I can only speak to nursing.
I remember the requirements to apply for my MSN program required biochem but not o-chem (couldn't have, b/c I have not taken it), calc, stats, microbio, chem, the usual A&P, a performing art and 2 years of a foreign language. That last two actually kept out more potential students than biochem and stats, lol. Somehow lots of people get through undergrad without language and the arts. (I thought that was what undergrad was primarily for?) I did take a basic physics course as an undergrad, but I don't think it was required for my MSN program.
Petersons guide , fwiw, calls my school "Most Competitive," and it is rated in the top 5 Nursing APN programs. GPA and GRE scores were all well above the 90th percentile. (I had a 4.0 and a 1350/5- see the vlaue of a good liberal arts eucation? 😉 ) They said they accepted 12% of the applicants the year I applied. There was also a personal interview required. Not a big deal, but it still shocks me that not every school requires the GRE and an interview. Regardless, apps to APN programs are up, so it stands to reason the competition is stiffer.
Selection for my DNP program (I stayed at the same school, but had to apply all over again) was based on both committee and 1:1 personal interviews after the initial 1st round application screening. I do not know how big an emphasis they placed on GPA (which was 3.87 in grad school), or GRE in that initial screening. They did say letters of recommendation, publications, presentations, speaking engagements and demonstrated leadership weighed heavily. I had my name waaay down on the list of 2 publications after doing some of the research as a grad student, strong letters of rec, and many speaking engagements because I have a leadership position in an advocacy organization related to public health, but totally unrelated to nursing/medicine. I am a good public speaker. I am actually a Professional member of the National Speakers Association. I wouldn't have thought that to be too impressive with regard to getting accepted, but who knows what they are looking for. They said they accepted 10% of the applicants. I have a classmate who works for Kathleen Sebelius, one who is the head of her entire country's public health service and another who's DNP project has been adopted by her Governor as a state wide health initiative. I'm in some very humbling company and I have no idea why they chose me.