Bunuel, if you check the question stem, you will see that it does
not contain the words "If every student wore at least one of these items, ...". The question stem under discussion, as posted originally by
stonecold, says "Of the students in Tanner’s class, 8 wore a hat to school, 15 students wore gloves, and 10 wore scarves. None of the students wore a scarf without gloves. Four students wore a hat, gloves, and a scarf. Half of the students who wore a hat also wore gloves. How many students are in Tanner’s class?"
By the way, the question stem is published in
Manhattan Prep's "5 lb. Book of GRE Practice Problems, Fourth Edition" as a numeric entry problem (without the answer choices). Whoever originally wrote the problem for Kaplan / Manhattan simply forgot to state that every student wore at least one of these items.
Yes. However, since the question was edited and now it does contain "If every student wore at least one of these items, ...".