<p>If assumption is GPA=4.0 and high SAT score, why not to look into Merit awards? There are plenty of UGs (including great privates) that offer very good Merit packages (including full tuition or close) to such students? Some research is required since the same stats will not yeild the same level of Merit awards at different UGs.<br>
I do not think that Vandy is one of such schools. But you might be pleasantly surprised by Case Western offers (as one private that very well known for both great Merit offers and pre-med and engineering programs)</p>