<p>^^ You certainly CAN. It’s a perfectly reasonable, though flawed, hypothetical. You may of course add as many caveats as you wish, but the posed hypothetical is reasonable.</p>
<p>Most LACs don’t have engineering schools or graduate programs, yes; I can think of several that do have engineering (Swarthmore, Bucknell, Lafayette, Union) and more that have graduate programs (you never specified they had to be top-X grad programs–lots of colleges offer a master’s in education, for instance, and even aside from that, cf. Wesleyan).</p>