If r and s are positive integers such that (2^r)(4^s) = 16, then 2r + : GMAT Problem Solving (PS)
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

It is currently 03 Dec 2016, 02:44
GMAT Club Tests

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If r and s are positive integers such that (2^r)(4^s) = 16, then 2r +

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 35840
Followers: 6828

Kudos [?]: 89683 [0], given: 10381

If r and s are positive integers such that (2^r)(4^s) = 16, then 2r + [#permalink]

Show Tags

New post 10 Jan 2016, 06:47
Expert's post
6
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

76% (02:19) correct 24% (01:31) wrong based on 119 sessions

HideShow timer Statistics

Expert Post
1 KUDOS received
Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Joined: 02 Aug 2009
Posts: 4130
Followers: 305

Kudos [?]: 3221 [1] , given: 100

Re: If r and s are positive integers such that (2^r)(4^s) = 16, then 2r + [#permalink]

Show Tags

New post 10 Jan 2016, 07:11
1
This post received
KUDOS
Expert's post
Bunuel wrote:
If r and s are positive integers such that (2^r)(4^s) = 16, then 2r + s =

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6


lets get the eq into simplest orm..
(2^r)(4^s) = 16..
(2^r)(2^2s) = 2^4..
or r+2s=4..
since r and s are positive integers, only r as 2 and s as 1 satisfy the Equation..
so 2r+s=2*2+1=5..
D
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Expert Post
EMPOWERgmat Instructor
User avatar
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 7958
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Followers: 358

Kudos [?]: 2366 [0], given: 163

Re: If r and s are positive integers such that (2^r)(4^s) = 16, then 2r + [#permalink]

Show Tags

New post 13 Jan 2016, 15:41
Expert's post
1
This post was
BOOKMARKED
Hi All,

This question has a great 'brute force' element to it - you don't need to do any advanced math, but you have to be willing to 'play around' with the prompt to figure out what's possible (and what's not).

We're told that R and S are POSITIVE INTEGERS and that (2^R)(4^S) = 16. We're asked for the value of 2R + S....

Since the two variables are positive integers, that significantly restricts the possibilities. Each 'term' (2^R) and (4^S) will end up being a positive integer greater than 1 (remember, the variables are positive integers, so neither R nor S can equal 0 and neither 'term' can equal 1).

IF...
S = 2, then (2^R)(16) = 16 but we know that R CANNOT be 0, so this option is impossible. We now know that S can ONLY be 1...

When...
S = 1
(2^R)(4) = 16
2^R = 4
R = 2

Now we know that S=1 and R=2 is the only possible solution, so the answer to the question is (2)(2) + 1 = 5

Final Answer:
[Reveal] Spoiler:
D


GMAT assassins aren't born, they're made,
Rich
_________________

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests

60-point improvement guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Expert Post
1 KUDOS received
VP
VP
User avatar
Joined: 08 Jul 2010
Posts: 1432
Location: India
GMAT: INSIGHT
WE: Education (Education)
Followers: 65

Kudos [?]: 1339 [1] , given: 42

If r and s are positive integers such that (2^r)(4^s) = 16, then 2r + [#permalink]

Show Tags

New post 13 Jan 2016, 22:33
1
This post received
KUDOS
Expert's post
Bunuel wrote:
If r and s are positive integers such that (2^r)(4^s) = 16, then 2r + s =

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6



(2^r)(4^s) = 16
2^(r+2s) = (2^4)

i.e. r+2s = 4
i.e. r=2 and s=1

i.e. 2r+s=2*2+1 = 5

Answer: option D
_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com
Call us : +91-9999687183 / 9891333772
http://www.GMATinsight.com/testimonials.html



Feel free to give a Kudos if it is a useful post .

Manager
Manager
avatar
Joined: 24 Jun 2014
Posts: 51
Concentration: Social Entrepreneurship, Nonprofit
Followers: 0

Kudos [?]: 16 [0], given: 77

GMAT ToolKit User CAT Tests
Re: If r and s are positive integers such that (2^r)(4^s) = 16, then 2r + [#permalink]

Show Tags

New post 15 Jan 2016, 01:01
(2^r ) (4^s) =16
=> (2^2)(4^1)=16

r=2
s=1
Hence 2(r)+s =2(2)+1=5
Hence D
Re: If r and s are positive integers such that (2^r)(4^s) = 16, then 2r +   [#permalink] 15 Jan 2016, 01:01
    Similar topics Author Replies Last post
Similar
Topics:
7 Experts publish their posts in the topic If r and s are positive integers, and r^2 + r/s is an odd integer, whi nehabansal123 10 08 Jul 2015, 16:01
Experts publish their posts in the topic In the formula, V = 1/(2r)^2, if r is tripled, then V is enigma123 2 19 Feb 2012, 15:54
Experts publish their posts in the topic Is r > s ? (1) -r + s < 0 (2) r < |s| devinawilliam83 1 17 Feb 2012, 21:30
20 Experts publish their posts in the topic The greatest common factor of 16 and the positive integer n krishan 13 21 Dec 2008, 04:18
14 Experts publish their posts in the topic The greatest common factor of 16 and the positive integer n dancinggeometry 14 16 Sep 2008, 06:44
Display posts from previous: Sort by

If r and s are positive integers such that (2^r)(4^s) = 16, then 2r +

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.