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 = positiveBy 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 = NThis 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 statementsWe 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