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Integers

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Integers

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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 number then f(p) =

(a) p-1

(b) p-2

(c) $$\frac{p+1}{2}$$

(d) $$\frac{p-1}{2}$$

(e) 2

OA is A

Can an Expert give me the mathematical approach to solve this question? Thanks in anticipation

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GMAT/MBA Expert

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Hi Roland2rule,

To start, this question has a 'typo' in it - P must be a PRIME number (NOT "any number").

We're told that 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. We're asked for the value of f(P) if P is a PRIME number. This question can be solved by TESTing VALUES.

IF.... P = 5
then the positive integers that are LESS than 5 and have NO factors in common with 5 (other than the number 1) are 1, 2, 3 and 4.
Thus, the f(5) = 4, so we're looking for an answer that equals 4 when we plug P=5 into the answer choices. There's only one answer that matches.

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

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