Data Sufficiency

Is the area of circle X larger than the area of square Y?

(1) The diagonal of square Y is greater than the diameter of circle X.
(2) The perimeter of square Y is equal to the circumference of circle X.

OA : B

manik11 wrote:Is the area of circle X larger than the area of square Y?

(1) The diagonal of square Y is greater than the diameter of circle X.
(2) The perimeter of square Y is equal to the circumference of circle X.

OA : B

Statement 1:
Case 1:
In Y, diagonal = 2√2, implying that s = 2.
In X, diameter = 2, implying that r = 1.
Area of Y = s² = 2² = 4.
Area of X = πr² = π(1)² = π ≈ 3.
In this case, X<Y, so the answer to the equation stem is NO.

Case 2:
In Y, diagonal = 3√2, implying that s = 3.
In X, diameter = 4, implying that r = 2.
Area of Y = s² = 3² = 9.
Area of X = πr² = π(2)² = 4π ≈ 12.
In this case, X>Y, so the answer to the equation stem is YES.

Since the answer is NO in Case 1 but YES in Case 2, INSUFFICIENT.

Statement 2:
Let s = side in Y and r = radius of X.
Since perimeter of Y = circumference of X, we get:
4s = 2Ï€r.
s = 2πr/4 = πr/2.

Thus:
Area of Y = s² = (πr/2)² = (π/4)(πr²) ≈ (3/4)πr².
Area of X = πr².
Since πr² > (3/4)πr², X>Y.
SUFFICIENT.

The correct answer is B.