Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 47920

If r and s are positive integers such that (2^r)(4^s) = 16, then 2r +
[#permalink]
Show Tags
10 Jan 2016, 07:47
Question Stats:
70% (01:11) correct 30% (01:13) wrong based on 863 sessions
HideShow timer Statistics




Math Expert
Joined: 02 Aug 2009
Posts: 6522

Re: If r and s are positive integers such that (2^r)(4^s) = 16, then 2r +
[#permalink]
Show Tags
10 Jan 2016, 08:11
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
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor




EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12176
Location: United States (CA)

Re: If r and s are positive integers such that (2^r)(4^s) = 16, then 2r +
[#permalink]
Show Tags
13 Jan 2016, 16:41
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: 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
CoFounder & 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!***********************



SVP
Joined: 08 Jul 2010
Posts: 2136
Location: India
GMAT: INSIGHT
WE: Education (Education)

If r and s are positive integers such that (2^r)(4^s) = 16, then 2r +
[#permalink]
Show Tags
13 Jan 2016, 23:33
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 email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne 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



Manager
Joined: 24 Jun 2014
Posts: 50
Concentration: Social Entrepreneurship, Nonprofit

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



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3161
Location: United States (CA)

Re: If r and s are positive integers such that (2^r)(4^s) = 16, then 2r +
[#permalink]
Show Tags
15 Mar 2017, 16:34
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 reexpress 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 WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Manager
Joined: 03 Jan 2017
Posts: 178

Re: If r and s are positive integers such that (2^r)(4^s) = 16, then 2r +
[#permalink]
Show Tags
18 Mar 2017, 14:58
2^(r+2s)=2^4 since r,s are integers, r=2, s=1 2*2+1=5 D



Manager
Joined: 01 Dec 2016
Posts: 115
Concentration: Finance, Entrepreneurship
WE: Investment Banking (Investment Banking)

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



Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3757
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)

Re: If r and s are positive integers such that (2^r)(4^s) = 16, then 2r +
[#permalink]
Show Tags
22 Mar 2017, 08:43
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 )



Manager
Joined: 21 Jun 2017
Posts: 84

Re: If r and s are positive integers such that (2^r)(4^s) = 16, then 2r +
[#permalink]
Show Tags
07 Oct 2017, 02:49
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 1. First step is to simplify what has been given. (2^r) (4^s) = 16 <can be simplified into this > (2^r)(2^2s) = 2^4 (2^r)(2^2s) = 2^4 is simpd further into > (2^r +2s) = 2^3 (2^r +2s) = 2^3 > r + 2s = 42. Second is to find the value of the variables, by isolating the above simplified expression r = 4  2s (isolating r) 2(42s) + s = 84s + s = 8  3s = 8 = 3s 8/3 = s (value of s) r = 4  2(8/3) r= 2/3(value of r) 3. finally, plug in the values of r and s 2(2/3) + 8/3 2 2/3 + 2 2/3 = 5 therefore the answer is D



Intern
Joined: 16 Sep 2017
Posts: 10

Re: If r and s are positive integers such that (2^r)(4^s) = 16, then 2r +
[#permalink]
Show Tags
07 Nov 2017, 06:46
If there was 8 in option then it would be a problem.
I mean s=0 and r=4 making sum 8
Posted from my mobile device



Intern
Joined: 27 Apr 2016
Posts: 6

Re: If r and s are positive integers such that (2^r)(4^s) = 16, then 2r +
[#permalink]
Show Tags
19 Feb 2018, 10:52
Nice question. I solved it the following way:
(2^r) (4^s) = 16 (2^r) (4^s) = 2^2 * 4^1
therefore, this means: r = 2 and s = 1
plug into the target question: 2r + s = ? 2(2) + 1 = 5



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12176
Location: United States (CA)

Re: If r and s are positive integers such that (2^r)(4^s) = 16, then 2r +
[#permalink]
Show Tags
21 Feb 2018, 20:01
Anantz wrote: If there was 8 in option then it would be a problem.
I mean s=0 and r=4 making sum 8
Posted from my mobile device Hi Anantz, If this question were to appear on Test Day, then it's certainly possible that '8' could be among the answer choices. However, we're told that S and R are POSITIVE INTEGERS, so S=0, R=4 is NOT an option here (and '8' is not a correct answer). In that same way, S=2, R=0 is not a correct answer either (even though the answer "2" does appear among the five answer choices). 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
CoFounder & 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!***********************



Senior Manager
Joined: 17 Mar 2014
Posts: 353

Re: If r and s are positive integers such that (2^r)(4^s) = 16, then 2r +
[#permalink]
Show Tags
16 Jul 2018, 20:00
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 Bunuel, as per Wiley Efficient Learning (app.efficientlearning.com), it is sub600 level question.




Re: If r and s are positive integers such that (2^r)(4^s) = 16, then 2r + &nbs
[#permalink]
16 Jul 2018, 20:00






