AHSME 1968 Problem 22

A segment of length $1$ is divided into four segments. Then there exists a quadrilateral with the four segments as sides if and only if each segment is: $\text{(A) equal to } \frac{1}{4} \\ \text{(B) equal to or greater than } \frac{1}{8} \text{ and less than }\frac{1}{2} \\ \text{(C) greater than } \frac{1}{8} \text{ and less than }\frac{1}{2} \\ \text{(D) equal to or greater than } \frac{1}{8} \text{ and less than }\frac{1}{4} \\ \text{(E) less than }\frac{1}{2}$