Yes, and none of the three main science/math high schools (Stuyvesant, Bronx Science, Brooklyn Tech) are lottery schools, they all rely on the SSAT exam (and a similar student ranking system). As an applicant you rank your HS choices and those plus your score determine where you are offered a space.

Also, having attended one of these schools (admittedly in a different decade), students who were not ready for the work didn't do well. Not to say those kids weren't also smart kids, but you had to be a certain kind of kid to mesh with the school.

It was a fantastic place, not just for the education, but for spending 4 years with a gigantic group of diverse, interesting kids, almost all of whom were truly brilliant. To this day I think it had more to do with my success than college or grad school.