Last visit was: 06 Sep 2026, 05:05 It is currently 06 Sep 2026, 05:05
Home
Messages
Tests
Schools
Events
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
   1   2 
User avatar
exc4libur
User avatar
Joined: 24 Nov 2016
Last visit: 22 Mar 2022
Posts: 1,678
Own Kudos:
1,495
Given Kudos: 607
Location: United States
Posts: 1,678
Kudos: 1,495
What is the value of mn? 09 Dec 2019, 11:07
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Quote:

What is the value of mn?

(1) \(5^m∗3^n=45\)

(2) 9(m−1)(n−2)=1
Show more

(1) \(5^m∗3^n=45\) insufic

\(5^m∗3^n=5*3^2…(m,n)=(1,2;ln(45)/ln(5),0;0,ln(45)/ln(3)\)

(2) \(9^{(m−1)(n−2)}=1\) insufic

(m,n)=(1,any;any,2)

(1)&(2) sufic

From (2) we know that they are integers ≠ 0, so from (1) mn=(1,2)=2.

Ans (C)
User avatar
Kinshook
User avatar
Major Poster
Joined: 03 Jun 2019
Last visit: 04 Sep 2026
Posts: 6,129
Own Kudos:
6,089
Given Kudos: 164
Location: India
Schools: HBS '26 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Products:
My Reviews
Schools: HBS '26 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
Posts: 6,129
Kudos: 6,089
What is the value of mn? 04 Jan 2020, 10:57
Kudos
Add Kudos
Bookmarks
Bookmark this Post
gmatbusters

GMATBusters’ Quant Quiz Question -1



What is the value of mn?

(1) \(5^m*3^n=45\)

(2) \(9^{(m-1)(n-2)}=1\)
Show more

Asked: What is the value of mn?

(1) \(5^m*3^n=45\)
Since m & n may not be positive integers
NOT SUFFICIENT

(2) \(9^{(m-1)(n-2)}=1\)
(m-1)(n-2) = 0
Either m=1 or n=2 or both
NOT SUFFICIENT

(1) + (2)
(1) \(5^m*3^n=45\)
(2) \(9^{(m-1)(n-2)}=1\)
m = 1 or n=2 or both
If m=1
5^1*3^n=45
n=2
If n=2
5^m*3^2 = 45
m=1
m=1 & n=2
mn=2
SUFFICIENT

IMO C
User avatar
uchihaitachi
User avatar
Joined: 20 Aug 2017
Last visit: 06 Jul 2024
Posts: 88
Own Kudos:
244
Given Kudos: 174
Posts: 88
Kudos: 244
What is the value of mn? 12 Mar 2020, 11:29
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Sir, we factorise a number into prime factors.
In statement A, 15 is not a prime factor.
So, how did you eliminate A?

Archit3110
value of m*n
#1
45= 3^2*5^1
so m=1 and n=2 ; mn= 2
sufficient
Or 15^1*3^1 mn =1 insufficient
#2
9^(m−1)(n−2)=1
possible 9^0
so either m=1 or n=2
but value of m and n can be different if either of them is m=1 or n=2 or could be same as well
m*n could vary
insufficient
From 1&2
M =1 n=2
IMO c


What is the value of mn?

(1) 5m∗3n=45

(2) 9^(m−1)(n−2)=1
Show more
User avatar
NandishSS
User avatar
Joined: 06 Jan 2015
Last visit: 28 Jan 2021
Posts: 700
Own Kudos:
1,823
Given Kudos: 579
Location: India
Concentration: Operations, Finance
GPA: 3.35
WE:Information Technology (Computer Software)
Posts: 700
Kudos: 1,823
What is the value of mn? 29 Mar 2020, 05:04
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Quote:

GMATBusters’ Quant Quiz Question -1



What is the value of mn?

(1) \(5^m*3^n=45\)

(2) \(9^{(m-1)(n-2)}=1\)
Show more

HI VeritasKarishma, Bunuel, GMATBusters

Can you please show me how apart from m=1 & n=2 doesn't satisfy?

Any other values please.
User avatar
GMATBusters
User avatar
GMAT Tutor
Joined: 27 Oct 2017
Last visit: 21 Aug 2026
Posts: 1,925
Own Kudos:
7,041
Given Kudos: 242
WE:General Management (Education)
Expert
Expert reply
Posts: 1,925
Kudos: 7,041
What is the value of mn? 29 Mar 2020, 05:12
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Please rephrase your question, I am unable to understand your doubt.

NandishSS
Quote:

GMATBusters’ Quant Quiz Question -1



What is the value of mn?

(1) \(5^m*3^n=45\)

(2) \(9^{(m-1)(n-2)}=1\)

HI VeritasKarishma, Bunuel, GMATBusters

Can you please show me how apart from m=1 & n=2 doesn't satisfy?

Any other values please.
Show more
User avatar
NandishSS
User avatar
Joined: 06 Jan 2015
Last visit: 28 Jan 2021
Posts: 700
Own Kudos:
1,823
Given Kudos: 579
Location: India
Concentration: Operations, Finance
GPA: 3.35
WE:Information Technology (Computer Software)
Posts: 700
Kudos: 1,823
What is the value of mn? 29 Mar 2020, 05:19
Kudos
Add Kudos
Bookmarks
Bookmark this Post
GMATBusters
Please rephrase your question, I am unable to understand your doubt.

NandishSS
Quote:

GMATBusters’ Quant Quiz Question -1



What is the value of mn?

(1) \(5^m*3^n=45\)

(2) \(9^{(m-1)(n-2)}=1\)

HI VeritasKarishma, Bunuel, GMATBusters

Can you please show me how apart from m=1 & n=2 doesn't satisfy?

Any other values please.
Show more

Can you show how A is not sufficient if m & n are positive. Any example .

\(5^m*3^n=45 ==> 5^m*3^n=5^1*3^2\)

I couldn't figureout anyother value than m=1 & n=2
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 06 Sep 2026
Posts: 113,157
Own Kudos:
839,470
Given Kudos: 111,335
Products:
GMAT Club Tests
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 113,157
Kudos: 839,470
What is the value of mn? 29 Mar 2020, 05:21
Kudos
Add Kudos
Bookmarks
Bookmark this Post
NandishSS


Can you show how A is not sufficient if m & n are positive. Any example .

\(5^m*3^n=45 ==> 5^m*3^n=5^1*3^2\)

I couldn't figureout anyother value than m=1 & n=2
Show more

Already replied tho your question: https://gmatclub.com/forum/what-is-the- ... l#p2483882
User avatar
GMATBusters
User avatar
GMAT Tutor
Joined: 27 Oct 2017
Last visit: 21 Aug 2026
Posts: 1,925
Own Kudos:
7,041
 [1]
Given Kudos: 242
WE:General Management (Education)
Expert
Expert reply
Posts: 1,925
Kudos: 7,041
 [1]
What is the value of mn? 29 Mar 2020, 05:22
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ST1 : \(5^2 = 25\)
\(5^3 = 125\)
hence there is a number m , such that 2<m<3 and \(5^m = 45\)

Similarly, \(3^3 = 27 \) and \( 3^4 = 81\)
hence there is a number n , such that 3<n<4 and \(3^n = 45\)

I hope it is clear now


NandishSS
Quote:

GMATBusters’ Quant Quiz Question -1



What is the value of mn?

(1) \(5^m*3^n=45\)

(2) \(9^{(m-1)(n-2)}=1\)

HI VeritasKarishma, Bunuel, GMATBusters

Can you please show me how apart from m=1 & n=2 doesn't satisfy?

Any other values please.
Show more
User avatar
NandishSS
User avatar
Joined: 06 Jan 2015
Last visit: 28 Jan 2021
Posts: 700
Own Kudos:
1,823
Given Kudos: 579
Location: India
Concentration: Operations, Finance
GPA: 3.35
WE:Information Technology (Computer Software)
Posts: 700
Kudos: 1,823
What is the value of mn? 29 Mar 2020, 05:26
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Thanks Bunuel, GMATBusters

It is Clear now :-)
User avatar
pranayeekarmakar
User avatar
Joined: 14 Jun 2014
Last visit: 10 Apr 2023
Posts: 106
Own Kudos:
45
Given Kudos: 362
Location: India
Schools: ISB'22 IIM Booth '22
GPA: 4
Schools: ISB'22 IIM Booth '22
Posts: 106
Kudos: 45
What is the value of mn? 06 Apr 2020, 11:49
Kudos
Add Kudos
Bookmarks
Bookmark this Post
St1.
5^m . 3^n = 5.3^2
or 5^(m-1)= 3^(2-n)
or m-1=2-n
or m+n=3
so m=1 , n=2 or m=-3, n=5 so imsufficient

St2.
3^2(m-1) (n-2)=1
or 2(m-1) (n-2) = 0
so m=1 or n=2 or m=1 & n=2
so insufficient

St1 + St2

if m=1, n=3-1=2 so mn =2
if n=2 , m=1 so mn=2

sufficient hence C
avatar
fireagablast
avatar
Joined: 30 Jun 2019
Last visit: 17 Aug 2021
Posts: 259
Own Kudos:
133
Given Kudos: 8
Posts: 259
Kudos: 133
What is the value of mn? 06 Apr 2020, 14:44
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Answer is C

(1) right off the bat, i noticed it doesn't say m and n are integers. This leaves the door wide open for odd combinations of numbers to make the statement true. INSUFFICIENT
(2) as long as m or n is 1 or 2 and the exponent equals 0, the other number can be anything. INSUFFICIENT

C -> (2) states that m or n has to be 1 or 2, and placing that condition on (1) forces the other number to a single value. SUFFICIENT
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 39,212
Own Kudos:
1,157
Posts: 39,212
Kudos: 1,157
What is the value of mn? 15 Dec 2024, 08:56
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
   1   2 
Moderators:
Bunuel
Math Expert
113157 posts
FrozenDragon
DI Forum Moderator
409 posts