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# M61-18

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8011
GMAT 1: 760 Q51 V42
GPA: 3.82

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18 Jun 2018, 05:04
00:00

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

_________________
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" Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8011 GMAT 1: 760 Q51 V42 GPA: 3.82 Re M61-18 [#permalink] ### Show Tags 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 _________________ 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"
Intern
Joined: 14 Jun 2018
Posts: 46
Location: India

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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!
Intern
Joined: 08 Aug 2018
Posts: 5

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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!
Intern
Joined: 04 Sep 2016
Posts: 16

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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 $$n = 12$$.

The solution isn't clear. Can someone help out?
Manager
Joined: 18 Apr 2019
Posts: 87
Location: India
GMAT 1: 720 Q48 V40
GPA: 4

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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 $$n = 12$$.

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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# M61-18

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