Sounds like the cat to me. A bad rear o2 won't affect your gas mileage. Winter gas will bring it down along with this cold weather but that's a good drop so I'd suspect a larger issue. Cheapest way would be to get an o2 sim to get through inspection but you'd eventually have to replace the cat. You can also clear the code and then set all monitors but the cat monitor. State inspection allows for one monitor to be not set. If the monitor isn't set, you won't have a code, you win a sticker. How many miles are on the car?
Federal emissions warranty is 8 years/80,000 miles, not 7/70.
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