Data Sufficiency

lheiannie07 wrote:If P and Q are circular regions, what is the radius of the larger of these regions?

(1) The area of P plus the area of Q is equal to 90�
(2) The larger circular region has a radius that is 3 times the radius of the smaller circular region

Statement 1:
Case 1: larger circle = 50Ï€, smaller circle = 40Ï€
Case 2: larger circle = 60Ï€, smaller circle = 30Ï€
Since the larger circle can have different areas, its radius cannot be determined.
INSUFFICIENT.

Statement 2:
Here, the radius of the larger circle can be any positive value.
INSUFFICIENT.

Statements combined:
Let r = the radius the smaller circle and 3r = the radius of the larger circle.
Area of the smaller circle = πr².
Area of the larger circle = π(3r)² = 9πr².
Since the sum of the two areas is 90Ï€, we get:
πr² + 9πr² = 90π
10πr² = 90π
r² = 9
r = 3.
Thus, the radius of the larger circle = 3r = 3*3 = 9.
SUFFICIENT.

The correct answer is C.