15, 2010 9:45 am; Thanked: 1 times

by rnaah » Sun Oct 09, 2011 12:07 pm

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

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Source: Beat The GMAT — Problem Solving | Sun Oct 09, 2011 12:07 pm

Proleefeek: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Fri Aug 05, 2011 6:49 pm

by Proleefeek » Sun Oct 09, 2011 12:41 pm

let us see an example.

5 is a suitable candidate.

f(5) = {4,3,2}

Exclude 5 itself and 1 too because of the fact that 1 itself is a common factor. thus for a Prime number the function becomes

f(p)=p-2

IMO B.

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gmatclubmember: Master | Next Rank: 500 Posts; Posts: 158; Joined: Sat Sep 03, 2011 10:31 amFollowed by: 2 members; Thanked: 29 times

by gmatclubmember » Sun Oct 09, 2011 12:50 pm

Ans is B (p-2).
If p is a prime no. then all the nos. 1 through p-1 wont divide p.
so the no. of terms (for f(p)) would be 2 through p-1 (since we dont have to count 1 and p).
total no. of terms would be p-1 - 2 + 1= p-2.

a lil' Thank note goes a long way

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Sun Oct 09, 2011 9:37 pm

rnaah 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) = ?

Refer to the solution here : https://www.beatthegmat.com/gmat-prep-t73368.html#331739

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