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function

by gmatnmein2010 » Sat Feb 13, 2010 1:47 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
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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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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
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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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