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

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

by EricImasogie » Fri Dec 12, 2014 5:34 am
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!


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Last edited by EricImasogie on Fri Dec 12, 2014 5:52 pm, edited 1 time in total.
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by Brent@GMATPrepNow » Fri Dec 12, 2014 6:37 am
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]

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by [email protected] » Fri Dec 12, 2014 10:52 am
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

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by Mathsbuddy » Tue Dec 16, 2014 7:55 am
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
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