Problem 18 (2023 AMC 12B)

Last academic year Yolanda and Zelda took different courses that did not necessarily administer the same number of quizzes during each of the two semesters. Yolanda's average on all the quizzes she took during the first semester was $3$ points higher than Zelda's average on all the quizzes she took during the first semester. Yolanda's average on all the quizzes she took during the second semester was also $3$ points higher than Zelda's average on all the quizzes she took during the second semester. Which of the following statements must be true?