A test was conducted in class. It is known that at least $\frac{2}{3}$ of the problems were hard. Each such problems were not solved by at least $\frac{2}{3}$ of the students. It is also known that at least $\frac{2}{3}$ of the students passed the test. Each such student solved at least $\frac{2}{3}$ of the suggested problems. Is this possible? Previous problem with $\frac{2}{3}$ replaced by $\frac{3}{4}$. Previous problem with $\frac{2}{3}$ replaced by $\frac{7}{10}$.