avohden wrote:

Is the perimeter of square S greater than the circumference of circle C ?

(1) S is inscribed in circle C.

(2) The ratio of the area of S to the area of C is 2:pi.

GH-05.22.13 | OE to follow

Is 4s>2*pi*r

let side of the square S be 's' and radius of the circle C be 'r'

From stmt1) S is inscribed in circle C, then Diameter 2r becomes the diagonal of the square S, then s^2 + s^2=(2r)^2

=>s^2=2r^2

=>s=r sqrt{2}

then 4*r sqrt{2} is not greater than 2*pi*r (pi=3.14 and sqrt{2} =1.414)

Hence stmt 1 alone is sufficient

From stmt 2) s^2/pi*r^2 = 2/pi

=>s^2=2r^2

=>s=r sqrt{2}

then 4*r sqrt{2}is not greater than 2*pi*r (pi=3.14 and sqrt{2} =1.414)

Hence stmt 2 alone is sufficient

Each stmt alone is sufficient