Observation #1. Compound A contains a carbonyl group.
Observation #2. Compound A does not have an oxidizable group, such as alcohol, aldehyde, alkene, or alkyne.
Observation #3. Compound A is not an aldehyde or ketone (both of these functional groups give a dinitrophenylhydrazone product with DNP).
Observation #4. For acid hydrolysis to give two products, an ester for Compound A comes to mind. The hydrolysis products are a carboxylic acid and an alcohol.
Hope this gets you going in the right direction!
Steve