7.1. Each student in the 7th grade attends a math club or an informatics club, and two students attend both the math club and the informatics club. Two-thirds of all students attend the math club, and $40 \%$ attend the informatics club. How many students are there in this class?
Answer: 30.

Solution: Note that $40\%$ is $\frac{2}{5}$ of all students. Adding $\frac{2}{3}$ and $\frac{2}{5}$ gives $\frac{16}{15}$. The two students who are involved in both the math and informatics clubs were counted twice. Therefore, these two students represent $\frac{1}{15}$ of the entire class, meaning there are $2 \cdot 15 = 30$ students in the class.

Comment: Correct solution - 7 points. Correct idea but incorrect answer - 3 points. Problem solved by trial and error, no proof that there are no other solutions - 2 points. Solution started, some progress made - 1 point. Correct answer given without explanation - 1 point.