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

It is currently 14 Nov 2018, 13:53

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 (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

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50585
If (1/2)^24*(1/81)^k = 1/18^24, then k =  [#permalink]

Show Tags

New post 13 Dec 2017, 04:58
2
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

89% (01:26) correct 11% (01:24) wrong based on 59 sessions

HideShow timer Statistics

Senior SC Moderator
avatar
V
Joined: 22 May 2016
Posts: 2092
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
Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3302
Location: India
GPA: 3.12
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)
_________________

You've got what it takes, but it will take everything you've got

GMAT Club Bot
If (1/2)^24*(1/81)^k = 1/18^24, then k = &nbs [#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  


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®.