8. An $A M C$ exam consists of 30 questions, with the scoring rules specifying 5 points for each correct answer, 0 points for each wrong answer, and 2 points for each unanswered question. 
The sum of the points a participant earns for each question is called the participant's total score. Assuming there are enough participants, the number of different possible total scores is $\qquad$
8. Solution: Let $x, y$ represent the number of questions a contestant answers correctly and the number of questions they leave unanswered, respectively. Then we need to find the number of elements in $M=\{5 x+2 y \mid x, y \in \mathbf{N}, x+y \leqslant 30\}$. If $5 x_{1}+2 y_{1}=5 x_{2}+2 y_{2}$, it is easy to see that $5 \mid y_{1}-y_{2}$, so when $y_{1}, y_{2} \in\{0,1,2,3,4\}$ and $y_{1} \neq y_{2}$, it must be that $5 x_{1}+2 y_{1} \neq 5 x_{2}+2 y_{2}$. Note that for each $y \in\{0,1,2,3,4\}$, $x$ can take on $30-y+1$ values from 0 to $30-y$, so the number of elements in $M$ is 31 $+30+29+28+27=145$.

Alternative solution: We only need to consider which numbers in $S=\{0,1,2,3, \cdots, 150\}$ cannot be achieved: a perfect score is 150 points; answering 29 questions correctly can yield 145 or 147 points, so 149, 148, and 146 cannot be achieved; answering 28 questions correctly can yield 140, 142, or 144 points, and answering 27 questions correctly can yield 135, 137, 139, or 141 points, so 143 cannot be achieved; continuing this pattern, we see that the middle numbers can all be achieved, and finally, 1 and 3 cannot be achieved. Thus, out of the 151 integers from 0 to 150, only 6 cannot be achieved, so the number of achievable numbers is 145.