<p>Here is a math question to keep your mind off of obtaining your scores -- see if you can get the answer to it:</p>
<p>Let r and s be two positive rational numbers in reduced form. The product of r and the reciprocal of s exceeds the sum of r and s by 1/2 and is also 8/5 times the sum of r and s. Find the rational number 3r + 2s, if the numerator of r is double the numerator of s, and the denominator of r exceeds the denominator of s by 7. (Give the answer in exact rational form.)</p>
<p>15/7 ?!
If this is right, the problem can be solved even without the last explanation "if the numerator of r is double the numerator of s, and the denominator of r exceeds the denominator of s by 7" :)</p>
<p>Giovanni: you're the ETS rep of yore, aren't you</p>
<p>i got 20/3 o wells ~</p>
<p>hahahaha..... someone went to cjml this weds. !</p>
<p>Yup! It's 15/7. The part where it says "the numerator of r is double the numerator of s, and the denominator of r exceeds the denominator of s by 7" is just an extra information (I think it's purposely given so that we think of it too much that it distracts our attention, thus, leading us to the wrong answer). r is 10/21, and s is 5/14.</p>
<p>You are correct - the answer is 15/7. Here is a geometry question: One base of an isosceles trapezoid inscribed in a circle is a diameter of the circle; the other base of the trapezoid is one-third as long as this base and the distance between the bases is 88 inches. Find the area and the perimeter of the trapezoid.</p>
<p>By the way Lbtg47, I am planning to major in mechanical/aerospace engineering. What type of engineering were/are you interested in?</p>
<p>p = 704 / (3)^(1/2)
a = 15488 / (3)^(1/2)</p>
<p>just a guess. that's a tough problem</p>
<p>Indeed it is a tough problem. However, keep in mind that the trapezoid is inscribed in a circle, and the upper base is one third the length of the lower base, which is the ... diameter of that circle!!! Draw a line perpendicular to the upper base that passes through the center of the circle. </p>
<p>Because of the fact that the trapezoid is isosceles, the line will intersect the upper base at its center. Using the given information and phytagorean theorem, we can then find the circle's radius, from which the remaining of the problem is just the matter of simple algebra and geometry (and some trigs).</p>
<p>Anyway, if I'm not mistaken in calculating it, the area is 7744<em>2^(1/2) (~=10951.6698), and the perimeter is 88</em>[(6)^(1/2)]+172*[(2)^(1/2)]</p>
<p>~464.5 or something like that.</p>
<p>Asbereth: You obtained the correct answer for the area; however, you made one little mistake in finding the perimeter - see if you can find and correct it.</p>
<p>You had the perimeter right before, except that the perimeter is (88 root 6) + (176 root 2). You said 172 root 2 instead of 176 root 2. The explanation to this problem is as follows:</p>
<p>If the circle has radius length r, the length of the bases of the trapezoid are 2t and 6t, respectively, and the other sides (legs) of the trapezoid are w inches long then:</p>
<p>r = 3t, w^2 = (2t)^2 + 88^2, r^2 = t^2 + 88^2,
w^2 - r^2 = 3t^2, w^2 = 12t^2, t^2 = 8 x 11^2</p>
<p>t = 11 root 8, w = 2 root 3 (t) = 44 root 6</p>
<p>The trapezoid has an area of 1/2(8t)(88) = 7744 root 2 sq. in.
It has a perimeter of 2w + 8t = 88 root 6 + 176 root 2</p>
<p>im considering mechanical as well. aerospace sounds fun but i dont want to get locked into such a specific field right out of college. civil also sounds fun. from what i have heard you spend most of your time out on the field(construction sites etc) and that sounds like a much better way to make a living than doing repetitive mindless engineering work infront of a monitor all day.</p>
<p>however, as i get closer to college i think i may become a sellout and major in economics. i feel uneasy about having a limited pay late in my career compared to other career options. though a mba + a masters in engineering sounds very attractive! gah, im confusing myself just by thinking about it.</p>
<p>but uh yea, to answer your question, mech.</p>
<p>LOL, that's a stupid typo [I was wondering what the hell I got wrong, and just realized it when you pointed that out]! 176 root 2 + 88 root 6 is ~= 464.5, which is what I said on my previous post. Ah well... Anyway, are these the kind of questions that I can expect from Math IIC?</p>
<p>These are the kinds of questions that you can expect at CJML/AIME meets. So Lbtg47, that's unique to hear that you want to try to get an MBA and an engineering degree. What part of NJ are you from? I am in central NJ (15 minutes from New Brunswick, 20 minutes from Princeton).</p>