It is not unusual to receive an acceptance letter from one of the eight high schools before you get a letter with your SHSAT scores. The letter sounds legitimate (the schools only tell you whether you are accepted or not, not your score).
Students are notified of their scores by the Department of Education in February.
The results of the SHSAT are ordered from the highest score to the lowest score. The list is processed in order by score, with each students being placed in their most-preferred school that still has open seats, and continuing until there are no remaining open seats at any school.
The student's absolute score does not matter as long as it is higher than the cutoff score, which is found by the results of all the students who took that score that year. For example, if there are 500 seats available at Stuyvesant the top 500 students who put Stuyvesant as their first choice scores will be admitted. The lowest score admitted is the cut off score.
The Specialized High Schools Admissions Test (SHSAT) is the only way for students to get into eight of the top public high schools in New York City:
Bronx High School of Science
Brooklyn Latin School (newly designated)
Brooklyn Technical High School
High School of Mathematics, Science and Engineering at City College
High School of American Studies at Lehman College
Queens High School for the Sciences at York College
Staten Island Technical High School (newly designated)
Stuyvesant High School
There isn’t a cut off score to get into each school- it depends on how many students take the test each year, and how well they do. However, to give you a general idea, only about 15% of students who take the test are accepted to any of the schools.