I need help on this math problem

Question

On a ten question math test, each correct answer is worth 5 points, each unanswered question is worth 1 point, and each incorrect answer is worth 0 points. What scores greater than 40 are not possible to achieve?

Answer 1

I recommend that you go at this with a "brute force" method. To begin with, consider what scores you would get if you answered 7, 8 or 9 correct (irrespective of whether the remaining questions were left blank or incorrect).

 

7 right: 35+

8 right: 40+

9 right: 45+

10 right: 50

 

With this alone, you can already see that the only way to score 40 or more is to get 8 right. There are three options for each of the remaining two answers; right (5), blank (1) or incorrect (0). If you just work through the possible permutations manually, you'll end up with your answer. The total score is going to be 40 plus one of the following:

 

 

0,0 (for 40)

0,1 (41)

0,5 (45)

1,0 (already counted)

1,5 (46)

5,0 (already counted)

5,1 (already counted)

5,5 (50)

 

From here it is a trivial matter to arrive at the answer to your question.

 

Make sense?

 

---

 

Ah, I was just notified that I missed a possible permutation/combination of answer states. And there is the danger of "brute force" methods. Be sure to account for it! :)