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# If s, u, and v are positive integers and 2^s = 2^u + 2^v,

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VP
Joined: 30 Jun 2008
Posts: 1007
If s, u, and v are positive integers and 2^s = 2^u + 2^v, [#permalink]

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29 Sep 2008, 22:12
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If s, u, and v are positive integers and $$2^s = 2^u + 2^v$$, which of the following must be true?

I. s = u
II. v≠ u
III. s > v

(A) None
(B) Ι only
(C) ΙI only
(D) ΙII only
(E) ΙΙ and ΙΙΙ

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VP
Joined: 17 Jun 2008
Posts: 1477

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29 Sep 2008, 22:24
D for me.

The original equation can be translated into 2^(u-s) + 2^(v-s) = 1.

In the above equation, u cannot be equal to s as in that case one of the terms will become 1 and since none of terms can be equal to zero, u <>s and v <>s.

Similarly, u and v can be the same and in that case 2*2^(u-s) = 1 => u-s = -1

Now, looking at the original equation itself, since none of the terms can be equal to zero, s will at least be more than both u and v.
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Joined: 29 Mar 2008
Posts: 341

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Updated on: 29 Sep 2008, 22:39
amitdgr wrote:
If s, u, and v are positive integers and $$2^s = 2^u + 2^v$$, which of the following must be true?

I. s = u
II. v≠ u
III. s > v

(A) None
(B) Ι only
(C) ΙI only
(D) ΙII only
(E) ΙΙ and ΙΙΙ

Will go with (D).

2^4=2^3+2^3

I. s = u => Not true
II. v≠ u => Not true
III. s > v => True

--== Message from GMAT Club Team ==--

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If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

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Originally posted by leonidas on 29 Sep 2008, 22:29.
Last edited by leonidas on 29 Sep 2008, 22:39, edited 1 time in total.
Re: PS: Exponents   [#permalink] 29 Sep 2008, 22:29
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# If s, u, and v are positive integers and 2^s = 2^u + 2^v,

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