"Yes, I am seven years old."
Translation:Так, мені сім років.
Could you say "я маю сім років", or are "years" something you cannot posses, indicated by verb "маю"?
You could say "У мене сім котів" because cats are something you can possess. Years are not, at least not in the same way. Perhaps this could be argued, but ultimately, it's just idiomatic!