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

It is currently 14 Nov 2018, 20:56

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
Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • $450 Tuition Credit & Official CAT Packs FREE

     November 15, 2018

     November 15, 2018

     10:00 PM MST

     11:00 PM MST

    EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299)
  • Free GMAT Strategy Webinar

     November 17, 2018

     November 17, 2018

     07:00 AM PST

     09:00 AM PST

    Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

If 3^m3^m3^m = 9^n, then m/n =

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50585
If 3^m3^m3^m = 9^n, then m/n =  [#permalink]

Show Tags

New post 04 Nov 2014, 09:21
2
1
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

74% (01:00) correct 26% (01:22) wrong based on 250 sessions

HideShow timer Statistics

Manager
Manager
avatar
Status: MBA Mentor
Joined: 28 Oct 2014
Posts: 67
Location: Korea, Republic of
Concentration: Strategy, Other
Schools: SDA Bocconi - Class of 2011
GMAT 1: 700 Q50 V34
GPA: 3.21
WE: Analyst (Telecommunications)
Re: If 3^m3^m3^m = 9^n, then m/n =  [#permalink]

Show Tags

New post 04 Nov 2014, 17:10
2
3^m3^m3^m = 9^n
3^(m+m+m)=(3^2)^n
3^3m=3^2n
3m=2n
m/n = 2/3



Bunuel wrote:

Tough and Tricky questions: Exponents.



If 3^m3^m3^m = 9^n, then m/n =

A. 1/3
B. 2/3
C. 1
D. 3/2
E. 3

Kudos for a correct solution.

_________________

Dhiraj Jha
http://www.globalmba-gyan.com
MBA 2011 - SDA Bocconi School of Management (Milan, Italy)
Global Account Management, Samsung Electronics Headquarters (Korea)

Intern
Intern
avatar
Joined: 16 Jul 2014
Posts: 5
GMAT Date: 01-23-2015
GPA: 3
WE: Human Resources (Investment Banking)
GMAT ToolKit User
Re: If 3^m3^m3^m = 9^n, then m/n =  [#permalink]

Show Tags

New post 04 Nov 2014, 22:23
1
3^m*3^m*3^m= 9^n
3^(m+m+m)= 3^2n
3^3m=3^2n

=> 3m=2n => m/n=2/3

answer is b...
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1827
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If 3^m3^m3^m = 9^n, then m/n =  [#permalink]

Show Tags

New post 12 Nov 2014, 18:12
1
\(3^m 3^m 3^m = 9^n\)

\((3*3*3)^{m} = 3^{2n}\)

\(3^{3m} = 3^{2n}\)

Bases are same; equating powers

3m = 2n

\(\frac{m}{n} = \frac{2}{3}\)

Answer = B
_________________

Kindly press "+1 Kudos" to appreciate :)

Senior Manager
Senior Manager
User avatar
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 422
Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)
Re: If 3^m3^m3^m = 9^n, then m/n =  [#permalink]

Show Tags

New post 15 Feb 2015, 13:44
I also soved it, but a bit differently. Thank you for reminding me of this much easier and logical way!

What I did was to test powers of 3 that would lead to 9.

So, we have 3 raised to the same power 3 times and 9 raised to another power one time: 3^m3^m3^m = 9^n

What I did was test 3 raised to the power of 2 like this:
3^2*3^2*3^2 = 9*9*9 = 9^3. This means that m=2 and n=3. So, m/n=2/3.

It wouldn't be that hard ot back solve using the answer choices as well.
Senior Manager
Senior Manager
User avatar
Joined: 20 Aug 2015
Posts: 389
Location: India
GMAT 1: 760 Q50 V44
Re: If 3^m3^m3^m = 9^n, then m/n =  [#permalink]

Show Tags

New post 23 Feb 2016, 01:53
Bunuel wrote:

Tough and Tricky questions: Exponents.



If 3^m3^m3^m = 9^n, then m/n =

A. 1/3
B. 2/3
C. 1
D. 3/2
E. 3

Kudos for a correct solution.


The easiest way to solve such questions is to bring the numbers in the same base.
Always try to bring the base to the lowest number possible, in this case: 3

3^m*3^m*3^m = 9^n
3^(3m) = 3^2n
Since the bases are same, we can equate the powers.

3m = 2n
Therefore m/n = 2/3
Option B
Intern
Intern
avatar
Joined: 07 Dec 2017
Posts: 1
Re: If 3^m3^m3^m = 9^n, then m/n =  [#permalink]

Show Tags

New post 22 Feb 2018, 23:21
TeamGMATIFY wrote:
Bunuel wrote:

Tough and Tricky questions: Exponents.



If 3^m3^m3^m = 9^n, then m/n =

A. 1/3
B. 2/3
C. 1
D. 3/2
E. 3

Kudos for a correct solution.


The easiest way to solve such questions is to bring the numbers in the same base.
Always try to bring the base to the lowest number possible, in this case: 3

3^m*3^m*3^m = 9^n
3^(3m) = 3^2n
Since the bases are same, we can equate the powers.

3m = 2n
Therefore m/n = 2/3
Option B



---

Hi sorry for a stupid question. The question asked for m/n right?

why is the answer 2/3 and NOT 3/2? the answer we got is 2m=2n
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50585
Re: If 3^m3^m3^m = 9^n, then m/n =  [#permalink]

Show Tags

New post 22 Feb 2018, 23:34
1
GMATasian wrote:
TeamGMATIFY wrote:
Bunuel wrote:

Tough and Tricky questions: Exponents.



If 3^m3^m3^m = 9^n, then m/n =

A. 1/3
B. 2/3
C. 1
D. 3/2
E. 3

Kudos for a correct solution.


The easiest way to solve such questions is to bring the numbers in the same base.
Always try to bring the base to the lowest number possible, in this case: 3

3^m*3^m*3^m = 9^n
3^(3m) = 3^2n
Since the bases are same, we can equate the powers.

3m = 2n
Therefore m/n = 2/3
Option B



---

Hi sorry for a stupid question. The question asked for m/n right?

why is the answer 2/3 and NOT 3/2? the answer we got is 2m=2n


If \(3^m3^m3^m = 9^n\), then \(\frac{m}{n} =\)

A. 1/3
B. 2/3
C. 1
D. 3/2
E. 3

\(3^m3^m3^m = 9^n\);

\(3^{(m+m+m)} = 3^{2n}\)

\(3^{3m} = 3^{2n}\)

\(3m = 2n\);

Divide by n: \(3*\frac{m}{n}=2\).

Divide by 3: \(\frac{m}{n}=\frac{2}{3}\).

Answer: B.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

VP
VP
User avatar
V
Status: It's near - I can see.
Joined: 13 Apr 2013
Posts: 1283
Location: India
Concentration: International Business, Operations
GMAT 1: 480 Q38 V22
GPA: 3.01
WE: Engineering (Consulting)
Premium Member Reviews Badge CAT Tests
Re: If 3^m3^m3^m = 9^n, then m/n =  [#permalink]

Show Tags

New post 21 Mar 2018, 02:04
Bunuel wrote:

Tough and Tricky questions: Exponents.



If \(3^m3^m3^m = 9^n\), then \(\frac{m}{n} =\)

A. 1/3
B. 2/3
C. 1
D. 3/2
E. 3

Kudos for a correct solution.


\(3^m3^m3^m = 9^n\)

\(3^3m = 3^2n\)

As bases are same , we can equate powers,

\(3m = 2n\)

\(\frac{m}{n}= \frac{2}{3}\)

(B)
_________________

"Do not watch clock; Do what it does. KEEP GOING."

Manager
Manager
User avatar
B
Joined: 28 Jan 2018
Posts: 54
Location: Netherlands
Concentration: Finance
GMAT 1: 710 Q50 V36
GPA: 3
Re: If 3^m3^m3^m = 9^n, then m/n =  [#permalink]

Show Tags

New post 21 Mar 2018, 02:18
Bunuel wrote:

Tough and Tricky questions: Exponents.



If \(3^m3^m3^m = 9^n\), then \(\frac{m}{n} =\)

A. 1/3
B. 2/3
C. 1
D. 3/2
E. 3

Kudos for a correct solution.


\(3^m3^m3^m = 9^n => 3^{3m} = 3^{2n} => 3m = 2n => \frac{m}{n} = \frac{2}{3}\) => (B)
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: If 3^m3^m3^m = 9^n, then m/n =  [#permalink]

Show Tags

New post 22 Mar 2018, 14:45
Bunuel wrote:

Tough and Tricky questions: Exponents.



If \(3^m3^m3^m = 9^n\), then \(\frac{m}{n} =\)

A. 1/3
B. 2/3
C. 1
D. 3/2
E. 3


When bases are the same, we add the exponents. Thus, 3^m*3^m*3^m = 3^3m. Simplifying the equation, we have:

3^3m = 9^n

3^3m = 3^2n

3m = 2n

m/n = 2/3

Answer: B
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

e-GMAT Representative
User avatar
P
Joined: 04 Jan 2015
Posts: 2191
Re: If 3^m3^m3^m = 9^n, then m/n =  [#permalink]

Show Tags

New post 26 Mar 2018, 10:08

Solution:



Given:

    • 3^m* 3^m * 3^m = 9^n

Working out:

We need to find the value of \(m/n\)

Per our conceptual knowledge, we know that if the numbers are in multiplicative form. We can add their powers, provided their bases are same.

Here, applying the same concept, we get:

    • \(3^{m+m+m} = 9^n\)

    • Or, \(3^{3m} = 9^n\)

    • Or, \(3^{3m} = (3^2)^n\)

    • Or, \(3^{3m} = 3^{2n}\)

Since the bases are same, we can equate the exponents.

Following the above process, we get:

    • \(3m = 2n\)

    • Or, \(m/n = 2/3\)

Answer: Option B
_________________








Register for free sessions
Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Must Read Articles
Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

GMAT Club Bot
Re: If 3^m3^m3^m = 9^n, then m/n = &nbs [#permalink] 26 Mar 2018, 10:08
Display posts from previous: Sort by

If 3^m3^m3^m = 9^n, then m/n =

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.