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If 2^x - 2^(x-2) = 3(2^13), what is the value of x? A) 9 B)

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If 2^x - 2^(x-2) = 3(2^13), what is the value of x? A) 9 B) [#permalink] New post 07 Mar 2008, 02:35
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
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Re: GMAT Prep Explanation please! [#permalink] New post 07 Mar 2008, 05:41
Choice D

2^13( 2^2-1)= 3(2^13)
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Re: GMAT Prep Explanation please! [#permalink] New post 07 Mar 2008, 06:11
japped187 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


d

factor out 2^x and move all variables to one side
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Re: GMAT Prep Explanation please! [#permalink] New post 12 Mar 2008, 03:36
Could you please write out the process please!! Thanks!!
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Re: GMAT Prep Explanation please! [#permalink] New post 12 Mar 2008, 03:49
see below
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Re: GMAT Prep Explanation please! [#permalink] New post 12 Mar 2008, 06:37
japped187 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/2^2=3(2^13)

2^x(1-1/4)=3(2^13) ---> 2^x(3/2^2)=3(2^13)

cancel the 3's. and multiply the 2^2

thus 2^x=2^15 or x=15

D
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Re: GMAT Prep Explanation please! [#permalink] New post 27 Mar 2008, 20:08
bmwhype...thanks for the full answer...but can anyone help me? I'm still confused on this one..
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Re: GMAT Prep Explanation please! [#permalink] New post 28 Mar 2008, 06:57
You could just plug in the answer choices and solve until the right = left side.
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Re: GMAT Prep Explanation please! [#permalink] New post 28 Mar 2008, 19:36
japped187 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



since u need the LHS to come to 3(2^13), start substituting the values for x from the choices given.

first substitute 17 - it becomes 2^17-2^15 = 2^15(2^2 - 1) = 3. 2^15 - which is not what we want

so try the second bigger choice - 15

2^15-2^13 = 2^13( 2^2 - 1) = 3. 2^13 - which is what we want

hence , D is the choice
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Re: GMAT Prep Explanation please! [#permalink] New post 28 Mar 2008, 19:42
A much shorter and direct way is following
2^x = 2^2 * 2^(x-2)
So expression in question should read
2^2 * 2^(x-2) - 2^(x-2) = 3(2^13)
2^(x-2)*3 = 3*2^13
=> x-2 = 13
=> x = 15

No need to put values or anything just plain straight forward.
Re: GMAT Prep Explanation please!   [#permalink] 28 Mar 2008, 19:42
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