The answer is B, admit to the hospital. This patient is most likely suffering from an anorexia nervosa, an eating disorder. The treatment for eating disorders includes a variety of specialized therapy techniques and sites. However, when a patient is in medical danger, such as this patient, it is important to stabilize them in the hospital, and supervise initial refeeding. There are several indications to admit, but it is important that a medical student recognize that a BMI <75% of normal is enough. This patient also has syncope, which also meets criteria. Bradycardia, electrolyte derangements, arrhythmias, orthostatic blood pressure problems, seizures, and more are also indications, some of which may be revealed by further workup of this patient. She needs to be admitted to the hospital to supervise her initial refeeding and to avoid refeeding syndrome. After she has been medically stabilized in the hospital, she and her physicians can determine the next best step in treatment for her eating disorder. Note: SSRIs like Fluoxetine can be used for comorbid depression and anxiety but will not be sufficient to treat the eating disorder on their own. Eating disorder mortality has decreased in recent years, but remain a psychiatric condition with high mortality rates, either by suicide or medical complications.

Publication reference : Campbell K, Peebles R. Eating disorders in children and adolescents: state of the art review. Pediatrics. 2014 Sep;134(3):582-92. doi: 10.1542/peds.2014-0194. Review. PubMed PMID: 25157017.
Reference URL: http://pediatrics.aappublications.org/content/134/3/582.long#T4