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M61-18

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Math Revolution GMAT Instructor
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M61-18  [#permalink]

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New post 18 Jun 2018, 05:04
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A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

83% (01:42) correct 17% (02:24) wrong based on 18 sessions

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If \(2^n+2^{n-2}=5120\), then \(n=?\)


A. 8
B. 9
C. 10
D. 11
E. 12

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Re M61-18  [#permalink]

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New post 18 Jun 2018, 05:04
Official Solution:


If \(2^n+2^{n-2}=5120\), then \(n=?\)


A. 8
B. 9
C. 10
D. 11
E. 12


Factoring yields

\(2^{n}+2^{n-2}=2^{2}2^{n-2}+2^{n-2}=(2^2+1)2^{n-2}=5*2^{n-2}=5120=5*1024\).

Therefore, \(2^{n-2}=1024=2^{10}\) and \(n-2 = 10\). It follows that \(n = 12\).


Answer: E
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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
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Re: M61-18  [#permalink]

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New post 14 Sep 2018, 06:08
MathRevolution wrote:
If \(2^n+2^{n-2}=5120\), then \(n=?\)


A. 8
B. 9
C. 10
D. 11
E. 12


Hello Can anyone please explain this question in a simpler manner? it would be of great help. Thank you!
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Re: M61-18  [#permalink]

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New post 25 Oct 2018, 04:43
I agree with Shri15kumar. The explanation is not clear. I got the answer correct but only because I guessed and I would really like to learn how to solve a problem like this. Thank you!
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Re: M61-18  [#permalink]

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New post 02 Aug 2019, 01:04
MathRevolution wrote:
Official Solution:


If \(2^n+2^{n-2}=5120\), then \(n=?\)


A. 8
B. 9
C. 10
D. 11
E. 12


Factoring yields

\(2^{n}+2^{n-2}=2^{2}2^{n-2}+2^{n-2}=(2^2+1)2^{n-2}=5*2^{n-2}=5120=5*1024\).

Therefore, \(2^{n-2}=1024=2^{10}\) and \(n-2 = 10\). It follows that \(n = 12\).


Answer: E


The solution isn't clear. Can someone help out?
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Re: M61-18  [#permalink]

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New post 16 Aug 2019, 04:33
1
gbengoose wrote:
MathRevolution wrote:
Official Solution:


If \(2^n+2^{n-2}=5120\), then \(n=?\)


A. 8
B. 9
C. 10
D. 11
E. 12


Factoring yields

\(2^{n}+2^{n-2}=2^{2}2^{n-2}+2^{n-2}=(2^2+1)2^{n-2}=5*2^{n-2}=5120=5*1024\).

Therefore, \(2^{n-2}=1024=2^{10}\) and \(n-2 = 10\). It follows that \(n = 12\).


Answer: E


The solution isn't clear. Can someone help out?


Here you go.
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Re: M61-18   [#permalink] 16 Aug 2019, 04:33
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