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

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

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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 20 Mar 2012, 00:17, edited 1 time in total.
Added the OA

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

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dzodzo85 wrote:
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.

Answer: D.

Check Must or Could be True questions to practice: search.php?search_id=tag&tag_id=193

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

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New post 16 Apr 2012, 00:51
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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?
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Re: If s,u, and v are positive integers and 2s=2u+2v [#permalink]

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New post 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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New post 16 Apr 2012, 00:55
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?


none if s,u and v can have value=0 as they are positive that is >0

hope this helps...!!
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Re: If s,u, and v are positive integers and 2s=2u+2v [#permalink]

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New post 18 Jul 2012, 11:44
2s = 2u + 2v

2(3) =2(2) +2(1)
2(4)=2(2)+2(2)

from the above two instances ,
(i) s= u (NOT ALWAYS)
(ii) u not equal to v (not always)
(iii) s > v (ALWAYS)

you can plug in various values and see . the third statement holds true always.

Ans : D

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

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New post 19 Jul 2012, 03:38
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


i. There is no way we can conclude that s=u from the given information

ii. There is no way we can conclude that u is not qual to v

iii. 2s = 2u + 2v => s= u +v since u is positive so S will be greater than V so its True!

Hence, Answer is D


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

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

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

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New post 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] 19 Sep 2017, 08:15
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