rush

literally dozens of things
if the girl has a letter of recommendation
what year she is (freshman, sophomore, etc)
good grades
connections to girls in the house
if they are a legacy (bonus points if they are a legacy to the Texas Tech chapter of the sorority)
appropriate social media (no drinking, language, etc)
looks
...and that's all before they even meet a pnm
once they meet the pnm, they could drop her based on how well she holds a conversation, if she seems like a good fit with the chapter, what she talks about, etc.
this is all really just scratching the surface. If a girl doesn't like a pnm, they will find a reason to cut her