Alice and Bob took different courses over two semesters. Alice's average on all quizzes in the first semester was points higher than Bob's average on all quizzes he took during the first semester. Alice's average on all quizzes she took during the second semester was points higher than her average for the first semester and was again points higher than Bob's average on all quizzes Bob took during his second semester. Which one of the following statements cannot possibly be true?
Alice's average for the academic year was points higher than Bob's.
Bob's average for the academic year was higher than Alice's.
Alice's average for the academic year was points higher than Bob's.
Alice's average for the academic year equaled Bob's.
If Bob had scored points higher on each quiz he took, then he would have had the same average for the academic year as Alice.
