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A is corrent. Batch obtained automatic perfection when it had a purchase money security interest in consumer goods since the steps for attachment took place and Conrad bought the refrigerator for his household use. However, automatic perfection is not effective against a good-faith purchaser for value who buys from a consumer for consumer use. Backus’s purchase from Conrad qualifies.
B is incorrect because Batch has neither a contract nor an effective security interest with Backus.
C is incorrect. Batch obtained automatic perfection when it had a purchase money security interest in consumer goods since the steps for attachment took place and Conrad bought the refrigerator for his household use. However, automatic perfection is not effective against a good-faith purchaser for value who buys from a consumer for consumer use. Backus’s purchase from Conrad qualifies. 
D is incorrect. Batch obtained automatic perfection when it had a purchase money security interest in consumer goods since the steps for attachment took place and Conrad bought the refrigerator for his household use. However, automatic perfection is not effective against a good-faith purchaser for value who buys from a consumer for consumer use. Backus’s purchase from Conrad qualifies.