GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Oct 2019, 03:46 GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  For positive integer n, with distinct prime factors p1, p2,…,pn, the f

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8009
GMAT 1: 760 Q51 V42 GPA: 3.82
For positive integer n, with distinct prime factors p1, p2,…,pn, the f  [#permalink]

Show Tags 00:00

Difficulty:   35% (medium)

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

HideShow timer Statistics

[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

_________________
Retired Moderator D
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

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 V
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

=>

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.

_________________ Re: For positive integer n, with distinct prime factors p1, p2,…,pn, the f   [#permalink] 03 Jan 2018, 01:41
Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  