Should I keep her as a friend in FB?

Well I have this girl as a friend in FB, but she never talks to me in person. Every time I try to say hi to her, she ignores me. I post something like "hello" or "how are you" in her wall, but she never responds. She responds when other ppl post things on her wall. In person, I try to talk to her and she always ignores me. One time she told me that I never talk to her, which is untrue, b/c I always try to talk to her. BTW, she was the one who friend requested me. Should I keep her as a friend in FB?