7. Solution. To increase the average score in both groups, it is necessary to transfer students from group A to group B whose average score is higher than the average in group B but lower than the average in group A. Two students have a score higher than the average in B but lower than the average in A: Lopatin and Filin. If only Filin is transferred, the average score in group B will become

$$
\frac{41.8 \cdot 10 + 44}{11} = 42.475$, while in group A it will be $\frac{41.8 \cdot 10 + 44 + 47}{12} = 42 \frac{5}{12} > 42.2$.
Answer: It is necessary to transfer Lapatin and Fylin from Group A to Group B.

Note: The solution may not be the only one.

| Evaluation Criterion | Score |
| :--- | :---: |
| The solution is complete and correct | 2 |
| The solution is basically correct, but it is not shown that both students need to be transferred, not just one | 1 |
| The solution is incorrect or missing (for example, only the answer is given) | 0 |