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<p>Could it be that you are talking about a different test. I really doubt that every student applying to a top tier school would do very well the MIT test, let alone ace the geometry section. I believe that most would have serious problems, especially without the typical crutch of a graphic calculator.</p>
<p>[MIT</a> Entrance Examination, 1869-70: Exhibits: : Institute Archives & Special Collections: MIT](<a href=“http://libraries.mit.edu/archives/exhibits/exam/geometry.html]MIT”>http://libraries.mit.edu/archives/exhibits/exam/geometry.html)</p>
<p>I think it would be an eye-opener to reproduce the question number 6 in the SAT forum. My guess is that almost everyone would claim there is information missing and a great number of students would simply be unable to visualize the problem correctly. Expecting many students to know the laws of proportional mean might be illusory.</p>
<p>PS The problem is “The perpendicular dropped from the vertex of the right triangle upon the hypothenuse divides it into two segments of 9 and 16 feet respectively. Find the lengths of the perpendicular and the two legs of the triangle.”</p>