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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
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GMAT 1: 760 Q51 V42
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For positive integer n, with distinct prime factors p1, p2,…,pn, the f  [#permalink]

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01 Jan 2018, 02:34
00:00

Difficulty:

35% (medium)

Question Stats:

70% (01:55) correct 30% (02:03) wrong based on 67 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

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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Retired Moderator Joined: 25 Feb 2013 Posts: 1178 Location: India GPA: 3.82 For positive integer n, with distinct prime factors p1, p2,…,pn, the f [#permalink] ### Show Tags 01 Jan 2018, 04:14 1 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: 8009 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: For positive integer n, with distinct prime factors p1, p2,…,pn, the f [#permalink] ### Show Tags 03 Jan 2018, 01:41 => Since $$30 = 2*3*5$$,$$f(30) = 30*(1-\frac{1}{2})(1-\frac{1}{3})(1-\frac{1}{5})$$$$= 30*(\frac{1}{2})(\frac{2}{3})(\frac{4}{5})=8.$$ Therefore, the answer is D. Answer : D _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
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Re: For positive integer n, with distinct prime factors p1, p2,…,pn, the f   [#permalink] 03 Jan 2018, 01:41
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# For positive integer n, with distinct prime factors p1, p2,…,pn, the f

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