A2. A test consists of six questions worth 1 to 6 points respectively. If you answer a question correctly, the number of points for that question is added to your score. If not, it is subtracted from your score. If you only answer questions 1, 3, and 4 correctly, your score would thus be $1-2+3+4-5-6=-5$. How many different final scores are possible?
A) 20
B) 22
C) 41
D) 43
E) 64
A2. B) 22 The possible final scores are exactly the odd numbers $-21, -19, \ldots, 19, 21$. That only odd scores are possible can be seen as follows. Answering all questions correctly yields a score of 21. For each incorrectly answered question, an even number of points is deducted from these 21 points, so the score remains odd.

That all odd scores between -21 and 21 are also possible can be seen as follows. By answering no or exactly one question incorrectly, you can achieve scores of 21, 19, 17, 15, 13, 11, and 9. Answering question 6 and one of the first four questions incorrectly yields 7, 5, 3, or 1 point. By answering exactly one question correctly or only question 6 and one of the first four questions incorrectly, you get scores of $-21, -19, \ldots, -1$.