Four numbers w,x,y,z satisfy w<x<y<z. Each of the six possible pairs of distinct numbers has a different sum. The four smallest sums are 1,2,3, and 4. What is the sum of all possible values of z?
Answer Choices
A. 4
B. \frac{13}{2}
C. \frac{17}{2}
D. \frac{15}{2}
E. 7