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GMAT Prep? (Function) Pract 2

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by dferm » Tue May 13, 2008 3:36 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

Please Explain...
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by aatech » Wed May 14, 2008 12:46 pm
I will go with A...

IMO, best approach will be to calculate f(n) for few nos

f(2) = 1 => 1 no

f(3) = 2, 1 => 2 nos

f(5) = 4, 3, 2, 1 => 4 nos

f(7) = 6, 5, 4, 3, 2, 1 => 6 nos

and A satisfies the condition for all prime nos

OA please??
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by dferm » Wed May 14, 2008 1:57 pm
The answer is A but don't quite understand this question..

Can you please put a little more light..


Thanks..

PS. ur the best
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by aatech » Thu May 15, 2008 5:38 am
Thanks for the compliments...

I will try my best to explain.. hope I am able to do so...

the question says f(n) is NUMBER of positive integers those are less than n and these numbers do
not have any common factors with n itself..

So, for any +ve integer n the function will contain all numbers less than n.. Since question is
concerned about only prime numbers you should not worry about the latter part as, for sure, there
will not be any common factors for prime numbers...
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