A Classic “Donut” Problem
This comic from XKCD is not only hilarious, but presents a remarkably GRE-like scenario:
So, here’s a question — what is the area of the “donut” shape in which the man in the comic is legally permitted to move?
Answer the question yourself before clicking “More.”
Solution: The 600-yard distance can be thought of as a radius, with the woman at the center of the circle. Using Area = πr2, the area of a circle with radius 600 yards is 360,000π square yards.
The 500-yard distance can also be thought of as a radius of the same circle. The area of a circle with radius 500 yards is 250,000π square yards.
On the GRE, a problem of this type would likely show a diagram like this and ask for the area of the shaded region — this is the same region that the man in our cartoon is allowed to move in:
This image should make it obvious that our final move is simply to subtract the area of the smaller circle from the area of the larger circle.
360,000π – 250,000π = 110,000π
110,000π square yards is about 345,400 square yards (π = 3.1415…), but on the GRE, answers are generally written in with the π intact, so 110,000π would be our final answer.
Note that, as the woman moves around, the area of the donut shape will not be affected. Instead, the entire figure (two concentric circles with the woman at the center) will simply translate in some direction. While this would make it very hard for the man to obey the ridiculous restraining order, it does not affect the answer to this problem.