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

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Manager
Joined: 09 Feb 2006
Posts: 129
Location: New York, NY
If s, u, and v are positive integers, and 2^s = 2^u + 2^v, [#permalink]

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19 Mar 2006, 16:26
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35% (medium)

Question Stats:

69% (02:03) correct 31% (00:57) wrong based on 87 sessions

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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:

1: s=u
2: u does not equal v
3: s > v

A) None
B) I only
C) II only
D) III only
E) II and III only
[Reveal] Spoiler: OA

Last edited by Vyshak on 09 May 2016, 11:42, edited 1 time in total.
Updated OA
VP
Joined: 29 Dec 2005
Posts: 1341
Re: If s, u, and v are positive integers, and 2^s = 2^u + 2^v, [#permalink]

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19 Mar 2006, 16:37
[quote="jcgoodchild"]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....... not possible cuz even if v is o or -ve, s must be > u.

ii. u does not equal v ............ not true. if s = 3, u=v=2. so not true.

iii. s > v. it is a must cuz even if either u or v is -ve, s must be > v.

so D is correct.
Manager
Joined: 20 Mar 2005
Posts: 201
Location: Colombia, South America
Re: If s, u, and v are positive integers, and 2^s = 2^u + 2^v, [#permalink]

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19 Mar 2006, 16:40
jcgoodchild wrote:
If s, u, and v are positive integers, and 2^s = 2^u + 2^v, which of the following must be true:

1: s=u
2: u does not equal v
3: s > v

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

for 1:
s,u,v > 0
therefore v > = 1 thus
s cannot be equal to u

for 2:
is actually the opposite for s,u,v > 0 and integers u does always equal v

for 3:

s,u,v > 0

from 2 we know that U=V then s>v

so I would say D
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5043
Location: Singapore
Re: If s, u, and v are positive integers, and 2^s = 2^u + 2^v, [#permalink]

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19 Mar 2006, 21:50
1) Not true.
If s = u, then v must be 0 which cannot be the case since v must be a positive integer.

2) Not true.
u and v can be equal. If s = 3, u and v = 2

3) True
If s, u and v are positive integers, then s must always be greater than v.

I go with D
Manager
Joined: 14 Jun 2012
Posts: 123
GMAT 1: 560 Q36 V31
GMAT 2: 580 Q39 V31
GMAT 3: 630 Q41 V35
GPA: 4
If s, u, and v are positive integers and [#permalink]

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09 May 2016, 11:24
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. u not equal v
III. s > v

I searched for this problem here in the forum but couldn't find it.
Math Expert
Joined: 02 Sep 2009
Posts: 39609
Re: If s, u, and v are positive integers, and 2^s = 2^u + 2^v, [#permalink]

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09 May 2016, 12:30
Silviax 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. u not equal v
III. s > v

I searched for this problem here in the forum but couldn't find it.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-s-u-and-v-are-positive-integers-and-2s-2u-2v-which-168231.html
_________________
Re: If s, u, and v are positive integers, and 2^s = 2^u + 2^v,   [#permalink] 09 May 2016, 12:30
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