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

It is currently 25 Aug 2019, 22:12

Close

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
Your Progress

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.

Close

Request Expert Reply

Confirm Cancel

If n is a positive integer, greater than 2, what is the greatest prime

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Manager
Manager
User avatar
G
Joined: 13 May 2017
Posts: 114
Location: Finland
Concentration: Accounting, Entrepreneurship
GMAT 1: 530 Q42 V22
GMAT 2: 570 Q36 V31
GPA: 3.14
WE: Account Management (Entertainment and Sports)
Reviews Badge
If n is a positive integer, greater than 2, what is the greatest prime  [#permalink]

Show Tags

New post 25 Nov 2018, 06:33
1
4
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

57% (01:30) correct 43% (01:58) wrong based on 37 sessions

HideShow timer Statistics

If n is a positive integer, greater than 2, what is the greatest prime factor of \(3^n+3^n+3^n-3^n^-^2?\)

A. 3
B. 5
C. 7
D. 11
E. 13
NUS School Moderator
avatar
V
Joined: 18 Jul 2018
Posts: 1032
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Reviews Badge CAT Tests
Re: If n is a positive integer, greater than 2, what is the greatest prime  [#permalink]

Show Tags

New post 25 Nov 2018, 07:02
1
\(3^n+3^n+3^n-3^{n-2}\)

= \(3^n (1+1+1-\frac{1}{3^2})\)

= \(3^n (3-\frac{1}{9})\)

= \(3^n (26/9)\)

Hence the largest prime factor is 13.

E is the answer.
_________________
Press +1 Kudos If my post helps!
GMATH Teacher
User avatar
P
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 937
Re: If n is a positive integer, greater than 2, what is the greatest prime  [#permalink]

Show Tags

New post 25 Nov 2018, 13:09
rencsee wrote:
If n is a positive integer, greater than 2, what is the greatest prime factor of \(3^n+3^n+3^n-3^n^-^2?\)

A. 3
B. 5
C. 7
D. 11
E. 13

\(?\,\,\,:\,\,\,\,3 \cdot {3^n} - {3^{n - 2}} = {3^{n + 1}} - {3^{n - 2}}\,\,\,{\rm{max}}\,\,{\rm{prime}}\,\,{\rm{factor}}\,\,\,\,\,\,\,\left[ {n \ge 3\,\,{\mathop{\rm int}} \,\,\left( * \right)} \right]\)


\({3^{n + 1}} - {3^{n - 2}} = {3^{n - 2}}\left( {{3^3} - 1} \right) = {3^{n - 2}} \cdot 2 \cdot 13\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\,? = 13\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left( {\rm{E}} \right)\,\,\,\,\,\,\)



This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
GMAT Club Bot
Re: If n is a positive integer, greater than 2, what is the greatest prime   [#permalink] 25 Nov 2018, 13:09
Display posts from previous: Sort by

If n is a positive integer, greater than 2, what is the greatest prime

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





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