6. Three friends - Masha, Olya, and Svetlana - enrolled in the economic, information, and mathematics classes at the lyceum. If Masha is an economist, then Svetlana is not an informatician. If Olya is not an informatician, then Masha is an economist. If Svetlana is not an economist, then Olya is a mathematician. Determine which classes the girls enrolled in. It is known that each girl enrolled in one class, and the classes are different..(15 points)
Solution.

Let Olya not be an informatics student, then according to condition 2, Masha is an economist. If Masha is an economist, then Svetlana, according to condition 1, is not an informatics student. We have a contradiction (Masha is both an informatics student and an economist). Therefore, Olya is an informatics student. Then Svetlana is an economist, otherwise, according to condition 3, Olya would be a mathematician. Therefore, Masha is a mathematician, Olya is an informatics student, and Svetlana is an economist.

Answer: Masha enrolled in the mathematics class, Olya in the informatics class, and Svetlana in the economics class.

Grading Criteria for 8th Grade Assignments

| Assignment | 1 | 2 | 3 | 4 | 5 | 6 | Total |
| :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |
| Points | 15 | 15 | 20 | 20 | 15 | 15 | 100 |

Problem 1

| Points |  |
| :---: | :--- |
| 15 | Correct and justified solution to the problem |
| 10 | The number is found correctly, but there is a calculation error when finding the remainder. |
| 0 | Variants are found using the divisibility rule for 11 and 9, but the required number is not found or is found incorrectly |

Problem 2

| Points |  |
| :---: | :--- |
| 15 | Correct and justified solution to the problem |
| 10 | The system is set up correctly, but the time is found with a calculation error |
| 5 | The system is set up correctly, but the solution is not completed |

Problem 3

| Points |  |
| :---: | :--- |
| 20 | Correct and justified solution to the problem |
| 15 | Both cases are considered, but the solution is insufficiently justified |
| 10 | One case is considered correctly |
| 5 | There is progress in the solution (for example, properties of the exterior angle, bisector, etc. are considered), but it is not completed |

Problem 4

| Points |  |
| :---: | :--- |
| 20 | Correct and justified solution to the problem |
| 15 | The system is solved correctly, but the minimum value is found incorrectly or not found. Or the system is solved, the minimum value is found correctly, but cases \( \mathrm{a} = \pm 1 \) are not considered. |
| 10 | The system is solved without considering cases \( \mathrm{a} = \pm 1 \), the minimum value is not found. |
| 5 | There is progress in solving the system, but it is not completed |

Problem 5

| Points |  |
| :---: | :--- |
| 15 | Correct and justified solution to the problem |
| 10 | The problem is solved with insufficient justification (for example, only two out of three inequalities are set up) |
| 5 | One or two out of three inequalities are set up correctly, but the solution is not completed or completed with an error |

Problem 6

| Points |  |
| :---: | :--- |
| 15 | Correct and justified solution to the problem |
| 10 | The solution is correct, but insufficiently justified |
| 5 | There are correct conclusions in the solution, but it is not completed or completed with an error |