smc

Question

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 18 points higher than her average for the first semester and was again 3 points higher than Zelda's average on all the quizzes Zelda took during her second semester. Which one of the following statements cannot possibly be true?

Accepted Answer

Denote by A_i the average of person with initial A in semester i 1, 2 Thus, Y_1 = Z_1 + 3, Y_2 = Y_1 + 18, Y_2 = Z_2 + 3. Denote by A_12 the average of person with initial A in the full year. Thus, Y_12 can be any number in ( Y_1 , Y_2 ) and Z_12 can be any number in ( Z_1 , Z_2 ). Therefore, the impossible solution is Yolanda's quiz average for the academic year was 22 points higher than Zelda's.