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gmatnmein2010: Master | Next Rank: 500 Posts; Posts: 185; Joined: Thu Feb 04, 2010 3:06 am; Thanked: 6 times

by gmatnmein2010 » Sat Feb 13, 2010 1:47 am

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Source: Beat The GMAT — Problem Solving | Sat Feb 13, 2010 1:47 am

thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members; Thanked: 137 times

by thephoenix » Sat Feb 13, 2010 2:28 am

If P is prime it's only factors are P and 1. So no number below it will have a common factor with it except 1. Therefore answer should just be P-1.

for eg
if p=2, then f(p) = 1 and 1 does not have a common factor with 2

So the answer sud be p-1

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Sat Feb 13, 2010 6:56 am

gmatnmein2010 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 prime, then f(p) =
(A) P-1
(B) P-2
(C) (P+1)/2
(D) (P-1)/2
(E) 2

how i sud approach in reverse direction...i.e from ans

f(n) has n-1 positive integers less than n maximum value of f(n) = n-1
Now in the case of a prime number all the positive integers each of which is less than prime number will have no positive factor in common with prime number. Thus f(p) attains its maximum value of p-1 when p is a prime number

Alternatively take a prime 5
4 is not a factor
3 is not a factor
2 is not a factor
1 is not a factor

f(5) is 4 A may be true; B is ruled out; C is ruled out, D is ruled out, E is ruled out

only A can be the answer

Always borrow money from a pessimist, he doesn't expect to be paid back.

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komal: Legendary Member; Posts: 777; Joined: Fri Jan 01, 2010 4:02 amFollowed by: 47 members; Location: Mumbai, India; Thanked: 117 times

by komal » Tue Feb 16, 2010 9:02 am

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 prime, then f(p) =
(A) P-1
(B) P-2
(C) (P+1)/2
(D) (P-1)/2
(E) 2

how i sud approach in reverse direction...i.e from ans[/quote]

1 is not prime number.

n and f(n) can't have any factor in common. if n is a prime integer and f(n)=n-1, the GCD of n and of (n-1) is 1.

(A) is correct

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