Is xy an integer? (1) x is the ratio of the area of a squar

[BTGmoderatorDC]

Is xy an integer?

(1) x is the ratio of the area of a square to the area of the largest possible circle inscribed within that square.

(2) y is the ratio of the area of a circle to the area of the largest possible square inscribed within that circle.

OA C

Source: Manhattan Prep

[Ian Stewart]

Strange question - you obviously need to know about both x and y, so neither statement could be sufficient alone. But Statement 1 gives us the value of x, and Statement 2 gives us the value of y, so of course we can answer any question in the universe about x and y using both Statements, and the answer is C.

There's no reason to bother doing any calculation here, but if you do find the values of x and y, you'll find that x = 4/π, and y = π/2, so xy = 2.