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18 Jun 2018, 05:04
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E
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Difficulty:
35%
(medium)
Question Stats:
82% (01:45) correct
18%
(02:26)
wrong
based on 33
sessions
History
Date
Time
Result
Not Attempted Yet
18 Jun 2018, 05:04
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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
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
Shri15kumar
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14 Sep 2018, 06:08
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MathRevolution
If \(2^n+2^{n-2}=5120\), then \(n=?\)
A. 8
B. 9
C. 10
D. 11
E. 12
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!
