Bunuel wrote:

Is the area of circle C greater than the area of square S?

(1) The diameter of C is equal to the diagonal of square S.

(2) The perimeter of S is less than the circumference of C.

Hi,

Area of a circle is dependent on radius, r, and That of square on side, say a..

so if we know the ratio between radius and the side we can answer the Q..

(1) The diameter of C is equal to the diagonal of square S.This tells us that \(2r=\sqrt{2}a\)..

Suff..

(2) The perimeter of S is less than the circumference of C.since we are dealing with inequality sign, always better to check for the values..

\(4a<2*pi*r................. a<pi*\frac{r}{2}\).....................

since both sides are +ive, square both sides...

\(a^2<(pi*\frac{r}{2})^2.........................a^2<pi*r^2*\frac{pi}{4}\).......................

since pi/4 <1, we can safely say \(a^2<pi*r^2\) OR area of square < area of circle

Suff

D

_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372

2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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