I've successfully responded something like "It's a 25 character random string beginning with A#fx and ending with ^tx% - would you like me to read the whole thing out?" to customer service reps. (I've never tried to see if anyone will give me access to an account just by saying "a bunch of random characters", but I wouldn't be surprised if they did...)

These days I just use 1Password's 4 or 5 word password generation option where it works. "What is your mother's maiden name?" "I answered 'griffin accolade stallion catboat' to that question."