What is the length of DE

nce BE=EC, BC = 2BE. According the principle of proportionality of triangle, BE/DE=BC/AC.

This can be re-written as:

BE/DE = 2BE / AC

DE = AC * (BE/2BE)

DE = AC * (0.5)

Since we do not know the value of AC from statement (2) therefore not sufficient. However substituting the value of AC from statement (1), we get DE = 14 * 0.5 = 7

Therefore answer is C, both statements together are sufficient but neither alone is sufficient.