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# If m is not equal to n,

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SC Moderator
Joined: 25 Sep 2018
Posts: 871
Location: United States (CA)
Concentration: Finance, Strategy
GPA: 3.97
WE: Investment Banking (Investment Banking)
If m is not equal to n,  [#permalink]

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16 May 2019, 09:58
1
00:00

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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Intern
Joined: 19 Feb 2019
Posts: 4
Re: If m is not equal to n,  [#permalink]

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16 May 2019, 11:02
1
take 2^(m-n) = a
hence 2^(n-m) = 1/a
now it can be easily solved
Director
Status: Manager
Joined: 27 Oct 2018
Posts: 801
Location: Egypt
GPA: 3.67
WE: Pharmaceuticals (Health Care)
Re: If m is not equal to n,  [#permalink]

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16 May 2019, 11:08
2

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