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

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

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New post 26 Nov 2019, 13:51
hi there, can someone help guide on how I can solve this question?
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Re: 2^x - 2^(x-2) = 3*(2^13) what is x?  [#permalink]

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New post 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.

Let's TEST answer D: 15

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
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Contact Rich at: Rich.C@empowergmat.com
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Re: 2^x - 2^(x-2) = 3*(2^13) what is x?   [#permalink] 26 Nov 2019, 14:48
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