Incidentally, the record youth unemployment rate doesn't take into account young people who are economically inactive. It's a measure of those under 25 who are looking for work, compared to the total youth labour force.
The raw fact is that 3.577m people aged 15-24 in the eurozone were looking for work in October, 15,000 more than a year ago, out of a youth labour force of over 14 million.