They take your grades and assign points to them, then take your entrance exam and add up all the scores to see if you get in or not.
This is pretty typical. Generally speaking for acceptance into a competitive program, you are going to face 3x elements. [[EDIT: Apologies to all for the random discussion ...]]
[] First, and worth probably 45% of your total package is your grades. Above 3.5 (out of 4.0) in the sciences will keep you sufficiently competitive. Most schools will publish their acceptable range.
[] Secondly, your standardized entrance exam. Also accounting for about 45% of your total package. Most schools publish the range of accepted applicants, and many will post the 25, 50, and 75th percentiles. You want to be at least over the 50. High grades will permit a lower standardized test score. Lower grades will require a higher standardized test score.
Grades are the most difficult part because they take an eternity to earn and cannot be undone. Your standardized test score can be dramatically increased, if necessary, by taking courses and many many practice exams. This is the easiest thing to influence, with some cost and effort, to make you competitive. But if you already have high grades (for the school to which you apply, not just in general), and a good test score, then no worries.
[] Thirdly, and worth about 10% roughly is your essay and resume. You have good work experience and are not a kid fresh out of high school, so this is helpful. But this will only sway you slightly based on the 2x above factors, e.g. if you are marginal, it can bump you onto an accepted list or wait list.
You note above that only 16x positions are available. That's shocking low, but perhaps is offset by the location. I don't know. But here is my other advice (which is free and we all know how much "free" advise is worth) ... apply to more than one school. Apply to at least 3x minimum, and preferably more. Rank them according to your best pick, then viable alternatives, then back-up schools 8-9 would be ideal if you want to essentially guarantee an opportunity pursue the program.
You will spend time and also $50 to $100 to apply to each, but you need to put that in the context of the fact that you are trying to position yourself for a $60 to $80K per year job. The schooling is worth the investment, and so is a few hundred dollars in application fees to ensure you are accepted somewhere. You can always move back afterwards, despite this being less than ideal.
Okay, sorry for going off on a tangent. It's an area if interest to me and I've had this conversation with a great many. I'll end with the following quote:
An investment in knowledge pays the best interest. - Benjamin Franklin