Last visit was: 20 Nov 2025, 06:05 It is currently 20 Nov 2025, 06:05
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
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 Level|   Algebra|      
User avatar
Anasarah
User avatar
Joined: 25 Aug 2013
Last visit: 17 Jun 2014
Posts: 3
Own Kudos:
7
 [6]
Posts: 3
Kudos: 7
 [6]
Given 2m^2 + n^2 = 27, what is the value of m? Updated on: 29 Mar 2018, 21:17
Originally posted by Anasarah on 28 Feb 2014, 09:55.
Last edited by Bunuel on 29 Mar 2018, 21:17, edited 2 times in total.
RENAMED THE TOPIC.
2
Kudos
Add Kudos
4
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:

73% (01:09) correct 27% (01:18) wrong based on 231 sessions

History

Date
Time
Result
Not Attempted Yet
Given 2m^2 + n^2 = 27, what is the value of m?

(1) n is positive.
(2) m = n


Show Spoiler
The answer to the question according to the manual is C, but I don't understand How.
ShowHide Answer
Official Answer
C
User avatar
mikemcgarry
User avatar
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Last visit: 06 Aug 2018
Posts: 4,479
Own Kudos:
30,537
Given Kudos: 130
Expert
Expert reply
Posts: 4,479
Kudos: 30,537
Given 2m^2 + n^2 = 27, what is the value of m? 28 Feb 2014, 14:39
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Anasarah
I ran into this question which looked easy and yet confusing.

Given 2 M^2 + N^2=27, what is the value of M?

I. N=positive
II. M=N
The answer to the question according to the manual is C, but I don't understand How.
Show more
Dear Anasarah,
I'm happy to respond. :-)

Keep in mind, before looking at the statements, we have no idea whether M or N is even an integer. It could be that M = 0 and N = sqrt(27), or M = sqrt(27/2) and N = 0. We don't know.

Statement #1: N = positive
By itself, this is useless. We could have
M = 0, N = sqrt(27), or
M = 1, N = 5, or
M = 2, N = sqrt(23), or
M = 3, N = sqrt(21), or etc.
Many many possibilities. With this statement alone, we can determine absolutely nothing. This statement is insufficient.

Statement #2: M = N
This is intriguing. We can substitute M for N, and get

2(M^2) + (M^2) = 3(M^2) = 27

M^2 = 9

Now, here's the tricky part. What is the solution to the equation "something squared equals 9"? The benighted masses think the answer is only 3, and because of that, the GMAT nails them time and time again. We know, though, that the solution is either M = +3 or M = -3. M and N can have either one of those values. Since this statement does not determine a single unique value, it is not sufficient.

Combined statements
We almost got to the answer with the information in statement #2. When we add the information from statement #1, we reject the negative value and take the positive only. M = N = +3. This is now sufficient.

Does all this make sense?
Mike :-)
avatar
nvijayprasanna
avatar
Joined: 17 Apr 2012
Last visit: 10 May 2017
Posts: 12
Own Kudos:
45
 [1]
Given Kudos: 5
Location: United States
WE:Information Technology (Computer Software)
Posts: 12
Kudos: 45
 [1]
Given 2m^2 + n^2 = 27, what is the value of m? 11 Sep 2014, 06:48
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Quite a tricky one.

First statement, N is positive is not conclusive. will have multiple possibilities, like
m = 1, n = 5
m = 3, n = 3
m = 5, n = 1
Statement 1 not sufficient.

Second statement. we can derive to two possible solution. M = N
2M^2 + N^2 = 27
2 M^2 + M^2 = 27
3 M^2 = 27
M^2 = 9
M = +3 or - 3
So M=N=+3 or M=N=-3
Statement II not sufficient

Combining both, we have one solution M=N=3. So C
User avatar
Skywalker18
User avatar
Retired Moderator
Joined: 08 Dec 2013
Last visit: 15 Nov 2023
Posts: 2,039
Own Kudos:
9,963
Given Kudos: 171
Status:Greatness begins beyond your comfort zone
Location: India
Concentration: General Management, Strategy
GPA: 3.2
WE:Information Technology (Consulting)
Products:
My Reviews
Posts: 2,039
Kudos: 9,963
Given 2m^2 + n^2 = 27, what is the value of m? 24 Jan 2016, 08:32
Kudos
Add Kudos
Bookmarks
Bookmark this Post
2* m^2 + n^2 =27
(1) n is positive.
m can take different values depending on value of n
Not sufficient
(2) m = n
2* m^2 + n^2 =27
=> 3*m^2 = 27
=> m^2 = 9
=> m = 3 or -3
Not sufficient

Combining 1 and 2 , we get
Since n is positive and m=n . Therefore m = 3

Answer C
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,070
Own Kudos:
19,394
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,070
Kudos: 19,394
Given 2m^2 + n^2 = 27, what is the value of m? 25 Jan 2016, 17:59
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Given 2m^2 + n^2 = 27, what is the value of m?

(1) n is positive.
(2) m = n


When you modify the original condition and the question, there are 2 variables(m,n) and 1 equation (2m^2 + n^2 = 27), which should match with the number of equations. So you need 1 more equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), (n,m)=(1,5),(3,3), which is not unique and not sufficient.
For 2), (n,m)=(3,3),(-3,-3), which is not unique and not sufficient.
When 1) & 2), (n,m)=(3,3) is unique and sufficient.
Therefore, the answer is C.


 For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
User avatar
v12345
User avatar
Joined: 01 Mar 2015
Last visit: 22 Aug 2025
Posts: 399
Own Kudos:
1,084
Given Kudos: 44
Location: India
Posts: 399
Kudos: 1,084
Given 2m^2 + n^2 = 27, what is the value of m? 13 Aug 2021, 08:59
Kudos
Add Kudos
Bookmarks
Bookmark this Post
\(2m^2 + n^2 = 27\)
m can be rational or irrational.

(1) n is positive. Insufficient
m can have many values.

(2) m = n . Insufficient
\(3m^2 = 27\)
\(m^2 = 9\)
m = 3 or -3 . (two values)

Combining both, Sufficient
n is positive, m=n=3

Hence, OA is (C).
User avatar
SalahT
User avatar
Joined: 11 Jun 2021
Last visit: 10 Feb 2025
Posts: 278
Own Kudos:
421
Given Kudos: 18
GPA: 3.86
Posts: 278
Kudos: 421
Given 2m^2 + n^2 = 27, what is the value of m? 15 Aug 2021, 08:05
Kudos
Add Kudos
Bookmarks
Bookmark this Post
This can be done without any calculation:

1)
n can be any positive number \((1,5,1000.....)\)
Substituting a different value for n in the equation, will yield a different value of m.
Thus, Multiple value of m.
Thus, insufficient.

2)
m = n
the equation (2m^2 + n^2=27 => 3m^2 = 27) is quadratic equation where discriminant not equal to 0 .This equation will have two unequal values.
Thus, Multiple value of m.
Thus, insufficient.

1+2)
Form 2 we know it has two values 1 positive 1 negative.
Form 1 we know it has to be positive.
Thus, one value of m.
Thus, sufficient.

IMO Answer is C
Moderators:
Bunuel
Math Expert
105416 posts
kingbucky
496 posts