It will made you crazy, because it's not picking correct index.
Do your own analysis and see why it's not picking correct index.
MY thought is if you execute this query with FULL hint it'll finish much faster.
Here since it's picking wrong index it's doing lot of buffer gets and scanning memory is CPU intensive.
Can you execute this query with FULL hint and get back to us with the autotrace details.

Did you answer when was the last time statistics gathered and how do you excatly gather statistics.
Also do provide the wait event details.