It is currently 21 Sep 2017, 09:19

Happening Now:

Live Chat with Amy Mitson, Sr. Associate Director of Admissions at Tuck Dartmouth


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

Confirm Cancel

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
V
Joined: 02 Sep 2009
Posts: 41660

Kudos [?]: 124306 [0], given: 12077

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

Show Tags

New post 10 Jan 2016, 07:47
Expert's post
12
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

66% (01:10) correct 34% (01:11) wrong based on 382 sessions

HideShow timer Statistics

Kudos [?]: 124306 [0], given: 12077

Expert Post
3 KUDOS received
Math Forum Moderator
avatar
P
Joined: 02 Aug 2009
Posts: 4909

Kudos [?]: 5224 [3], given: 112

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, 08:11
3
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

Kudos [?]: 5224 [3], given: 112

Expert Post
1 KUDOS received
EMPOWERgmat Instructor
User avatar
P
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 9800

Kudos [?]: 3311 [1], given: 171

Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
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, 16:41
1
This post received
KUDOS
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
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free

Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

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

Kudos [?]: 3311 [1], given: 171

Expert Post
1 KUDOS received
SVP
SVP
User avatar
G
Joined: 08 Jul 2010
Posts: 1808

Kudos [?]: 2201 [1], given: 50

Location: India
GMAT: INSIGHT
WE: Education (Education)
Reviews Badge
If r and s are positive integers such that (2^r)(4^s) = 16, then 2r + [#permalink]

Show Tags

New post 13 Jan 2016, 23:33
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 I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Kudos [?]: 2201 [1], given: 50

Manager
Manager
avatar
B
Joined: 24 Jun 2014
Posts: 52

Kudos [?]: 21 [0], given: 97

Concentration: Social Entrepreneurship, Nonprofit
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, 02:01
(2^r ) (4^s) =16
=> (2^2)(4^1)=16

r=2
s=1
Hence 2(r)+s =2(2)+1=5
Hence D

Kudos [?]: 21 [0], given: 97

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 17586

Kudos [?]: 270 [0], given: 0

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

Show Tags

New post 10 Mar 2017, 02:32
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 270 [0], given: 0

Expert Post
1 KUDOS received
Target Test Prep Representative
User avatar
S
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 1510

Kudos [?]: 766 [1], given: 2

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

Show Tags

New post 15 Mar 2017, 16:34
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


We can re-express 4 as 2^2:

2^r * (2^2)^s = 2^4

2^r * 2^(2s) = 2^4

When we have an exponential equation in which the bases are the same, the exponents are equal. Thus we have:

2^(r + 2s) = 4

r + 2s = 4

Since r and s must be positive integers, we see that the only possible choice for r and s is r = 2 and s = 1 (notice that if s = 2, then r = 0, and if s > 2, then r < 0). Therefore, 2r + s = 2(2) + 1 = 5.

Answer: D
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 766 [1], given: 2

Manager
Manager
avatar
S
Joined: 03 Jan 2017
Posts: 200

Kudos [?]: 9 [0], given: 4

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

Show Tags

New post 18 Mar 2017, 14:58
2^(r+2s)=2^4
since r,s are integers, r=2, s=1
2*2+1=5
D

Kudos [?]: 9 [0], given: 4

Manager
Manager
User avatar
S
Joined: 01 Dec 2016
Posts: 112

Kudos [?]: 13 [0], given: 30

Location: Cote d'Ivoire
Concentration: Finance, Entrepreneurship
WE: Investment Banking (Investment Banking)
GMAT ToolKit User
Re: If r and s are positive integers such that (2^r)(4^s) = 16, then 2r + [#permalink]

Show Tags

New post 22 Mar 2017, 00:10
Tricky and very nice question. I oversighted that s and r are positive.
was trying to solve an algebric equation to get 2r+s.
Pfff.......
_________________

What was previously thought to be impossible is now obvious reality.
In the past, people used to open doors with their hands. Today, doors open "by magic" when people approach them

Kudos [?]: 13 [0], given: 30

Math Forum Moderator
User avatar
S
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 2991

Kudos [?]: 1051 [0], given: 325

Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User Premium Member
Re: If r and s are positive integers such that (2^r)(4^s) = 16, then 2r + [#permalink]

Show Tags

New post 22 Mar 2017, 08:43
1
This post was
BOOKMARKED
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


Least possible value of s here will be 1 , as \(4^2 = 16\)

Now, we have -

\((2^r)(4^1) = 16\)

Or, \((2^r)(2^2) = 2^4\)

Or, \(2^{ r + 2} = 2^4\)

So, \(r + 2 = 4\)

Or, \(r = 2\)


Then \(2r + s = 2*2 + 1\)

Or, \(2r + s = 5\)

Answer must be (D) 5
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Kudos [?]: 1051 [0], given: 325

Re: If r and s are positive integers such that (2^r)(4^s) = 16, then 2r +   [#permalink] 22 Mar 2017, 08:43
    Similar topics Author Replies Last post
Similar
Topics:
1 EXPERTS_POSTS_IN_THIS_TOPIC The positive integer n is divisible by 16. If sqrt(n) is megafan 2 07 Mar 2013, 02:20
52 EXPERTS_POSTS_IN_THIS_TOPIC The greatest common factor of 16 and the positive integer n ajit257 22 04 Jun 2017, 19:07
21 EXPERTS_POSTS_IN_THIS_TOPIC The greatest common factor of 16 and the positive integer n krishan 13 19 Apr 2014, 08:26
20 EXPERTS_POSTS_IN_THIS_TOPIC The greatest common factor of 16 and the positive integer n dancinggeometry 16 22 Mar 2017, 08:51
EXPERTS_POSTS_IN_THIS_TOPIC In the formula, V = 1/(2r)^2, if r is tripled, then V is enigma123 2 19 Feb 2012, 22:02
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 | Emoji artwork provided by EmojiOne

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®.