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If 2^x - 2^(x - 2) = 3*2^13 what is the value of x?

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Bunuel
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Re: If 2^x - 2^(x - 2) = 3*2^13 what is the value of x? [#permalink] New post   07 Sep 2020, 00:20
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costcosized wrote:
Bunuel wrote:
\(2^x*\frac{3}{2^{2}}=3*2^{13}\);

\(2^x=2^{15}\);

\(x=15\).

Answer: D.
Bunuel do you have any similar problems?


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Re: If 2^x - 2^(x - 2) = 3*2^13 what is the value of x? [#permalink] New post   22 Aug 2021, 01:07
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Trying another approach to solve this question.
2^x - 2^(x - 2) = 3*2^13
From this equation, we can say that x should be greater than 13
2^x - 2^(x - 2) > 2^13) ==> x > 13

Option A,B and C can be eliminated.

Lets check option D, x= 15.

2^15 - 2^(13)= 2^13( 2^2 - 1) = 3* 2^ 13

Then option D is the correct answer.

Thanks,
Clifin J Francis,
GMAT SME
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TheGMATStrategy
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If 2^x - 2^(x - 2) = 3*2^13 what is the value of x? [#permalink] New post   Updated on: 23 Feb 2023, 20:53
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Video solution by TGS - The GMAT® Strategy:



Want to reach your goal score faster? Resources to show you how: http://linktr.ee/thegmatstrategy

Originally posted by TheGMATStrategy on 01 Feb 2023, 11:27.
Last edited by TheGMATStrategy on 23 Feb 2023, 20:53, edited 1 time in total.
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Re: If 2^x - 2^(x - 2) = 3*2^13 what is the value of x? [#permalink] New post   23 Feb 2023, 15:20
Bunuel wrote:
If \(2^x-2^{x-2}=3*2^{13}\) what is the value of x?

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

\(2^x-2^{x-2}=3*2^{13}\);

\(2^x-2^{x}*2^{-2}=3*2^{13}\);

\(2^x-\frac{2^{x}}{2^{2}}=3*2^{13}\);

\(2^x(1-\frac{1}{2^{2}})=3*2^{13}\);

\(2^x*\frac{3}{2^{2}}=3*2^{13}\);

\(2^x=2^{15}\);

\(x=15\).

Answer: D.


NO idea how to solve this still, particulalrly step 3-4 . Totally confused.
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Re: If 2^x - 2^(x - 2) = 3*2^13 what is the value of x? [#permalink] New post   23 Feb 2023, 18:50
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Rags2Riches wrote:
Bunuel wrote:
If \(2^x-2^{x-2}=3*2^{13}\) what is the value of x?

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

\(2^x-2^{x-2}=3*2^{13}\);

\(2^x-2^{x}*2^{-2}=3*2^{13}\);

\(2^x-\frac{2^{x}}{2^{2}}=3*2^{13}\);

\(2^x(1-\frac{1}{2^{2}})=3*2^{13}\);

\(2^x*\frac{3}{2^{2}}=3*2^{13}\);

\(2^x=2^{15}\);

\(x=15\).

Answer: D.


NO idea how to solve this still, particulalrly step 3-4 . Totally confused.


Hi Rags2Riches,

Most Quant questions on the GMAT are written so that they can be approached in more than one way. By extension, if you're reading through an explanation that involves lots of step-heavy techincal math, then there is likely a Tactical approach that would be faster and easier.

Factoring the equation is a useful approach here. You can actually take it a step further by TESTing THE ANSWERS (you might find it easier to manipulate numbers than to manipulate variables). One of those numbers IS the value of X, so you can plug the answers 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 (as 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

Contact Rich at: Rich.C@empowergmat.com
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Re: If 2^x - 2^(x - 2) = 3*2^13 what is the value of x? [#permalink] New post   23 Feb 2023, 20:56
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Rags2Riches wrote:
Bunuel wrote:
If \(2^x-2^{x-2}=3*2^{13}\) what is the value of x?

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

\(2^x-2^{x-2}=3*2^{13}\);

\(2^x-2^{x}*2^{-2}=3*2^{13}\);

\(2^x-\frac{2^{x}}{2^{2}}=3*2^{13}\);

\(2^x(1-\frac{1}{2^{2}})=3*2^{13}\);

\(2^x*\frac{3}{2^{2}}=3*2^{13}\);

\(2^x=2^{15}\);

\(x=15\).

Answer: D.


NO idea how to solve this still, particulalrly step 3-4 . Totally confused.


Hey there - did you happen to check out our video solution? Right here: https://gmatclub.com/forum/if-2-x-2-x-2 ... l#p3150333

Or are you looking for a specific explanation of those specific steps?

Let us know :)
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Re: If 2^x - 2^(x - 2) = 3*2^13 what is the value of x? [#permalink] New post   24 Feb 2023, 01:54
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Rags2Riches wrote:
Bunuel wrote:
If \(2^x-2^{x-2}=3*2^{13}\) what is the value of x?

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

\(2^x-2^{x-2}=3*2^{13}\);

\(2^x-2^{x}*2^{-2}=3*2^{13}\);

\(2^x-\frac{2^{x}}{2^{2}}=3*2^{13}\);

\(2^x(1-\frac{1}{2^{2}})=3*2^{13}\);

\(2^x*\frac{3}{2^{2}}=3*2^{13}\);

\(2^x=2^{15}\);

\(x=15\).

Answer: D.


NO idea how to solve this still, particulalrly step 3-4 . Totally confused.


Although testing options is an important and effective technique for the GMAT, it is still important to have the ability to work with algebra. So, here are steps 3 and 4 in more details:

\(2^{-2}=\frac{1}{2^2}\), thus \(2^x-2^{x}*2^{-2}=3*2^{13}\) becomes \(2^x-\frac{2^{x}}{2^{2}}=3*2^{13}\). Here we can factor out 2^x from \(2^x-\frac{2^{x}}{2^{2}}\) and get \(2^x(1-\frac{1}{2^{2}})=3*2^{13}\).

If you are still unclear about the above,, I recommend checking out the following links.

7. Algebra



Check below for more:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread
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Re: If 2^x- 2^(x-2) = 3*2^13, what is x? 9 11 13 15 17 [#permalink] New post   19 Jun 2023, 09:44
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Re: If 2^x- 2^(x-2) = 3*2^13, what is x? 9 11 13 15 17 [#permalink]
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