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

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Given 2m^2 + n^2 = 27, what is the value of m?  [#permalink]

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Updated on: 29 Mar 2018, 20:17
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Given 2m^2 + n^2 = 27, what is the value of m?

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

The answer to the question according to the manual is C, but I don't understand How.

Originally posted by Anasarah on 28 Feb 2014, 08:55.
Last edited by Bunuel on 29 Mar 2018, 20:17, edited 2 times in total.
RENAMED THE TOPIC.
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Re: Given 2m^2 + n^2 = 27, what is the value of m?  [#permalink]

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28 Feb 2014, 13:39
Anasarah wrote:
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.

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
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Re: Given 2m^2 + n^2 = 27, what is the value of m?  [#permalink]

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11 Sep 2014, 05:48
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
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Re: Given 2m^2 + n^2 = 27, what is the value of m?  [#permalink]

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24 Jan 2016, 07:32
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

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Re: Given 2m^2 + n^2 = 27, what is the value of m?  [#permalink]

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25 Jan 2016, 16:59
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.

 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.
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Re: Given 2m^2 + n^2 = 27, what is the value of m?  [#permalink]

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29 Mar 2018, 20:17
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Re: Given 2m^2 + n^2 = 27, what is the value of m?   [#permalink] 29 Mar 2018, 20:17
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# Given 2m^2 + n^2 = 27, what is the value of m?

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