@RichInPitt , NMSQT is based on taking the PSAT in October of junior year, followed by the SAT/ACT score. Sorry, I messed that up. A student aiming for NMSQT wants a score over a certain threshold on the PSAT, followed by a high SAT/ACT score.
ETA: I don’t know if a previous high score would be considered for NMSQT. Regardless, I don’t think a previous lower score is beneficial to anyone.
https://www.nationalmerit.org/s/1758/interior.aspx?sid=1758&gid=2&pgid=424