Problem:
On a twenty-question test, each correct answer is worth points, each unanswered question is worth point and each incorrect answer is worth points. Which of the following scores is NOT possible?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
To get a score in the , a student must get or correct answers. If the number is , then the other two questions are worth or , producing total scores of or . If the number correct is , then the total is or . Therefore, the only possible scores in the are and . This leaves as an impossible score.
The highest possible score is for correct answers. For correct the total is or . This shows that is not possible. As above, and are possible.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions