In a class, 60% and 68% of students passed their Physics and Mathematics examinations respectively. What is the minimum percentage of students who passed both examinations?

The minimum overlap is $28\%$. The union is at most $100\%$, so the intersection is at least $60\%+68\%-100\%=28\%$, which is attained when the two pass groups together cover the whole class. The value $60\%$ is the overlap when every Physics pass is also a Mathematics pass.