Proving circles that are indentical

Question

Here is a GRE problem

And the answer is B which is "Quantity B is greater". How do you prove that the three circles are identical given the area of the intersection of any two is the same, which is 15 here.

Answer 1

So, when two circles intersect, we know their area of overlap will be $15$. Also, we know the area of each circle is $40$.

Here we can do something clever: The bottom left shaded region is equal to the same shaped in the top right circle. That is, we know have area equal to a full circle minus a section of intersection. This place of intersection, however, has to be $15$ per the statement, and the area of a circle is $40$. So, $40-15=25$. Clearly, $25<30$..