Columbia University Science Honors Program ENTRANCE EXAMINATION

<p>@ninjacat14 I go to MHS too! What is the right answer for the cowboy question???</p>

<p>Was collegeconfidential blocked for you guys too? I tried going to this thread but it kept saying Warning! Malware!</p>

<p>@CalcBC sorry i meant the guessing penalty for wrong answers lol. Idk the curve for sophs</p>

<p>I’m sorry, but this question is very hard to explain without a visual representation. The key is to realize that by walking 4 miles straight up towards the river, you are already sacrificing optimal walking distance. The best route can be traced from walking on a diagonal towards the river, then diagonally back to the cabin. Like so: </p>

<p><a href=“http://■■■■■■■.com/view.php?pic=1z1woqq&s=5[/url]”>http://■■■■■■■.com/view.php?pic=1z1woqq&s=5&lt;/a&gt;&lt;/p&gt;

<p>By reflecting the cabin across the river, you are simply reflecting the diagonal the cowboy travels on when he goes from his river to the cabin. This does not change the distance, and allows you to visualize the problem more clearly: </p>

<p><a href=“http://■■■■■■■.com/view.php?pic=2nuhbvo&s=5[/url]”>http://■■■■■■■.com/view.php?pic=2nuhbvo&s=5&lt;/a&gt;&lt;/p&gt;

<p>Now write in the measurements and what is happening becomes more apparent. The cowboy is 4 miles south of the river, and he is 7 miles north of his cabin (in its original position). Thus, the original cabin was 11 miles south of the river.</p>

<p>Reflecting this across the river, the cabin is now 11 miles north of the river. Because the question says that the cowboy is 4 miles south of the river, the total vertical distance between the two is now 4+ 11=15 feet. The cowboy was also 8 miles west of his cabin, because reflecting across the river does not change lateral distance, that number remains constant. Now draw out the right triangle:</p>

<p>

<a href=“http://i41.■■■■■■■.com/2dgt2f6.png[/IMG]”>http://i41.■■■■■■■.com/2dgt2f6.png

</a></p>

<p>It is clear that the hypotenuse is sqrt.(8^2 + 15^2), or 17.</p>

<p>What’s the point in reflecting over the river? That doesn’t make sense…</p>

<p>The point is that by reflecting over the river, you are able to see the hypotenuse of the triangle. (As the path to the river and the cabin becomes one continuous diagonal rather than two discrete segments). There are other, more convoluted ways to get the answer, but this was the most elegant solution, and the one they were most likely looking for (as other methods would require a calculator). </p>

<p>I apologize for the cursory explanation, but take my word: the answer was undoubtedly, unequivocally 17, and not 4+ sqrt.(185)</p>

<p>@spazzer4501 Thank you so much for the pictures! That really helped, and I understand what you were doing before. You’re right, the answer is 17. </p>

<p>Stupid math problems that are so stupidly complicated. This is definitely an effective way of weeding out those who do not see these things.</p>

<p>wow so mad. i had the right idea of going diagonally but i never thought of reflecting it across the river -_-</p>

<p>@bbman888 MHS?</p>

<p>Idk, if I remembered the exact words of the question I think I would be able to understand it better. I’m still confused</p>

<p>@CalcBC MHS is a school in New Jersey (Montgomery High School). The order for science there is physics, chemistry, biology which screws all the students who take this test.</p>

<p>@ninjacat14
Ahhh. I see. I live on Long Island, so idk how other schools work :P.</p>

<p>@ninjacat14 what grade are you in?</p>

<p>Do they weigh grades or test scores more? </p>

<p>I would assume test scores?</p>

<p>That’s the order they teach science at Stuyvesant! </p>

<p>For Bronx Science, it’s Chemistry, Biology, Physics</p>

<p>(Though, these programs are reserved for select students; both schools usually teach sciences in bio, chem, physics order).</p>

<p>Guys when are the results coming out? Are the results coming out to New York first or the further states first (New Jersey) =(</p>

<p>Anyone hear anything about this yet?</p>

<p>…</p>

<p>1 week more.</p>

<p>…</p>