Last visit was: 15 May 2026, 04:49 It is currently 15 May 2026, 04:49
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
555-605 (Medium)|   Algebra|   Exponents|      
User avatar
GMATBusters
User avatar
GMAT Tutor
Joined: 27 Oct 2017
Last visit: 08 May 2026
Posts: 1,922
Own Kudos:
6,890
 [11]
Given Kudos: 241
WE:General Management (Education)
Expert
Expert reply
Posts: 1,922
Kudos: 6,890
 [11]
If a^m*a^n = a^(mn), what is the value of m(n-2)+n(m-2)? 15 Feb 2020, 18:58
2
Kudos
Add Kudos
9
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

25% (medium)

Question Stats:

81% (01:35) correct 19% (02:08) wrong based on 269 sessions

History

Date
Time
Result
Not Attempted Yet

GMATBusters’ Quant Quiz Question -1


If a^m*a^n = a^(mn), what is the value of m(n-2)+n(m-2)?

A. -1
B. -1/2
C. 0
D. ½
E. 2
ShowHide Answer
Official Answer
C
User avatar
shameekv1989
User avatar
Joined: 14 Dec 2019
Last visit: 17 Jun 2021
Posts: 816
Own Kudos:
1,012
 [3]
Given Kudos: 354
Location: Poland
Concentration: Entrepreneurship, Strategy
Schools: Cambridge '22 (D) WBS (A$) IIMA PGPX'22 (D) WHU MBA (WD) ISB'22 (D)
GMAT 1: 640 Q49 V27
GMAT 2: 660 Q49 V31
GMAT 3: 720 Q50 V38
GPA: 4
WE:Engineering (Consumer Electronics)
Products:
My Reviews
Schools: Cambridge '22 (D) WBS (A$) IIMA PGPX'22 (D) WHU MBA (WD) ISB'22 (D)
GMAT 3: 720 Q50 V38
Posts: 816
Kudos: 1,012
 [3]
If a^m*a^n = a^(mn), what is the value of m(n-2)+n(m-2)? Updated on: 15 Feb 2020, 19:05
Originally posted by shameekv1989 on 15 Feb 2020, 19:04.
Last edited by shameekv1989 on 15 Feb 2020, 19:05, edited 1 time in total.
1
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
If \(a^m*a^n = a^{mn}\), what is the value of \(m(n-2)+n(m-2)\)?
A. -1
B. -1/2
C. 0
D. ½
E. 2

\(a^m*a^n = a^{mn}\) => \(a^{m+n} = a^{mn}\)

=> m+n = mn

\(m(n-2)+n(m-2) = mn-2m+nm-2n = 2(mn-m-n) = 2(mn-(m+n)) = 0\) - Answer C
User avatar
pk123
User avatar
Joined: 16 Sep 2011
Last visit: 26 Apr 2020
Posts: 104
Own Kudos:
123
 [1]
Given Kudos: 158
Products:
My Reviews
Posts: 104
Kudos: 123
 [1]
If a^m*a^n = a^(mn), what is the value of m(n-2)+n(m-2)? 15 Feb 2020, 19:04
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
a^m*a^n = a^mn
a^m*a^n = a^m+n
Hence m+n=mn
m(n-2)+n(m-2)
=2mn - 2(m+n)
=2mn- 2mn
=0

C is the answer

Posted from my mobile device
User avatar
KhulanE
User avatar
McDonough School Moderator
Joined: 04 Jun 2019
Last visit: 20 Jul 2024
Posts: 154
Own Kudos:
162
Given Kudos: 102
Location: Mongolia
Concentration: Finance, Technology
Schools: Fuqua '24 (M$) Columbia CBS '24 (D) McDonough '24 (WD) Tepper '24 (WD)
GMAT Date: 08-28-2021
GRE 1: Q165 V153
GRE 2: Q167 V151
GPA: 3.7
WE:Securities Sales and Trading (Retail Banking)
Schools: Fuqua '24 (M$) Columbia CBS '24 (D) McDonough '24 (WD) Tepper '24 (WD)
GRE 1: Q165 V153
GRE 2: Q167 V151
Posts: 154
Kudos: 162
If a^m*a^n = a^(mn), what is the value of m(n-2)+n(m-2)? Updated on: 15 Feb 2020, 21:31
Originally posted by KhulanE on 15 Feb 2020, 19:14.
Last edited by KhulanE on 15 Feb 2020, 21:31, edited 1 time in total.
Kudos
Add Kudos
Bookmarks
Bookmark this Post
From the first formula we can find m+n=mn by simplifying the equation as did below.
a^m*a^n=a^(m+n)
a^(m+n)=a^mn => m+n=mm

Then we try to simplify the problem as did below
m(n-2)+n(m-2)=mn-2m+mn-2m=2mn-2m-2n=2(mn-m-n)=2(mn-(m+n))
As you can see the simplified outcome is 2(mn-(m+n))

Since m+n=mm we can substitute m+n for mn as did below
2(mn-(m+n)=2(mn-mn)=O
So C is right

Posted from my mobile device
User avatar
Raxit85
User avatar
Joined: 22 Feb 2018
Last visit: 02 Aug 2025
Posts: 761
Own Kudos:
1,206
 [1]
Given Kudos: 135
Posts: 761
Kudos: 1,206
 [1]
If a^m*a^n = a^(mn), what is the value of m(n-2)+n(m-2)? 15 Feb 2020, 19:25
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
a^m.a^n=a^mn
a^(m+n)=a^mn
m+n=mn
m(n-2)+n(m-2)
=mn-2m+mn-2n
=2mn-2(m+n)
=2mn-2mn
=0
Hence, Ans. is C.
avatar
ajaymahadev
avatar
Joined: 13 Nov 2019
Last visit: 25 Feb 2020
Posts: 26
Own Kudos:
11
Given Kudos: 59
Location: India
Concentration: International Business, Marketing
Schools: ESSEC MiM "22 HEC MiM "22 EDHEC MiM "22
GPA: 4
Schools: ESSEC MiM "22 HEC MiM "22 EDHEC MiM "22
Posts: 26
Kudos: 11
If a^m*a^n = a^(mn), what is the value of m(n-2)+n(m-2)? 15 Feb 2020, 19:41
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The answer would be 0. This is a pretty easy one.
Attachments

New Doc 2020-02-16 08.09.13_1.jpg
New Doc 2020-02-16 08.09.13_1.jpg [ 132.22 KiB | Viewed 5981 times ]

User avatar
globaldesi
User avatar
Joined: 28 Jul 2016
Last visit: 23 Feb 2026
Posts: 1,140
Own Kudos:
2,011
Given Kudos: 67
Location: India
Concentration: Finance, Human Resources
Schools: ISB '18 (D)
GPA: 3.97
WE:Project Management (Finance: Investment Banking)
Products:
My Reviews
Schools: ISB '18 (D)
Posts: 1,140
Kudos: 2,011
If a^m*a^n = a^(mn), what is the value of m(n-2)+n(m-2)? 15 Feb 2020, 21:05
Kudos
Add Kudos
Bookmarks
Bookmark this Post
given
mn = m+n

equation
m(n-2)+n(m-2)
mn-2m +mn-2n
2mn-2(m+n)
from given stmt
2mn -2mn =0
thus C
avatar
aditibarjatya
avatar
Joined: 25 Mar 2013
Last visit: 27 Sep 2020
Posts: 11
Given Kudos: 42
Posts: 11
Kudos: 0
If a^m*a^n = a^(mn), what is the value of m(n-2)+n(m-2)? 15 Feb 2020, 22:35
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Solution:

Question 1: If \(a^m*a^n = a^{mn}\), what is the value of \(m(n-2)+n(m-2)\)?


LHS = \(a^m*a^n = a^{m + n}\)

RHS = \(a^{mn} \)

By equating both the LHS and RHS, we get: \(a^{m + n} = a^{mn}\) [Equation 1]

Now, in order to find out the value of expression, \(m(n - 2) + n(m - 2)\), we would first expand the expression by removing the parenthesis.

Therefore, \(m(n - 2) + n(m - 2) = mn - 2m + mn - 2n = 2mn - 2(m + n) = 2(mn - m - n)\) [Equation 2]

From Equation 1 we get, \(m + n = mn\) since, base is ''a'' on LHS and RHS.

Thus, \(mn - m - n = 0 \) and by substituting this value in Equation 2 we get: \(2(mn - m - n) = 2*0 = 0\), which is the answer.

Therefore, Option C i.e., 0 is the correct answer of question 1.
User avatar
shridhar786
User avatar
Joined: 31 May 2018
Last visit: 08 Feb 2022
Posts: 322
Own Kudos:
1,761
Given Kudos: 132
Location: United States
Concentration: Finance, Marketing
Posts: 322
Kudos: 1,761
If a^m*a^n = a^(mn), what is the value of m(n-2)+n(m-2)? 16 Feb 2020, 00:07
Kudos
Add Kudos
Bookmarks
Bookmark this Post
If a^m*a^n = a^mn, what is the value of m(n-2)+n(m-2)?

a^m*a^n = a^mn

a^(m+n) = a^mn ---(laws of exponent)

from here we get -- (m+n) = mn
now,
m(n-2)+n(m-2) = mn-2m+mn-2n = 2mn-2(m+n) = 2{mn-(m+n)} = 0 (since m+n = mn)

C is the correct answer
User avatar
QuantMadeEasy
User avatar
Joined: 28 Feb 2014
Last visit: 01 Mar 2026
Posts: 502
Own Kudos:
805
Given Kudos: 78
Location: India
Concentration: General Management, International Business
GPA: 3.97
WE:Engineering (Education)
Posts: 502
Kudos: 805
If a^m*a^n = a^(mn), what is the value of m(n-2)+n(m-2)? 16 Feb 2020, 00:17
Kudos
Add Kudos
Bookmarks
Bookmark this Post
a^m*a^n = a^mn
a^{m+n} = a^mn
m+n = mn

let m=2, n=2
Substituting values of m and n in the expression m(n-2)+n(m-2) = 0

IMO C
avatar
asterias
avatar
Current Student
Joined: 16 Jan 2018
Last visit: 25 Jan 2022
Posts: 6
Own Kudos:
34
Given Kudos: 91
Posts: 6
Kudos: 34
If a^m*a^n = a^(mn), what is the value of m(n-2)+n(m-2)? Updated on: 16 Feb 2020, 07:21
Originally posted by asterias on 16 Feb 2020, 00:50.
Last edited by asterias on 16 Feb 2020, 07:21, edited 1 time in total.
Kudos
Add Kudos
Bookmarks
Bookmark this Post
GIVEN: \( a^{m} * a^{n} = a^{mn}\)
TO FIND: m(n-2)+n(m-2)

given: \( a^{m} * a^{n} = a^{mn}\)
=> \( a^{m+n} = a^{mn}\)
=> \(m+n = mn \)
=> \(m + n - mn = 0\) --- Eqn. (1)

We have to find the value of:
= \( m(n-2)+n(m-2) \)
= \( mn - 2m + mn - 2n \)
= \( 2mn - 2m - 2n \)
= \(2(mn - m - n)\) --- Eqn. (2)
= \( -2 (m + n - mn) \) {taking -1 as common from the bracket}
= \( -2 ( 0 ) = 0 \) {as we know from Eqn. (1) that: m + n - mn = 0}

Hence, our answer is 0.
User avatar
cantaffordname
User avatar
Joined: 27 Mar 2019
Last visit: 27 Dec 2025
Posts: 154
Own Kudos:
271
Given Kudos: 86
Products:
My Reviews
Posts: 154
Kudos: 271
If a^m*a^n = a^(mn), what is the value of m(n-2)+n(m-2)? 16 Feb 2020, 01:10
Kudos
Add Kudos
Bookmarks
Bookmark this Post
a^m.a^n=a^mn

a^(m+n)=a^mn

m+n=mn

Let it be equation 1

Now

m(n-2)+n(m-2)

=mn-2m+mn-2n

=2mn-2(m+n)

And from equation 1 (m+n)=mn

=2mn-2mn

=0
User avatar
gmatway
User avatar
Joined: 01 Dec 2018
Last visit: 05 Dec 2020
Posts: 140
Own Kudos:
164
Given Kudos: 333
Concentration: Entrepreneurship, Finance
Schools: HBS '21 ISB'22
GPA: 4
WE:Other (Retail Banking)
Schools: HBS '21 ISB'22
Posts: 140
Kudos: 164
If a^m*a^n = a^(mn), what is the value of m(n-2)+n(m-2)? 16 Feb 2020, 03:29
Kudos
Add Kudos
Bookmarks
Bookmark this Post
upon solving m(n-2)+n(m-2) we get 2(mn-m-n) =>2(mn - (m+n)) => 2(mn-mn) => ans zero (C)
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 15 May 2026
Posts: 110,428
Own Kudos:
814,984
 [1]
Given Kudos: 106,261
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 110,428
Kudos: 814,984
 [1]
If a^m*a^n = a^(mn), what is the value of m(n-2)+n(m-2)? 16 Feb 2020, 03:53
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
If a^m*a^n = a^(mn), what is the value of m(n-2)+n(m-2)?

A. -1
B. -1/2
C. 0
D. ½
E. 2

There should be some constraints given for a.

If a = 1, then any values of m and n satisfy a^m*a^n = a^(mn).
If a = 0, then any positive values of m and n satisfy a^m*a^n = a^(mn).
If a = -1, also many values of m and n satisfy a^m*a^n = a^(mn). For example, m = n = even.
User avatar
bM22
User avatar
Retired Moderator
Joined: 05 May 2016
Last visit: 17 Jul 2025
Posts: 519
Own Kudos:
810
Given Kudos: 1,316
Location: India
Schools: IIM (A) IIM (A) IIM-A '24 (A) ISB '24 (A)
Products:
My Reviews
Schools: IIM (A) IIM (A) IIM-A '24 (A) ISB '24 (A)
Posts: 519
Kudos: 810
If a^m*a^n = a^(mn), what is the value of m(n-2)+n(m-2)? 16 Feb 2020, 06:20
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Solution:

a^m*a^n = a^mn => m+n=mn => mn-m-n = 0

for the question asked:

value of mn-2m+mn-2n => 2(mn-m-n) => 0 since mn-m-n = 0;


Answer : 0
User avatar
itspC
User avatar
Joined: 05 Jul 2017
Last visit: 13 May 2026
Posts: 78
Own Kudos:
902
Given Kudos: 108
Location: India
GMAT 1: 760 Q51 V41 (Online)
GMAT 1: 760 Q51 V41 (Online)
Posts: 78
Kudos: 902
If a^m*a^n = a^(mn), what is the value of m(n-2)+n(m-2)? 16 Feb 2020, 08:26
Kudos
Add Kudos
Bookmarks
Bookmark this Post
OK lets do it in within 1 minute.

From the given equation :mn=m+n

-->2(mn-(m+n))=0
So
Ans: (C) 0
User avatar
Fdambro294
User avatar
Joined: 10 Jul 2019
Last visit: 20 Aug 2025
Posts: 1,330
Own Kudos:
774
Given Kudos: 1,656
Posts: 1,330
Kudos: 774
If a^m*a^n = a^(mn), what is the value of m(n-2)+n(m-2)? 06 Dec 2021, 02:41
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Was just going to write this, but of course the master beat me to it a long time ago 😊

Bunuel
If a^m*a^n = a^(mn), what is the value of m(n-2)+n(m-2)?

A. -1
B. -1/2
C. 0
D. ½
E. 2

There should be some constraints given for a.

If a = 1, then any values of m and n satisfy a^m*a^n = a^(mn).
If a = 0, then any positive values of m and n satisfy a^m*a^n = a^(mn).
If a = -1, also many values of m and n satisfy a^m*a^n = a^(mn). For example, m = n = even.
Show more

Posted from my mobile device
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 39,070
Own Kudos:
1,124
Posts: 39,070
Kudos: 1,124
If a^m*a^n = a^(mn), what is the value of m(n-2)+n(m-2)? 14 Apr 2026, 19:33
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.
Moderators:
Bunuel
Math Expert
110428 posts
Krunaal
Tuck School Moderator
852 posts