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# If 2^n+2^n-2=5120, then n=?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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02 Feb 2018, 02:04
1
1
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Difficulty:

25% (medium)

Question Stats:

77% (01:51) correct 23% (02:05) wrong based on 70 sessions

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[GMAT math practice question]

If $$2^n+2^{n-2}=5120,$$ then $$n$$=?

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

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"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" Manager Joined: 08 Sep 2008 Posts: 131 Location: India Concentration: Operations, General Management Schools: ISB '20 GPA: 3.8 WE: Operations (Transportation) Re: If 2^n+2^n-2=5120, then n=? [#permalink] ### Show Tags 02 Feb 2018, 02:10 E 2^n-2=5120/5 n-2=10 n=12 Sent from my ASUS_Z010D using GMAT Club Forum mobile app Senior Manager Joined: 17 Oct 2016 Posts: 305 Location: India Concentration: Operations, Strategy GPA: 3.73 WE: Design (Real Estate) Re: If 2^n+2^n-2=5120, then n=? [#permalink] ### Show Tags 02 Feb 2018, 02:18 E Method 1: 2^10 = 1024. This cannot be the value of n. So A, B and C are out. When n=11, 2^11= 2048 and 2^9=512. Hence n cannot be 11. So E is the only possible value. Method 2: 2^n + 2^(n-2) = 5120 2^n*(1+1/4) =5120 2^n*(5/4) = 5120 2^n =1096*4 2^n =2^12 n = 12 Posted from my mobile device Posted from my mobile device Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8235 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If 2^n+2^n-2=5120, then n=? [#permalink] ### Show Tags 04 Feb 2018, 18:16 => Factoring yields $$2^n+2^{n-2}=2^22^{n-2}+2^{n-2}=(2^2+1)2^{n-2}=5*2^{n-2}=5120=5*1024.$$ Therefore, $$2^{n-2}=1024=2^{10}$$ and $$n-2 = 10.$$ It follows that $$n = 12.$$ Therefore, the answer is E. 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"
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Re: If 2^n+2^n-2=5120, then n=?  [#permalink]

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05 Feb 2018, 10:20
1
MathRevolution wrote:

If $$2^n+2^{n-2}=5120,$$ then $$n$$=?

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

We can simplify the given equation:

2^n + 2^(n-2) = 5120

2^n + 2^n x 2^-2 = 5120

Factoring the common factor of 2^n from both terms on the left side of the equation, we have:

2^n(1 + 2^-2) = 5120

2^n(1 + 1/4) = 5120

2^n(5/4) = 5120

2^n = 5120 x 4/5

2^n = 4096

n = 12

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Re: If 2^n+2^n-2=5120, then n=?  [#permalink]

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23 Mar 2019, 14:47
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Re: If 2^n+2^n-2=5120, then n=?   [#permalink] 23 Mar 2019, 14:47
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