Joy has 30 thin rods, one each of every integer length from 1 \mathrm{~cm} through 30 \mathrm{~cm}. She places the rods with lengths 3 \mathrm{~cm}, 7 \mathrm{~cm}, and 15 \mathrm{~cm} on a table. She then wants to choose a fourth rod that she can put with these three to form a quadrilateral with positive area. How many of the remaining rods can she choose as the fourth rod?

**Answer Choices**

A. 16

B. 17

C. 18

D. 19

E. 20