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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
If 20/5 = 1/2^m + 1/2^n what is nm ?
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21 Nov 2021, 05:14
21 Nov 2021, 05:14
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If \(\frac{20}{2^{5}} = \frac{1}{2^{m}} + \frac{1}{2^{n}}\) what is nm ?
a) 0
b) 3
c) 8
d) 16
e) 24
a) 0
b) 3
c) 8
d) 16
e) 24
Re: If 20/5 = 1/2^m + 1/2^n what is nm ?
[#permalink]
22 Nov 2021, 03:38
22 Nov 2021, 03:38
3
\(\frac{20}{2^5} = \frac{4*5}{2^5} = \frac{2^2*5}{2^5} = \frac{5}{2^{5-2}} = \frac{5}{2^3} = \frac{4+1}{2^3}\)
\(\frac{4+1}{2^3} = \frac{4}{2^3} + \frac{1}{2^3} = \frac{2^2}{2^3} + \frac{1}{2^3} = \frac{1}{2^1} + \frac{1}{2^3} = \frac{1}{2^m} + \frac{1}{2^n}\)
Therefore, \(m = 1\) and \(n = 3\)
\(nm = 3*1 = \textbf{3}\)
Hence, Answer is B
\(\frac{4+1}{2^3} = \frac{4}{2^3} + \frac{1}{2^3} = \frac{2^2}{2^3} + \frac{1}{2^3} = \frac{1}{2^1} + \frac{1}{2^3} = \frac{1}{2^m} + \frac{1}{2^n}\)
Therefore, \(m = 1\) and \(n = 3\)
\(nm = 3*1 = \textbf{3}\)
Hence, Answer is B
gmatclubot
Re: If 20/5 = 1/2^m + 1/2^n what is nm ? [#permalink]
22 Nov 2021, 03:38
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