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

 It is currently 14 Nov 2018, 13:53

### 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

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

## Events & Promotions

###### Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### 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 =

Author Message
TAGS:

### Hide Tags

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

### Show Tags

13 Dec 2017, 04:58
2
00:00

Difficulty:

25% (medium)

Question Stats:

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

### HideShow timer Statistics

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

_________________
Senior SC Moderator
Joined: 22 May 2016
Posts: 2092
If (1/2)^24*(1/81)^k = 1/18^24, then k =  [#permalink]

### Show Tags

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:

$$-4k = - 48$$

$$k = 12$$

Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3302
Location: India
GPA: 3.12
If (1/2)^24*(1/81)^k = 1/18^24, then k =  [#permalink]

### Show Tags

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

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