2009 AMC 12B Problem 20

A convex polyhedron Q has vertices V_1,V_2,\ldots,V_n, and 100 edges. The polyhedron is cut by planes P_1,P_2,\ldots,P_n in such a way that plane P_k cuts only those edges that meet at vertex V_k. In addition, no two planes intersect inside or on Q. The cuts produce n pyramids and a new polyhedron R. How many edges does R have?

\textbf{(A)}\ 200\qquad \textbf{(B)}\ 2n\qquad \textbf{(C)}\ 300\qquad \textbf{(D)}\ 400\qquad \textbf{(E)}\ 4n

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.