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# For positive integer n, function f(n), which is the number of positive

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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For positive integer n, function f(n), which is the number of positive  [#permalink]

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07 Feb 2016, 23:21
00:00

Difficulty:

35% (medium)

Question Stats:

73% (01:59) correct 27% (02:48) wrong based on 59 sessions

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For positive integer n, function f(n), which is the number of positive integers less than n such that have no common factor with n except 1, is n×(1-1/p1 )×(1-1/p2 )×(1-1/p3 )×…. ×(1- 1/pn ), (pi are different prime factors of n). If n=60, what is the value of f(n) ?

A. 12 B. 14 C. 15 D. 16 E. 18

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For positive integer n, function f(n), which is the number of positive  [#permalink]

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05 Mar 2016, 03:43
1
60= 2^2 *3*5
No of relatively prime= 60(1-1/2)(1-1/3)(1-1/5) = 16

SO IMO- 16 should be the answer
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Re: For positive integer n, function f(n), which is the number of positive  [#permalink]

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28 Jul 2017, 07:03
MathRevolution Can you please post the detailed solution!!!

Tagging Moderators: Bunuel, Abhishek009
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Re: For positive integer n, function f(n), which is the number of positive  [#permalink]

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18 Sep 2018, 01:39
NandishSS wrote:
MathRevolution Can you please post the detailed solution!!!

Tagging Moderators: Bunuel, Abhishek009

Little bit late, but mabybe still helpful for others...

This question basically requires you to find the prime factors of 60! Which are $$2^2$$,3,5

When you plug these in in the equation you get --> 60*(1-$$\frac{1}{2}$$)*(1-$$\frac{1}{3}$$)*(1-$$\frac{1}{5}$$)

Which simplifies to --> 60*$$\frac{1}{2}$$*$$\frac{2}{3}$$*$$\frac{4}{5}$$ --> 2*2*4=16

Hence D
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Re: For positive integer n, function f(n), which is the number of positive &nbs [#permalink] 18 Sep 2018, 01:39
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