GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 06 Jul 2020, 20:07

### 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

# If 2^k + 2^(k-2) + 2^(k-3) = 2^(2k)*3^m, what is the value of k + m?​

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 27 Feb 2014
Posts: 288
Location: India
GMAT 1: 570 Q49 V20
GPA: 3.97
WE: Engineering (Education)
If 2^k + 2^(k-2) + 2^(k-3) = 2^(2k)*3^m, what is the value of k + m?​  [#permalink]

### Show Tags

Updated on: 15 Feb 2020, 20:22
2
00:00

Difficulty:

75% (hard)

Question Stats:

44% (02:17) correct 56% (02:16) wrong based on 34 sessions

### HideShow timer Statistics

If $$2^k + 2^{k-2} - 2^{k-3} = 2^{2k}*3^m$$, what is the value of k+m?​

A. -1​
B. 0​
C. 1​
D. 2​
E. 3 ​

_________________
Inspired by great content in some best books on GMAT, I have created my own YouTube channel-QUANT MADE EASY! I would love some support and feedback. Please hit subscribe and check it out!

Originally posted by kapil1 on 15 Feb 2020, 02:33.
Last edited by kapil1 on 15 Feb 2020, 20:22, edited 2 times in total.
GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4956
GMAT 1: 770 Q49 V46
Re: If 2^k + 2^(k-2) + 2^(k-3) = 2^(2k)*3^m, what is the value of k + m?​  [#permalink]

### Show Tags

15 Feb 2020, 08:39
Top Contributor
kapil1 wrote:
If $$2^k + 2^{k-2} + 2^{k-3} = 2^{2k}*3^m$$, what is the value of k+m?​

A. -1​
B. 0​
C. 1​
D. 2​
E. 3 ​

Are you sure you correctly transcribed the question?
_________________
Test confidently with gmatprepnow.com
GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4956
GMAT 1: 770 Q49 V46
Re: If 2^k + 2^(k-2) + 2^(k-3) = 2^(2k)*3^m, what is the value of k + m?​  [#permalink]

### Show Tags

16 Apr 2020, 09:48
Top Contributor
kapil1 wrote:
If $$2^k + 2^{k-2} - 2^{k-3} = 2^{2k}*3^m$$, what is the value of k+m?​

A. -1​
B. 0​
C. 1​
D. 2​
E. 3 ​

Given: $$2^k + 2^{k-2} - 2^{k-3} = 2^{2k}*3^m$$
Factor to get: $$2^{k-3}(2^3 + 2^1 - 1) = 2^{2k}*3^m$$
Evaluate: $$2^{k-3}(9) = 2^{2k}*3^m$$
Rewrite $$9$$ as a power of $$3$$ to get: $$2^{k-3}(3^2) = 2^{2k}*3^m$$

We can now conclude two things: $$2^{k-3}= 2^{2k}$$ and $$3^2 = 3^m$$

If $$2^{k-3}= 2^{2k}$$, then $$k-3= 2k$$, which means $$k = -3$$
If $$3^2 = 3^m$$, then $$m = 2$$

So, $$k+m = (-3) + 2 = -1$$

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Re: If 2^k + 2^(k-2) + 2^(k-3) = 2^(2k)*3^m, what is the value of k + m?​   [#permalink] 16 Apr 2020, 09:48