It is currently 19 Nov 2017, 23:21

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 09 Feb 2006
Posts: 129

Kudos [?]: 9 [0], given: 0

Location: New York, NY
If s, u, and v are positive integers, and 2^s = 2^u + 2^v, [#permalink]

### Show Tags

19 Mar 2006, 16:26
1
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

70% (01:00) correct 30% (00:57) wrong based on 89 sessions

### HideShow timer Statistics

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

Kudos [?]: 9 [0], given: 0

VP
Joined: 29 Dec 2005
Posts: 1337

Kudos [?]: 69 [0], given: 0

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

### Show Tags

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.

Kudos [?]: 69 [0], given: 0

Manager
Joined: 20 Mar 2005
Posts: 201

Kudos [?]: 16 [0], given: 0

Location: Colombia, South America
Re: If s, u, and v are positive integers, and 2^s = 2^u + 2^v, [#permalink]

### Show Tags

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

Kudos [?]: 16 [0], given: 0

GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5032

Kudos [?]: 453 [0], given: 0

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

### Show Tags

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

Kudos [?]: 453 [0], given: 0

Manager
Joined: 14 Jun 2012
Posts: 119

Kudos [?]: 29 [0], given: 28

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]

### Show Tags

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.

Kudos [?]: 29 [0], given: 28

Math Expert
Joined: 02 Sep 2009
Posts: 42254

Kudos [?]: 132741 [0], given: 12360

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

### Show Tags

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
_________________

Kudos [?]: 132741 [0], given: 12360

Re: If s, u, and v are positive integers, and 2^s = 2^u + 2^v,   [#permalink] 09 May 2016, 12:30
Display posts from previous: Sort by