Let A, B, C, D, E, & F represent Abstract, Baroque, Cubist, Digital, Expressionist, and Folk respectively
Let Gallery A, B & C be represented by Ga, Gb & Gc
Considering initial passage and first two statements,
Each artwork type is displayed in exactly one gallery, and no gallery is empty.
Gb has exactly 3 artworks; B & A are displayed together but not in Gc.
1.) For no gallery to be empty the artworks B & A that are together must be in Gb with 3 artworks. Leaving space for 1 more.
Considering rest of statements,
E & C are in different galleries; F is in Gc. This would provide multiple possibilities.
∴ considering the options to narrow this down, we see Gc can have F or F & C or F, C, & D as we already know Gc has F displayed.
2.) C and D cannot be together as Gb needs atleast 3 artwork displayed and D cannot be displayed with F in Gc as there is no such option
∴ only C and F are displayed in Gc
Then, This way D can be displayed only in Gb and and E is the only art displayed in Ga.
∴ Correct option is Gallery A : Expressionist Only
Gallery C : Cubist and Folk only