Final answer:
The condition most likely causing the reappearing patches on the student's back and arms that respond to abrasive lotion treatment but reappear is Tinea versicolor, a fungal infection that leads to patches of discolored skin.
Step-by-step explanation:
Among the conditions listed, Tinea versicolor is most likely to be the cause of the patches that disappeared after treatment with an abrasive lotion but reappeared. Tinea versicolor is a fungal infection of the skin caused by the yeast Malassezia, which is a part of the normal skin flora but can overgrow and cause symptoms when conditions are favorable.
It is characterized by patches of skin discoloration which may be lighter or darker than the surrounding skin, and commonly appear on the back and arms, just as the student described. Recurrence after treatment is common in Tinea versicolor.
The other skin conditions listed include Psoriasis, which generally results in itchy or sore patches of thick, red skin with silvery scales and is not primarily a condition that improves with abrasive lotions and then recurrent; Folliculitis, which presents as bumps and pimples around hair follicles; and Keratosis pilaris, a condition with rough patches and small, acne-like bumps, typically on the arms, thighs, cheeks, and buttocks, but these bumps are not easily removed with lotions and are not known to cause recurring discoloration patches.
Therefore answer is (B) Keratosis pilaris.