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M61-18

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Math Revolution GMAT Instructor
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Joined: 16 Aug 2015
Posts: 6832
GMAT 1: 760 Q51 V42
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M61-18  [#permalink]

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New post 18 Jun 2018, 04:04
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

82% (01:47) correct 18% (02:37) wrong based on 11 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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Math Revolution GMAT Instructor
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Re M61-18  [#permalink]

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New post 18 Jun 2018, 04:04
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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Re: M61-18  [#permalink]

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New post 14 Sep 2018, 05:08
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, 03:43
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 &nbs [#permalink] 25 Oct 2018, 03:43
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M61-18

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