The correct answer is B. HLA-Cw6.

The case describes early-onset plaque psoriasis with a postive family history. HLA-Cw6 is associated with early onset (<40) psoriasis with positive family history, expressed in 90% of early onset patients and only 50% in late onset (7% in control population). The characteristics of Type I psoriasis are: early-onset, positive family history, HLA-Cw6. Type II psoriasis is characterized by: late-onset, no family history, lack HLA-Cw6.

HLA-Cw2 is over-represented in “Type II psoriasis” with no family history. HLA-B51 is assocaited with Behcet’s Disease. HLA-B27 is associated with Sacroiliitis-associated Psoriasis, Reactive Arthritis (Reiter), and Psoriatic Arthritis. HLA-Bw35 is associated with Cutaneous Lichen Planus.

References:

Henseler T. Genetics of psoriasis. Archives of dermatological research. 1998 Oct 1;290(9):463-76.