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

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hi there, can someone help guide on how I can solve this question?
EMPOWERgmat Instructor V
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: 2^x - 2^(x-2) = 3*(2^13) what is x?  [#permalink]

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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
_________________ Re: 2^x - 2^(x-2) = 3*(2^13) what is x?   [#permalink] 26 Nov 2019, 14:48
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# 2^x - 2^(x-2) = 3*(2^13) what is x?  