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

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Math Revolution GMAT Instructor
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If 2^n+2^n-2=5120, then n=?  [#permalink]

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New post 02 Feb 2018, 02:04
1
1
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

74% (01:10) correct 26% (01:06) wrong based on 57 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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Re: If 2^n+2^n-2=5120, then n=?  [#permalink]

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New post 02 Feb 2018, 02:10
E
2^n-2=5120/5
n-2=10
n=12

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

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New post 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

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

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

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New post 05 Feb 2018, 10:20
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

Answer: E
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Re: If 2^n+2^n-2=5120, then n=? &nbs [#permalink] 05 Feb 2018, 10:20
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