It is currently 19 Jan 2018, 12:59

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

Events & Promotions in June
Open Detailed Calendar

If (1/2)^24*(1/81)^k = 1/18^24, then k =

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

Hide Tags

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43335

Kudos [?]: 139513 [1], given: 12794

If (1/2)^24*(1/81)^k = 1/18^24, then k = [#permalink]

Show Tags

New post 13 Dec 2017, 04:58
1
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

93% (00:58) correct 7% (00:05) wrong based on 42 sessions

HideShow timer Statistics

Kudos [?]: 139513 [1], given: 12794

VP
VP
avatar
P
Joined: 22 May 2016
Posts: 1250

Kudos [?]: 462 [0], given: 682

Premium Member CAT Tests
If (1/2)^24*(1/81)^k = 1/18^24, then k = [#permalink]

Show Tags

New post 13 Dec 2017, 08:36
Bunuel wrote:
If \((\frac{1}{2})^{24}*(\frac{1}{81})^k=(\frac{1}{18})^{24}\) then k =

A. 8
B. 12
C. 16
D. 24
E. 36

\((\frac{1}{2})^{24}*(\frac{1}{81})^k=(\frac{1}{18})^{24}\)


\((\frac{1}{2})^{24}*(\frac{1}{3^4})^k=(\frac{1}{2^13^2})^{24}\)


\(2^{-24} * (3^{-4})^{k} = (2^{-1})^{24}* (3^{-2})^{24}\)


\(2^{-24} * 3^{-4k} = 2^{-24} * 3^{-48}\)


\(2^{-24}\) is factored out. Bases \(3\) are identical. Set their exponents equal:

\(-4k = - 48\)

\(k = 12\)

Answer
[Reveal] Spoiler:
D

_________________

At the still point, there the dance is. -- T.S. Eliot
Formerly genxer123

Kudos [?]: 462 [0], given: 682

BSchool Forum Moderator
User avatar
D
Joined: 26 Feb 2016
Posts: 1809

Kudos [?]: 830 [0], given: 22

Location: India
Concentration: General Management, Leadership
WE: Sales (Retail)
Premium Member CAT Tests
If (1/2)^24*(1/81)^k = 1/18^24, then k = [#permalink]

Show Tags

New post 13 Dec 2017, 09:58
Bunuel wrote:
If \((\frac{1}{2})^{24}*(\frac{1}{81})^k=(\frac{1}{18})^{24}\) then k =

A. 8
B. 12
C. 16
D. 24
E. 36



Since \((\frac{1}{2})^{24}*(\frac{1}{81})^k=(\frac{1}{18})^{24}\), we can also say that \((2)^{24}*(81)^k=(18)^{24}\)

When prime factorized, \(18 = 2 * 3^2\)
In the right hand side of the expression, 18 has been raised to the power of 24,
we need \(2^{24}\) and \(3^{48}\) in the left hand side to balance the equation out.

In order to balance the equation \(81^k = (3^4)^k = 3^{4*k}\) must be equal to \(3^{48}\)

Therefore, 4k = 48 => k = 12(Option B)
_________________

Stay hungry, Stay foolish

2017-2018 MBA Deadlines

Class of 2020: Rotman Thread | Schulich Thread
Class of 2019: Sauder Thread

Kudos [?]: 830 [0], given: 22

If (1/2)^24*(1/81)^k = 1/18^24, then k =   [#permalink] 13 Dec 2017, 09:58
Display posts from previous: Sort by

If (1/2)^24*(1/81)^k = 1/18^24, then k =

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


GMAT Club MBA Forum Home| About| Terms and Conditions| 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®.