Just as many American high school seniors compete to enroll in the country’s most selective colleges and universities, younger students and their parents in a few cities aspire to coveted seats at top exam schools. Fewer than half of Boston’s exam school applicants win a seat at the John D. O’Bryant School, Boston Latin Academy, or the Boston Latin School (BLS); only one-sixth of New York applicants are offered a seat at one of the three original exam schools in the Big Apple (Stuyvesant, Bronx Science, and Brooklyn Tech).