Each statement by itself is insufficient, since we do not have any kind of relationship between the radii of the two circles or between any other related size.

But put together, you get that:
1. 2Pi*a + 2Pi*b = 20Pi, or a + b = 10, so b = 10 - a
2. Pi*a^2 + Pi*b^2 = 50Pi, or a^2 + b^2 = 50. Substitute the above and you get that:
a^2 + (10 - a)^2 = a^2 + 100 - 20a + a^2 = 50, or 2a^2 - 20a + 50 = 0. This is equivalent to a^2 - 10a + 25 = 0, which in turn is equivalent to (a - 5)^2 = 0. This means a = 5, so area of circle A = Pi*25

IMO C

raama

What if we combine the information. If we call a the radius of circle A, and b the radius of Circle B, then we are looking for numbers that satisfy the equations 2πa + 2πb = 20π and πa² + πb² = 50π. Or when simplified, a + b = 10 and a² + b² = 50. Can you figure out what a and b are? Hint: the GMAT doesn't make these problems impossible and they never require use of the quadratic formula. Think positive integers.

Did you get a = b = 5? Congratulations. Since we get a unique answer when we combine information, the correct answer is C.