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<p>It really depends on the field. If you want to go to a top med school or law school, you’ll need a top GPA and top test scores (MCAT, LSAT). Period. The nameplate on the undergrad degree will matter almost not at all.</p>
<p>If you want to go into engineering, you should look at the top engineering programs. These are not necessarily at the most well-known elite private schools. US News’ top 10 engineering schools includes a mix of privates (MIT, Caltech, Stanford, Carnegie Mellon, Cornell, Princeton) and publics (UC Berkeley, Georgia Tech, Illinois, Michigan, Purdue, Texas). Otherwise “prestigious” private schools like Yale, Brown, and Vanderbilt are much further down the list. But so are some “prestigious” publics like UVA. Of the public universities specifically mentioned by the OP, Arizona State is ranked a respectable #44 in engineering. If I could get that for in-state rates, I wouldn’t pay a premium to study engineering at a private school like #34 Vanderbilt, #39 Brown, #44 Dartmouth, #44 Notre Dame, #53 Boston U, #58 Tufts, or certainly not #96 U Miami. I would, however, take a close look at #23 USC. Truth is, you can have a fine engineering career coming out of just about any ABET-accredited engineering program, but you’ll have more entry-level job opportunities if you’re coming out of a highly respected engineering program. </p>
<p>For a business degree, there are two ways to go. You could go for a top undergrad business program, or you can do a liberal arts major in college, work for a few years, then try for admission into a top MBA program. The latter is somewhat riskier; you need a top undergrad GPA, top test scores, and probably some interesting business experience to get into a top MBA program. Many “prestigious” schools don’t offer undergrad business, and as with engineering, the top undergrad business programs are at a mix of privates (Penn Wharton, MIT, NYU, Carnegie Mellon, Cornell, NYU, USC) and publics (Michigan, UC Berkeley, UVA, UNC Chapel Hill, Texas, Indiana). Again, Arizona State is a very respectable #24 for undergrad business. An undergrad business degree from there probably won’t land you a hotshot job on Wall Street, but it could open up a lot of doors in a region of the country that is still on a pretty strong growth trajectory. And again, if I could get into ASU for in-state rates, I wouldn’t pay a premium to study business at a lower-ranked program like #40 Boston U or #72 U Miami. And if I wanted an undergrad business degree, I’d definitely go to a school that offered the program, which would rule out Vanderbilt.</p>
<p>As can clearly be seen, it’s a mistake to lump together all “prestigious” private schools, and it’s a mistake to lump together all publics. For engineering or business, ASU is clearly a cut above UNM (#96 engineering, #117 business) or UNLV (#162 Engineering, #199 business), and the most “prestigious” schools in these fields are not necessarily the usual well-known private suspects; a great many are public. For law or medicine, it probably doesn’t matter as much where you go, certainly not as much as a high GPA and strong test scores.</p>
<p>Problem: the student may not know which of these fields he wants, or he may choose one, then later change his mind. For that reason, I’d have ASU and USC very high on the list because they’d be highly respectable choices whichever way that decision ultimately went. All the other schools mentioned would be much more limiting for one or more of the fields identified by the OP.</p>