NEW HERE? LEARN MORE
closeclose
It is currently 03 Oct 2023, 17:40
Register
GMAT Club Tests
Decision Tracker
My Rewards
New posts
New comers' posts

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.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel

If (2/3)^n = (3/2)^2, what is the value of n?

7 posts Go to First Unread Post
Print view
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
SORT BY:
Date
Kudos
avatar
jsphcal
Intern
Intern
Joined: 27 Feb 2012
Posts: 27
If (2/3)^n = (3/2)^2, what is the value of n? [#permalink] New post  16 Jun 2012, 20:47
3
Kudos
8
Bookmarks
Quiz Dashboard Attempt only this question Same topic and source Same topic and difficulty Same source and difficulty Random Chronological Reverse chronological Learn more
00:00
A
B
C
D
E

Difficulty:

5% (low)

Question Stats:

88% (00:43) correct 12% (00:57) wrong based on 337 sessions

Hide Show timer Statistics

If \((\frac{2}{3})^n=(\frac{3}{2})^2\), what is the value of n?

A. -2
B. -1
C. 0
D. 1
E. 2
ShowHide Answer
Official Answer
Official Answer and Stats are available only to registered users. Register/Login.
Quiz Dashboard Attempt only this question Same topic and source Same topic and difficulty Same source and difficulty Random Chronological Reverse chronological Learn more
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 89459
CAT Tests Forum Quiz Mode
If (2/3)^n = (3/2)^2, what is the value of n? [#permalink] New post  17 Jun 2012, 02:58
2
Kudos
3
Bookmarks
Expert Reply
jsphcal wrote:
If (2/3)^n=(3/2)^2, what is the value of n?

A. -2
B. -1
C. 0
D. 1
E. 2



Since \((\frac{3}{2})^2=(\frac{2}{3})^{-2}\) then we have that \((\frac{2}{3})^n=(\frac{2}{3})^{-2}\) --> \(n=-2\).

Answer: A.

For more on number theory and exponents check: https://gmatclub.com/forum/math-number- ... 88376.html

DS questions on exponents: https://gmatclub.com/forum/search.php?s ... &tag_id=39
PS questions on exponents: https://gmatclub.com/forum/search.php?s ... &tag_id=60

Tough and tricky DS exponents and roots questions with detailed solutions: https://gmatclub.com/forum/tough-and-tr ... 25967.html
Tough and tricky PS exponents and roots questions with detailed solutions: https://gmatclub.com/forum/tough-and-tr ... 25956.html

Hope it helps.
_________________
New to the GMAT CLUB Forum?

My Signature Questions' Collection:


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
General Discussion
avatar
damham17
Intern
Intern
Joined: 06 Mar 2012
Posts: 32
GMAT ToolKit User
Re: If (2/3)^n = (3/2)^2, what is the value of n? [#permalink] New post  16 Jun 2012, 21:16
I was surprised to see this question in the 600-700 range. It's just testing the basic exponent property involving a negative sign.

(n)^-1 = (1/n)
avatar
damstamnd
Intern
Intern
Joined: 04 Apr 2011
Posts: 8
Schools: Sloan '16
Re: If (2/3)^n = (3/2)^2, what is the value of n? [#permalink] New post  17 Jun 2012, 10:14
2
Kudos
Answer: A

A negative exponent in a fraction leads to the reciprocal of the fraction. Thus the negative exponent of 2 is -2, allowing (2/3)^(-2) = (3/2)^2.
User avatar
PareshGmat
SVP
SVP
Joined: 27 Dec 2012
Status:The Best Or Nothing
Posts: 1573
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
Re: If (2/3)^n = (3/2)^2, what is the value of n? [#permalink] New post  27 Feb 2014, 20:58
(2/3)^n = (3/2)^2
= (2/3)^-2

n = -2 (Answer = A)
User avatar
L
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18022
Location: United States (CA)
Re: If (2/3)^n = (3/2)^2, what is the value of n? [#permalink] New post  12 May 2017, 13:19
2
Bookmarks
Expert Reply
jsphcal wrote:
If (2/3)^n=(3/2)^2, what is the value of n?

A. -2
B. -1
C. 0
D. 1
E. 2


(2/3)^n = (3/2)^2

Observe that 3/2 = (2/3)^-1. Then:

(2/3)^n = ((2/3)^-1)^2

(2/3)^n=(2/3)^-2

n = -2

Alternate Solution:

Let’s distribute the exponents to the numerator and the denominator:

2^n/3^n = 3^2/2^2

If we cross multiply, we have:

2^(n + 2) = 3^(n + 2)

We see that the exponents of 2 and 3 are equal. This is only possible if n + 2 = 0. Then, n = -2.

Answer: A
_________________
See why Target Test Prep is the top rated GMAT course on GMAT Club. Read Our Reviews
Signature Read More
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 29596
Re: If (2/3)^n = (3/2)^2, what is the value of n? [#permalink] New post  15 Jul 2023, 12:15
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources
Signature Read More
GMAT Club Bot
gmatclubot
Re: If (2/3)^n = (3/2)^2, what is the value of n? [#permalink]
15 Jul 2023, 12:15
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
Moderators:
Bunuel
Math Expert
89459 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

cron

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions