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

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by GMATGuruNY » Mon Oct 18, 2010 1:25 pm
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
We can plug in the answer choices for x.

Answer choice C: x= 13
2^13 - 2^(13-2) = 3(2^13)
2^13 - 2^11 = 3(2^13)
2^11(2^2 - 1) = 3(2^13)
2^11(3) = 3(2^13)

Plugging in x=13 made the exponent on the left 2^11.
To match 2^13 on the right side of the equation, the exponent needs to be increased by 2.
Thus, x = 13+2 = 15.

The correct answer is D.
Last edited by GMATGuruNY on Sun Sep 18, 2011 3:37 am, edited 1 time in total.
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by phoenixhazard » Mon Oct 18, 2010 1:29 pm
GMATGuruNY 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
We can plug in the answer choices for x.

Answer choice C: x= 13
2^13 - 2^(13-2) = 3(2^13)
2^13 - 2^11 = 3(2^13)
2^11(2^2 - 1) = 3(2^13)
2^11(3) = 3(2^13)

Plugging in x=13 made the exponent on the left 2^11.
To match 2^13 on the right side of the equation, the exponent needs to be increased by 2.
Thus, x = 13+2 = 15.

The correct answer is D.
excellent, thank you. i never thought to start with an answer and work backwards
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by smileforever41 » Tue May 01, 2012 4:05 am
GMATGuruNY 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
We can plug in the answer choices for x.

Answer choice C: x= 13
2^13 - 2^(13-2) = 3(2^13)
2^13 - 2^11 = 3(2^13)
2^11(2^2 - 1) = 3(2^13)
2^11(3) = 3(2^13)

Plugging in x=13 made the exponent on the left 2^11.
To match 2^13 on the right side of the equation, the exponent needs to be increased by 2.
Thus, x = 13+2 = 15.

The correct answer is D.


Mitch, my choice of words has come to a stand-still to appreciate your thought-process. All I can say is, "Thank you so much for being on this site". :D
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by aneesh.kg » Tue May 01, 2012 4:27 am
Why start with plugging in a number when we have a better approach?

RHS
= [2^(x - 2)]{4 - 1} (Taking 2^(x - 2) common)
= [2^(x - 2)]*(3)

For RHS = LHS, the exponent of 2 has to match because everything else is the same on both sides.
So (x - 2) = 13, or x = 15
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by shantanu86 » Tue May 01, 2012 5:59 am
I think its a simple question..
Just take 2^(x-2) out and you have

2^(x-2)* 3= 3*2^13
=>x=15

Hope it helps!!
If you feel like it, hit thanks :)
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