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

 It is currently 11 Dec 2019, 22:17

### 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

# 2^x - 2^(x-2) = 3*(2^13) what is x?

Author Message
TAGS:

### Hide Tags

Intern
Joined: 07 Sep 2019
Posts: 11
2^x - 2^(x-2) = 3*(2^13) what is x?  [#permalink]

### Show Tags

26 Nov 2019, 13:51
hi there, can someone help guide on how I can solve this question?
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15696
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: 2^x - 2^(x-2) = 3*(2^13) what is x?  [#permalink]

### Show Tags

26 Nov 2019, 14:48
Hi kevinkhan,

When posting subject-specific questions, you should make sure to post them in the appropriate sub-forum. For example, the Problem Solving forum can be found here:

https://gmatclub.com/forum/problem-solving-ps-140/

You should also make sure to post the ENTIRE prompt. The text of the full prompt includes the following 5 answers:

2^x - 2^(x-2) = 3*(2^13) what is x?

A. 9
B. 11
C. 13
D. 15
E. 17

There's a full discussion of this prompt here: https://gmatclub.com/forum/if-2-x-2-x-2 ... 30109.html

This question can be solved in a number of different ways, including by TESTing THE ANSWERS (you might find it easier to manipulate numbers than to manipulate variables). One of those 5 answers IS the value of X, so you can plug them in, do the necessary math and find the one value that balances out the equation. Here's how to approach it:

Since the "right side" of the equation is greater than 2^14, X must be bigger than 14 (since the "left side" of the equation involves subtraction). So we can eliminate A, B and C.

If X = 15, then...

2^15 - 2^13 can be factored into...
(2^13)(2^2 - 1) =
(2^13)(3)

This is EXACTLY what's on the "right side" of the equation, so X MUST be 15

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Re: 2^x - 2^(x-2) = 3*(2^13) what is x?   [#permalink] 26 Nov 2019, 14:48
Display posts from previous: Sort by