It's not easy to see that (√x + √y)² = x + 2√(xy) + y, however when we see that we have information about x and y and we need to find the value of √x and √y and y, we might start looking for possible relationships that might help us. One relationship is that (√x)² = x and that (√y)² =y
From there, it's a matter of exploring what (√x + √y)² might look like.
We can use the FOIL method to expand (√x + √y)²
We get: (√x + √y)² = (√x + √y)(√x + √y) = x + √xy + √xy +y = x + 2√xy + y
At this point, we can see that our exploration has paid off.

Keep in mind that solving math questions involves little explorations like this. Sometimes those explorations take us closer to the solution; sometimes they take us nowhere, in which case we need to try something else.

Cheers,
Brent
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Brent Hanneson – Founder of gmatprepnow.com

(1) 9+6=15
or, 12+3= 15
So, insufficient

(2) xy = 36
Which is : 4*9 = 36
12*3 = 36
So, there are two values of x and y.
insufficient.

Considering (1) and (2) x
([m]\sqrt{x} + \sqrt{y}[/m)^2= x+ y+2 [m]\sqrt{xy}
= 15+2.6
= 27
So, Ans is C.
_________________

Collections:-
PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html
DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html
100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html
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