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If s, u, and v are positive integers and 2s=2u+2v, which of the following must be true?

i. s=u ii. u is not equal to v iii. s > v

A. None B. I only C. II only D. III only E. II and III

Could someone explain this question a bit

Notice two things: 1. we are asked to find out which of the following MUST be true, not COULD be true and 2. s, u, and v are positive integers.

Given: 2s=2u+2v --> s=u+v. Now, since s, u, and v are positive integers then s is more than either u or v, so I is never true and III is always true. As for II: it's not necessarily true, for example 4=2+2. So, we have that only option III must be true.

Re: If s,u, and v are positive integers and 2s=2u+2v [#permalink]

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16 Apr 2012, 00:53

ENAFEX wrote:

Bunuel,

Not sure what I am missing here!!

s=u+v, why is S>V is always true?

Can we not have 2=2+0? In that case S=V, Right?

ooppss!! Sorry guys just realised my mistake.

0 is neither positive nor negative. So for this question because it says s,u,v are positive integers, the above argument is not valid.
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Re: If s,u, and v are positive integers and 2s=2u+2v [#permalink]

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09 Dec 2015, 07:16

I don't think this is an official question. There is a similar problem in OG 12, that says \(2^s = 2^u + 2^v\) Answer options are the same.
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Re: If s,u, and v are positive integers and 2s=2u+2v [#permalink]

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19 Sep 2017, 08:15

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