<p>Rice University offers a fair number of partial merit scholarships that you might be in range for with the 1540 SAT and a 4.0 UW gpa IF your course schedule is rigorous. Unlike UChicago, there is an engineering track. </p>
<p>Just stating your gpa doesn’t give a lot of information, particularly for prospective engineering students. Students collecting merit awards from schools that don’t use simple formulas have taken a lot of advanced math and a full slate of rigorous science courses. Those I have known have also competed in a lot of math and science competitions–not necessarily big national contests, but they have shown a long-term interest in engineering-related activities.</p>
<p>I agree with the above assessments about big merit awards at WashU–they seem to use them to expand their geographical diversity. I don’t know where you live, so that might not work against you, but they are both hard to get and unpredictable, at least compared with other privates with a similar reputation.</p>