√(xy) = xy.Vincen wrote:If $$\sqrt{xy}=xy$$ what is the value of x + y?
(1) x = -1/2
(2) y is not equal to zero
This equation is valid only in two cases:
xy=1.
xy=0.
Statement 1: x=-1/2
Case 1: x=-1/2 and y=-2, with the result that xy = 1 and x+y = (-1/2) + (-2) = -5/2
Case 2: x=-1/2 and y=0, with the result that xy = 0 and x+y = (-1/2) + 0 = -1/2.
Since x+y can be different values, INSUFFICIENT.
Statement 2: y≠0
Case 1 also satisfies Statement 2.
In Case 1, x+y = -5/2.
Case 3: x=0 and y=1, with the result that xy = 0 and x+y = 0+1 = 1.
Since x+y can be different values, INSUFFICIENT.
Statements combined:
Since x=-1/2 and y≠0, it is not possible that xy=0.
Thus, xy=1.
Since xy=1 and x=-1/2, y=-2.
Thus, x+y = -1/2 + (-2) = -5/2.
SUFFICIENT.
The correct answer is C.
