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# For positive integer n, with distinct prime factors p1, p2,…,pn, the f

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4715
GPA: 3.82
For positive integer n, with distinct prime factors p1, p2,…,pn, the f [#permalink]

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01 Jan 2018, 01:34
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Difficulty:

25% (medium)

Question Stats:

79% (00:52) correct 21% (00:43) wrong based on 47 sessions

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[GMAT math practice question]

For positive integer n, with distinct prime factors p1, p2,…,pn, the function $$f(n) = n(1-\frac{1}{p1})(1-\frac{1}{p2})(1-\frac{1}{p3})$$$$….(1- \frac{1}{pk})$$ gives the number of positive integers less than n which have no common factor with n except 1. What is the value of f(30) ?

A. 5
B. 6
C. 7
D. 8
E. 9
[Reveal] Spoiler: OA

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PS Forum Moderator
Joined: 25 Feb 2013
Posts: 836
Location: India
GPA: 3.82
For positive integer n, with distinct prime factors p1, p2,…,pn, the f [#permalink]

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01 Jan 2018, 03:14
MathRevolution wrote:
[GMAT math practice question]

For positive integer n, with distinct prime factors p1, p2,…,pn, the function $$f(n) = n(1-\frac{1}{p1})(1-\frac{1}{p2})(1-\frac{1}{p3})$$$$….(1- \frac{1}{pk})$$ gives the number of positive integers less than n which have no common factor with n except 1. What is the value of f(30) ?

A. 5
B. 6
C. 7
D. 8
E. 9

Prime factors of $$30=2*3*5$$

So $$f(30)=30*(1-\frac{1}{2})*(1-\frac{1}{3})*(1-\frac{1}{5})=8$$

Option D
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4715
GPA: 3.82
Re: For positive integer n, with distinct prime factors p1, p2,…,pn, the f [#permalink]

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03 Jan 2018, 00:41
=>

Since $$30 = 2*3*5$$,$$f(30) = 30*(1-\frac{1}{2})(1-\frac{1}{3})(1-\frac{1}{5})$$$$= 30*(\frac{1}{2})(\frac{2}{3})(\frac{4}{5})=8.$$

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Re: For positive integer n, with distinct prime factors p1, p2,…,pn, the f   [#permalink] 03 Jan 2018, 00:41
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