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GMAT Prep question please help

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by Anurag@Gurome » Sun Aug 07, 2011 7:11 pm
kriti87 wrote:Hi,
I could not find any solutions to this problem anywhere in the forums.

Please help.

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

A) 9
B) 11
C) 13
D) 15
E) 17
I am showing the algebraic approach, you can also plug-in the answer choices to get the right answer.

2^x - 2^(x-2) = 3(2^13)
2^x[1 - 2^(-2)] = 3(2^13)
2^x[1 - 1/4] = 3(2^13)
2^x * (3/4) = 3(2^13
2^x * 3 * 2^(-2) = 3(2^13)
2^(x - 2) * 3 = (2^13) * 3
Since the bases are the same on both sides, so equating the exponents,
x - 2 = 13 implies x = 15

The correct answer is D.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
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by GMATGuruNY » Mon Aug 08, 2011 3:02 am
I posted a solution here:

https://www.beatthegmat.com/2-x-2-x-2-3- ... 68661.html
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