Serum sickness is a Type 3 hypersensitivity reaction, in which the body responds to antigenic medical substances and produces antibodies. These antibodies in circulation then bind to the antigenic drugs and set off the complement cascade. Rheumatoid arthritis is also a Type 3 hypersensitivity reaction.
A) Apoptosis of macrophages- apoptosis is generally not a type of hypersensitivity reaction. B) Mast cel degranulation- this is part of a Type 1 hypersensitivity reaction/anaphylaxis, in which mast cells bind IgE on their surface, and IgE binding to the target antigen induces a conformational change in the IgE that sets off mast cell degranulation. C) Natural Killer Cell killing- plays a variety of roles, including cancer suppression and destruction of virally infected cells. If they play a role in hypersensitivity, it is part of Type 2 HSR in which they would respond to Ig on the cell surface. E) Wheel and flare reactions- This is also a Type 1 HSR.
Maybe they went with serum sickness (a type III hypersensitivity rxn) on this question based on the serology used to diagnose RA. Pts with RA have antibodies to immunoglobulin G (IgG), called rheumatoid factors (RFs). It makes some sense that upon these rheumatoid factors reacting with "self" circulating IgG, immune complexes would form that would later deposit in tissues (explaining in part the extraarticular manifestations seen with RA, ex. rheumatoid nodules, pleuritis, pericarditis etc..)