Help me solve this GMAT Quant Question (GMATPrep) #2

[EricImasogie]

I got the answer right but I'm not how to solve this question (I guessed).

exponent questions like these give me a hard time since they contain a variable set that is + or - another variable set. I typically see problems where perhaps 2^x = 3(2^x) ,which is easier to solve but Im not sure how to get this one. Please help!

[Brent@GMATPrepNow]

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

This requires some factoring.
2^x - 2^(x-2) = 3(2^13)
2^(x-2)[2^2 - 1] = 3(2^13)
2^(x-2)[3] = 3(2^13)
Divide both sides by 3 to get: 2^(x-2)= 2^13
So, x-2 = 13
[spoiler]x = 15[/spoiler]

Cheers,
Brent

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Hi EricImasogie,

Factoring the equation (as Brent showed) 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 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

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

[Mathsbuddy]

Alternatively, we can see that a SUBTRACTION is required, so we can use this clue to bring us closer to the answer on the right hand side of the equation:
3 x 2^13 = (4-1) x 2^13 = 4 x 2^13 - 2^13 = 2^15 - 2^13 = 2^n - 2^(n-2)
So n = 15