January 17, 2019 January 17, 2019 08:00 AM PST 09:00 AM PST Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL. January 19, 2019 January 19, 2019 07:00 AM PST 09:00 AM PST Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 09 Mar 2011
Posts: 15
Location: Mumbai
Schools: ISB, Insead, Harvard, Wharton

If n and m are integers, and x=3^n, and y=3^m, is the value
[#permalink]
Show Tags
Updated on: 12 Sep 2012, 23:36
Question Stats:
58% (01:45) correct 43% (01:36) wrong based on 200 sessions
HideShow timer Statistics
If n and m are integers, and x=3^n, and y=3^m, is the value of x greater than the value of 2y? (1) n=m+1 (2) n=2m
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by saurabhsingh24 on 12 Sep 2012, 18:09.
Last edited by Bunuel on 12 Sep 2012, 23:36, edited 1 time in total.
Renamed the topic and edited the question.




Director
Joined: 22 Mar 2011
Posts: 600
WE: Science (Education)

Re: If n and m are integers, and x=3^n, and y=3^m, is the value
[#permalink]
Show Tags
13 Sep 2012, 00:32
saurabhsingh24 wrote: If n and m are integers, and x=3^n, and y=3^m, is the value of x greater than the value of 2y?
(1) n=m+1 (2) n=2m The question is in fact "is \(3^n>2\cdot{3^m}\)?" (1) The given inequality becomes \(3^{m+1}>2\cdot{3^m}\). Dividing through by \(3^m\), which is for sure a positive number, we obtain \(3 > 2,\) obviously true. Sufficient. (2) Now the given inequality becomes \(3^{2m}>2\cdot{3^m}\). Dividing through again by \(3^m\), we obtain \(3^m>2\). This inequality holds only for \(m>0\). Not sufficient. Answer A.
_________________
PhD in Applied Mathematics Love GMAT Quant questions and running.




Manager
Joined: 02 Jun 2011
Posts: 56

Re: Data Sufficiency
[#permalink]
Show Tags
12 Sep 2012, 19:58
saurabhsingh24 wrote: If n and m are integers, and x=3^n, and y=3^m, is the value of x greater than the value of 2y? (1) n=m+1 (2) n=2m There will be three cases: when M is positive: option 1 is sufficient to answer. and option 2 also give answer When M is negative: Option 1 is sufficient to answer. But option 2 is not sufficient to answer. When M is Zero: option Option 1 is sufficient to answer But Option 2 is not sufficient to answer. Try with some nos. for these three cases. If you like the post, kindly give me 1 kudos.



GMAT Tutor
Status: Tutor  BrushMyQuant
Joined: 05 Apr 2011
Posts: 622
Location: India
Concentration: Finance, Marketing
GPA: 3
WE: Information Technology (Computer Software)

Re: Data Sufficiency
[#permalink]
Show Tags
12 Sep 2012, 23:10
If n and m are integers, and x=3^n, and y=3^m, is the value of x greater than the value of 2y? (1) n=m+1 (2) n=2m we have to find if x > 2y i.e. 3^n > 2*3^m STAT1: n = m+1 so we have to prove that 3^(m+1) > 2* 3^m => 3 * 3^m > 2*3^m => 3 * 3^m  2*3^m > 0 => 3^m > 0 So ALL integer value of m 3^m will be greater that 0 So, SUFFICIENT STAT2: n=2m so we have to prove that 3^(2m) > 2* 3^m 3^(2m)  2* 3^m > 0 3^m* (3^m  2) > 0 for ALL values of m 3^m will be greater than 0 So, 3^m* (3^m  2) > 0 if (3^m  2) is > 0 (3^m  2) > 0 for all positive values of m (3^m  2) < 0 for 0 and all negative values of m So, Answer will be A Hope it helps!
_________________
Ankit
Check my Tutoring Site > Brush My Quant
GMAT Quant Tutor How to start GMAT preparations? How to Improve Quant Score? Gmatclub Topic Tags Check out my GMAT debrief
How to Solve : Statistics  Reflection of a line  Remainder Problems  Inequalities



Director
Joined: 25 Apr 2012
Posts: 683
Location: India
GPA: 3.21
WE: Business Development (Other)

Re: If n and m are integers, and x=3^n, and y=3^m, is the value
[#permalink]
Show Tags
05 Sep 2013, 07:42
saurabhsingh24 wrote: If n and m are integers, and x=3^n, and y=3^m, is the value of x greater than the value of 2y?
(1) n=m+1 (2) n=2m Basically the Q asks whether 3^n> 2*3^m St 1 substituting for n we get 3^(m+1)  2*3^m > 0 3* 3^m 2 *3^m>0 3^m>0 > m can be 0 or 1 or 2 and so one so n= m+1 (1 or 2 or 3 for corresponding values of m) We see that 3^n > 2*3^m So A is sufficient so ruling out B,C and E From st 2 we have n= 2m We get 3^2m 2*3^m>0 9*3^m  2*3^m> 0 or 7*3^m>0 So m =0, n=0 >putting in the above equation we get (3^2m 2*3^m>0) > 12 =1 not greater than zero But if m=1,n=2 then we get 3^2m 2*3^m>0 >96>0 3>0 so 2 ans choices possible so D ruled out Ans is A
_________________
“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.”



Intern
Joined: 05 Aug 2012
Posts: 15

Re: If n and m are integers, and x=3^n, and y=3^m, is the value
[#permalink]
Show Tags
18 Sep 2013, 17:35
Here is how I solved it, x = 3^n and y =3^m 1. n = m +1; therefore, x = 3^m+1 => 3 * 3^m, now 3^m = y, therefore x = 3y and hence x > 2y Sufficient 2. n =2m; x = 3^2m; x = y^2; now nothing is given about x and y; therefore for y = 0; x =0 and hence the x is not greater than 2y whereas if y =1, x = 1 again not satisfied, if y = 2, x = 4 ; x = 2y; if y = 3, x = 9; hence NS
Therefore answer is .A.
Please let me know in case my line of reasoning is not correct, especially for the second statement.



Senior Manager
Joined: 07 Sep 2014
Posts: 345
Concentration: Finance, Marketing

Re: If n and m are integers, and x=3^n, and y=3^m, is the value
[#permalink]
Show Tags
23 Aug 2016, 21:57
If n and m are integers, and x=3^n, and y=3^m, is the value of x greater than the value of 2y?
(1) n=m+1 (2) n=2m
3^n > 2*3^m ? 3^nm >2
s0 nm >=1 A sufficient
2. n =2m
if n=0 m =0 no. if n=2 m =4 yes



NonHuman User
Joined: 09 Sep 2013
Posts: 9419

Re: If n and m are integers, and x=3^n, and y=3^m, is the value
[#permalink]
Show Tags
11 Jan 2019, 14:49
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




Re: If n and m are integers, and x=3^n, and y=3^m, is the value &nbs
[#permalink]
11 Jan 2019, 14:49






