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If m is not equal to n,

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If m is not equal to n,  [#permalink]

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New post 16 May 2019, 09:58
1
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

63% (02:22) correct 37% (02:51) wrong based on 43 sessions

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If m is not equal to n,
\(\frac{2}{2^{m-n} -1}\) +\(\frac{2}{2^{n-m}-1}\) =

A)-2
B)-1
C)\(2^{m-n}\)
D)\(2^{n-m}\)
E)0

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Re: If m is not equal to n,  [#permalink]

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New post 16 May 2019, 11:02
1
take 2^(m-n) = a
hence 2^(n-m) = 1/a
now it can be easily solved
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Re: If m is not equal to n,  [#permalink]

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New post 16 May 2019, 11:08
2
A is the answer:

\(\frac{2}{2^{m-n} -1}\) +\(\frac{2}{2^{n-m}-1}\)
= \(\frac{2}{\frac{2^m}{2^n} -1}\) + \(\frac{2}{\frac{2^n}{2^m} -1}\)
= \(\frac{2}{\frac{2^m - 2^n}{2^n}}\) + \(\frac{2}{\frac{2^n - 2^m}{2^m}}\)
= \(\frac{2(2^n)}{2^m - 2^n}\) + \(\frac{2(2^m)}{2^n - 2^m}\)
= \(\frac{2(2^n)}{2^m - 2^n}\) - \(\frac{2(2^m)}{2^m - 2^n}\)
= \(\frac{2(2^n) - 2(2^m)}{2^m - 2^n}\)
= \(\frac{-2(2^m - 2^m)}{2^m - 2^n}\)
= -2
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Re: If m is not equal to n,   [#permalink] 16 May 2019, 11:08

If m is not equal to n,

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