MathDB

[*] 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}

Problem Statement