If n and m are integers, and x=3^n, and y=3^m, is the value : GMAT Data Sufficiency (DS)
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 03 Dec 2016, 16:14

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If n and m are integers, and x=3^n, and y=3^m, is the value

Author Message
TAGS:

### Hide Tags

Intern
Joined: 09 Mar 2011
Posts: 15
Location: Mumbai
Followers: 0

Kudos [?]: 7 [0], given: 3

If n and m are integers, and x=3^n, and y=3^m, is the value [#permalink]

### Show Tags

12 Sep 2012, 18:09
6
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

56% (02:41) correct 44% (01:23) wrong based on 142 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
[Reveal] Spoiler: OA

Last edited by Bunuel on 12 Sep 2012, 23:36, edited 1 time in total.
Renamed the topic and edited the question.
Manager
Joined: 02 Jun 2011
Posts: 114
Followers: 0

Kudos [?]: 42 [2] , given: 5

### Show Tags

12 Sep 2012, 19:58
2
KUDOS
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.
Director
Status: Tutor - BrushMyQuant
Joined: 05 Apr 2011
Posts: 582
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 570 Q49 V19
GMAT 2: 700 Q51 V31
GPA: 3
WE: Information Technology (Computer Software)
Followers: 97

Kudos [?]: 544 [2] , given: 55

### Show Tags

12 Sep 2012, 23:10
2
KUDOS
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

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: 22 Mar 2011
Posts: 612
WE: Science (Education)
Followers: 97

Kudos [?]: 865 [4] , given: 43

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
4
KUDOS
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.

_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Director
Joined: 25 Apr 2012
Posts: 728
Location: India
GPA: 3.21
Followers: 43

Kudos [?]: 666 [0], given: 723

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) --> 1-2 =-1 not greater than zero
But if m=1,n=2 then we get 3^2m -2*3^m>0 ------>9-6>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: 18
Followers: 0

Kudos [?]: 1 [0], given: 2

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

Please let me know in case my line of reasoning is not correct, especially for the second statement.
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 12855
Followers: 559

Kudos [?]: 157 [0], given: 0

Re: If n and m are integers, and x=3^n, and y=3^m, is the value [#permalink]

### Show Tags

30 Sep 2014, 22:23
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 Club Legend
Joined: 09 Sep 2013
Posts: 12855
Followers: 559

Kudos [?]: 157 [0], given: 0

Re: If n and m are integers, and x=3^n, and y=3^m, is the value [#permalink]

### Show Tags

09 Jul 2016, 12:11
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.
_________________
Senior Manager
Joined: 07 Sep 2014
Posts: 362
Concentration: Finance, Marketing
Schools: Yale '18
Followers: 5

Kudos [?]: 36 [0], given: 244

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^n-m >2

s0 n-m >=1
A sufficient

2. n =2m

if n=0 m =0 no.
if n=2 m =4 yes
Re: If n and m are integers, and x=3^n, and y=3^m, is the value   [#permalink] 23 Aug 2016, 21:57
Similar topics Replies Last post
Similar
Topics:
m and n are positive integers. What is the value of m? 2 09 Mar 2016, 11:23
3 If m and n are positive integers, what is the value of m + n? 6 28 Oct 2015, 06:17
6 If m and n are integers, then what is the value of (-1)^m 8 01 Mar 2011, 00:00
If m and n are negative integers, what is the value of mn? 6 29 Dec 2011, 07:45
10 If m and n are negative integers what is the value of m*n 5 28 Jan 2011, 04:57
Display posts from previous: Sort by