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

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

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.

\(2m^2 + n^2 = 27\)
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).

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