I'm not an admissions expert. My approximate guess:
Top 11-15% requires an SAT score around 1270+
Top 16-20% requires an SAT score around 1290+
Top 21-30% requires an SAT score around 1320+
Top 31-40% requires an SAT score around 1360+
Top 41-50% requires an SAT score around 1420+
An SAT Score around 1450 will get accepted into non-business and non-engineering majors regardless of class rank (unless the essays or other parts of the application are terrible)
An admissions expert will of course say there are a number of factors that goes into the holistic applicant review process (essays, extracurricular, etc.), but the SAT scores and class rank will heavily determine whether an applicant is accepted or not. The above numbers are a gut approximation, but I think are reasonably accurate give or take 10-20 points (+/-).
If an applicant does not get accepted, but wants to be an Aggie, my suggestion is to go to community college for 24 credits (about a year's worth of credits) and transfer into the university. Before registering for community college courses, they should review the transfer credit equivalency page to ensure the credits will transfer (and only transferable credits can be applied to the 24 hour minimum).
Link to the course transfer equivalency can be found here:
https://howdy.tamu.edu/uPortal/p/tce-ui.ctf1/max/render.uPETA: There used to be an auto admit policy for top 25% students with a score of 1300 or greater, but it seems that it's no longer in effect now (I would be shocked though if the numbers have changed significantly for accepting students with similar stats, even if the criteria is not publicly shared/guaranteed).