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Number properties

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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: — Problem Solving |

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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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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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
Anurag Mairal, Ph.D., MBA
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