A4. Aline, Bram, and Cas are participating in a math competition with 12 questions. Beforehand, they are somewhat pessimistic and make the following statements.

Aline: "Bram will have at least two more questions correct than I do."

Bram: "I will not have more than five questions correct."

Cas: "I will have at most as many questions correct as Aline."

Their teacher tries to encourage them and says: "Together, you will definitely have more than 18 questions correct." After the competition, it turns out that all three students and their teacher made incorrect predictions. Who has/have the fewest questions correct?
A) only Aline
B) only Bram
C) only Cas
D) both Aline and Bram
E) you cannot say with certainty
A4. A) only Aline Since Bram's prediction was wrong, Bram has at least six questions correct. Aline's prediction was also wrong, so Bram has at most one more question correct than Aline. Therefore, Aline has at least five questions correct. Since Cas's prediction was wrong, he has more questions correct than Aline, so at least six. Aline cannot have more than five questions correct. After all, then Cas would have at least seven questions correct, and there would be at least $6+6+7=19$ questions correct in total, as the teacher (incorrectly) predicted. We conclude that Aline has five questions correct. Since the other two have at least six questions correct, Aline has the fewest questions correct.