December 15, 2018 December 15, 2018 10:00 PM PST 11:00 PM PST Get the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299) December 16, 2018 December 16, 2018 07:00 AM PST 09:00 AM PST Get personalized insights on how to achieve your Target Quant Score.
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 18 Feb 2013
Posts: 29

If m and n are integers and 36/3^4 = 1/3^m + 1/3^n , what is
[#permalink]
Show Tags
Updated on: 27 Mar 2013, 03:37
Question Stats:
59% (01:34) correct 41% (02:10) wrong based on 359 sessions
HideShow timer Statistics
If m and n are integers and \(\frac{36}{3^4}=\frac{1}{3^m}+\frac{1}{3^n}\), what is the value of m+n? A. 2 B. 0 C. 2 D. 3 E. 5
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by DoItRight on 26 Mar 2013, 13:32.
Last edited by Bunuel on 27 Mar 2013, 03:37, edited 1 time in total.
RENAMED THE TOPIC.




Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 611

Re: Exponent Question
[#permalink]
Show Tags
26 Mar 2013, 20:43
DoItRight wrote: If m and n are integers and \(\frac{36}{3^4}=\frac{1}{3^m}+\frac{1}{3^n}\), what is the value of m+n?
A. 2 B. 0 C. 2 D. 3 E. 5
Please explain your work. We have \(\frac{36}{3^4}\) = \(2^2/3^2\) = 4/9. Thus, 4/9 = \(\frac{1}{3^m}+\frac{1}{3^n}\) or (3+1)/9 = \(\frac{1}{3^m}+\frac{1}{3^n}\) or 1/3 + 1/9 = \(\frac{1}{3^m}+\frac{1}{3^n}\) Thus, m = 1, n =2, m+n = 3. D.
_________________
All that is equal and notDeep Dive Inequality
Hit and Trial for Integral Solutions




Manager
Joined: 11 Jun 2010
Posts: 74

Re: Exponent Question
[#permalink]
Show Tags
26 Mar 2013, 15:15
Not sure why I get this as m+n=2
My workings: 36 / 9 * 9 = 1 / 3^m + 1 / 3^n 4 / 9 = {3^n + 3^m} / 3^(n+m) since 9 = 3^2, we get 3^2=3^(m+n) hence m+n = 2
Ans C



Intern
Status: Attending Duke in May!
Joined: 07 Jan 2013
Posts: 25
Location: United States (NC)
Concentration: Leadership, Strategy

Re: Exponent Question
[#permalink]
Show Tags
26 Mar 2013, 20:37
\(\frac{36}{3^4}\) can be rewritten as \(\frac{36}{81}\) > \(\frac{12}{27}\). \(3^3=27\). Therefore, m+n=3.
To check \(\frac{1}{3^2}\) > \(\frac{3}{27}\) & \(\frac{1}{3^1}\) > \(\frac{9}{27}\)
\(\frac{3}{27}\) + \(\frac{9}{27}\) = \(\frac{12}{27}\)



Intern
Joined: 18 Feb 2013
Posts: 29

Re: If m and n are integers and 36/3^4 = 1/3^m + 1/3^n , what is
[#permalink]
Show Tags
28 Mar 2013, 10:03
Hey vinaymimani,
How did you know when to break 4/9 into 1/9+3/9? I tried using alegbra like srcc25anu did and got nowhere.



Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 611

Re: If m and n are integers and 36/3^4 = 1/3^m + 1/3^n , what is
[#permalink]
Show Tags
28 Mar 2013, 10:20
DoItRight wrote: Hey vinaymimani,
How did you know when to break 4/9 into 1/9+3/9? I tried using alegbra like srcc25anu did and got nowhere. Firstly, solving it algebraically, we have \(4/9 = 1/3^m + 1/3^n\) or 4 = 3^(2m)+3^(2n) Now we know that m,n are integers. Moreover, two expressions, both being powers of 3 add upto 4. Thus, it must be of the form : 3+1. Thus, m=2,n=1 or m=1,n=2. In either case, m+n = 3. Now as to how it struck me to split 4/9, when you observe \(4/9 = 1/3^m+1/3^n\), one might notice that after any cancelling of common factors on the rhs, we should end up with a 9 in the denominator. Also, seeing that 4 = 3+1, one can think that maybe there is a (1/3) and a (1/9) on the rhs, where the lcm is 9, which leads to the (3+1) part in the numerator. I hope it was of some help.
_________________
All that is equal and notDeep Dive Inequality
Hit and Trial for Integral Solutions



Intern
Joined: 18 Feb 2013
Posts: 29

Re: If m and n are integers and 36/3^4 = 1/3^m + 1/3^n , what is
[#permalink]
Show Tags
28 Mar 2013, 11:47
Quote: Firstly, solving it algebraically, we have or 4 = 3^(2m)+3^(2n) When I tried the alegbra way, I got 4 / 9 = 3^n + 3^m / 3^(n+m) I did this but i gave me n+m together but it made the numerator very messy, and hit a dead end. Quote: Now as to how it struck me to split 4/9, when you observe , one might notice that after any cancelling of common factors on the rhs, we should end up with a 9 in the denominator. Also, seeing that 4 = 3+1, one can think that maybe there is a (1/3) and a (1/9) on the rhs, where the lcm is 9, which leads to the (3+1) part in the numerator. I hope it was of some help. Kudos on recognizing the split. Thanks for breaking it down. Does anyone where I can practice these types of questions? Questions where you have to recognize certain splits?



Senior Manager
Joined: 07 Apr 2012
Posts: 367

Re: If m and n are integers and 36/3^4 = 1/3^m + 1/3^n , what is
[#permalink]
Show Tags
03 May 2014, 12:24
I tried cross multiplying the right side. got: 36/3^4 = (3^m)*(3^n)/(3^mn)
from this i wasn't able to find an answer.
Can someone help with this?
How did you guys find the way of breaking it down?



Director
Joined: 25 Apr 2012
Posts: 684
Location: India
GPA: 3.21
WE: Business Development (Other)

Re: If m and n are integers and 36/3^4 = 1/3^m + 1/3^n , what is
[#permalink]
Show Tags
04 May 2014, 19:02
ronr34 wrote: I tried cross multiplying the right side. got: 36/3^4 = (3^m)*(3^n)/(3^mn) from this i wasn't able to find an answer.
Can someone help with this?
How did you guys find the way of breaking it down? You don't cross multiply but take an LCMFor RHS, If you take the LCM, we get \((3^n+ 3^m)/ 3^{(m+n)}\) So, we have 36/81 or 4/9 = \((3^n+ 3^m)/ 3^{(m+n)}\) It is better to reduce the LHS to 4/9 and then take 9 to the RHS. The expression becomes 4= 9/3^m + 9/3^n or \(4= 3^{(2m)}+3^{(2n)}\) Now when you see a 4 on LHS this should tell you that one of the terms on RHS is of the type 3^0 =1 so either m=2 or n=2,plugging in these values and we can get value for n and m+n=3 in any case The best way forward is given above by mau5 or you end up pluggin in multiple values(If you don't simplify the algebra) and loose the plot as there will be too many iterations you may have to try before getting the answer. mau5's method is pretty neat. Hope it helps
_________________
“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”



Math Expert
Joined: 02 Aug 2009
Posts: 7107

Re: If m and n are integers and 36/3^4 = 1/3^m + 1/3^n , what is
[#permalink]
Show Tags
28 Feb 2015, 05:50
cherryli2015 wrote: If m and n are integers and 36/(3^4) = 1/(3^m) + 1/(3^n), what is the value of m+n?
Thanks very much ... hi cherry, right side = 36/3^4= 4/9.. left side = 1/(3^m) + 1/(3^n)=(3^m+3^n)/3^(m+n) =4/9... so one can solve for m as 1 when n=2 or m as 2 when n=1.. m+n =3, in each case...
_________________
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



Intern
Joined: 08 May 2015
Posts: 16
Location: United Arab Emirates
Concentration: General Management, Operations
GMAT 1: 690 Q49 V34 GMAT 2: 730 Q50 V38
GPA: 3.36
WE: Sales (Energy and Utilities)

Re: If m and n are integers and 36/3^4 = 1/3^m + 1/3^n , what is
[#permalink]
Show Tags
24 Jun 2015, 08:31
DoItRight wrote: If m and n are integers and \(\frac{36}{3^4}=\frac{1}{3^m}+\frac{1}{3^n}\), what is the value of m+n?
A. 2 B. 0 C. 2 D. 3 E. 5 My first thought was to try to write 36 in the form of \(3^x + 3^y\). \(3^0=1, 3^1=3, 3^2=9, 3^3=27.\) We can write 36 = 9 + 27 = \(3^2 + 3^3\) Using the above in LHS, \(\frac{36}{3^4}\) = \(\frac{3^2 + 3^3}{3^4}\) = \(\frac{3^2}{3^4}\) + \(\frac{3^3}{3^4}\) = \(\frac{1}{3^2}\) + \(\frac{1}{3^1}\) So m = 2, n = 1 => m + n=3 So D



Current Student
Status: DONE!
Joined: 05 Sep 2016
Posts: 377

Re: If m and n are integers and 36/3^4 = 1/3^m + 1/3^n , what is
[#permalink]
Show Tags
05 Nov 2016, 17:03
Easiest way to solve is to simplify the LHS and then test out values for m and n on RHS.
36 = (3^2)(2^2)
36/(3^4) = [(3^2)(2^2)]/(3^4) = (2^2)/(3^2) > 4/9
m and n combination that will give this is m+n=3 (i.e. 1+2)
D is the correct answer.



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13087
Location: United States (CA)

Re: If m and n are integers and 36/3^4 = 1/3^m + 1/3^n , what is
[#permalink]
Show Tags
04 Feb 2018, 11:59
Hi All, Quant questions on the GMAT are often built around number 'patterns' of some kind, so your ability to 'play around' with a question and find the pattern(s) behind it can help you to get past complexlooking questions without too much trouble. Here, we're told that M and N are INTEGERS and that 36/(3^4) = 1/(3^M) + 1/(3^N). We're asked for the value of M+N. To start, I'm going to do a quick comparison assuming that there were no variables at all... 36/(3^4) = 36/81 1/3 = 27/81 So 1/3 + 1/3 = 54/81 > 36/81. This proves that at least one of the two variables has to be greater than 1 (we have to make at least one of the denominators BIGGER so that we can shrink that fraction and get the sum to equal 36/81. Let's try making one of the variables 1 and one of the variables 2... 1/3 = 27/81 1/(3^2) = 1/9 = 9/81 27/81 + 9/81 = 36/81 This is an EXACT MATCH for the other side of the equation, so this MUST be the solution. M+N = 1+2 = 3 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!*****



Intern
Joined: 30 Apr 2018
Posts: 7

Re: If m and n are integers and 36/3^4 = 1/3^m + 1/3^n , what is
[#permalink]
Show Tags
25 Nov 2018, 10:15
The way I solved this was to first minimize the LHS to 4/9. (It makes the numbers easier to play with in your head). Then, I just plugged and played until I found something that works. Which is D. Also note that answer choice A and B have to have at least one negative number somewhere.
Posted from my mobile device




Re: If m and n are integers and 36/3^4 = 1/3^m + 1/3^n , what is &nbs
[#permalink]
25 Nov 2018, 10:15






