"How old am I?"
Translation:Berapa umur saya?
I believe we use 'berapa' because of the implied 'tahun' within the noun 'umur.' While in English we would say "How old are you?" and not "How many years old are you?", in Indonesian they would say "How many [Berapa] years of age [umur] am I [saya]?" In both languages, years are implied, unless, I guess, you're talking about very recent infants.