A data set contains 10 distinct positive integers. The mean of the data set is 25, and the median is 20. If a new number, 5, is added to this data set, which of the following statements must be true?

I. The mean of the new data set will be less than 25.
II. The median of the new data set will be less than 20.
III. The range of the new data set will increase.