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<p>The average math scores of prospective math/science/engineering majors, anywhere, will be higher than the average math scores of fine arts majors. Nevertheless, the most selective schools get a large surplus of qualified applicants. The private ones especially are free to pick and choose to create an entering class with diverse interests (this is one of their selling points, for those who care). The most selective public universities and honors colleges may do the same to some extent (though they are more constrained by their obligations to taxpayers). Chicago or Berkeley will get very high-scoring kids in anthropology or linguistics. Some very high stats kids will go into art history at Williams, philosophy at William and Mary, or architecture at Cornell. </p>
<p>At Amherst or Middlebury, fewer than 20% major in math and science (and they don’t even have engineering). At the Ivies and other very selective private schools that do have engineering programs, many (probably most) engineering majors will never become hands-on, practicing engineers. They go into investment banking and business consulting, start up their own IT firms, go to law/med school, and so forth. The focus of these schools is on the liberal arts and sciences, not on technical training for specific careers. There is lively debate on CC about whether Ivy engineering is up to the standards of state universities.</p>
<p>So if you are a prospective engineering major, a selective private school may not even be the kind of place you really want. Some serious, practical, smart kids wind up at these schools only to find the atmosphere a little too precious. Even if it is what you want, you can find a similar atmosphere in a public honors college. You certainly can find good engineering training at much lower cost, with a high concentration of scary-smart classmates, at many public universities. For that you are lucky to live in Texas (a very large state with high demand for skilled engineers). In case aid does not come through (and I think it will given your qualifications) it may come down to commuting from home for one or more years, or graduating in more than 4. After that you will have a very marketable degree (as well as a record of persistance and determination to impress employers).</p>