a. The difference between state and public schools is that state schools are funded and managed by the government and provide free education, while public schools in the context of the text are independent and private schools that charge high fees, relying mostly on the tuition paid by parents. Public schools in this sense do not operate under public control and are considered part of the private sector.
b. Children enter public schools primarily through an examination known as the Common Entrance exam, which they must pass after attending preparatory schools. Most public schools do not accept children directly from state schools, as those schools do not prepare students for the entrance examinations.
c. Some public schools are well-known throughout the country due to their long establishment and history, which has allowed them to gain a reputation for high academic standards as well as their exclusivity and social prestige. Notable examples include Eton, Harrow, and Westminster.