Based on the information provided, Emma's pet is a cat. The relevant parts of the text state: "Sarah owns a cat." "Emma's pet purrs and has whiskers." Since Emma's pet purrs and has whiskers, and these characteristics match those of a cat (which Sarah is known to own), it logically follows that Emma also owns a cat as her pet. The other animals mentioned - a dog and a hamster - do not fit the description given for Emma's animal companion. Therefore, the pet type that Emma owns based on this passage is a cat.<|end_header_id|>