A large online retailer tracks customer satisfaction ratings for two different product categories, P and Q. Ratings are on a scale of 1 to 5. The average (arithmetic mean) rating for each category, based on a large number of reviews, is shown below.
Category P: 10,000 reviews, mean rating 4.2
Category Q: 12,000 reviews, mean rating 3.9

Which of the following MUST be true?
I. The product in Category P with the lowest rating received a higher rating than the product in Category Q with the lowest rating.
II. More than half of the reviews for Category P are higher than the mean rating for Category Q.
III. There is at least one review for a product in Category P that is higher than at least one review for a product in Category Q.