Hard Math Question

Test Preparation SAT Preparation
1

<p>Here is the link to the question:</p>

<p><a href="http://img217.imageshack.us/img217/4156/mathquestion.jpg%5B/url%5D"&gt;http://img217.imageshack.us/img217/4156/mathquestion.jpg&lt;/a&gt;&lt;/p>

<p>First of all, the answer is (E).</p>

<p>Now please look at my steps (excuse me for putting lots of multiplication signs, but they're just to make clear):</p>

<ul>
<li><p>To get the equation of the smaller arc: angle/360 *pi *2r = 6</p></li>
<li><p>The equation for the larger arc: angle/360 * pi * 2(r+3) = angle/360 <em>2</em>p*r +6 pi</p></li>
<li><p>By substituting the first equation into the second, we get: x = 6 + 6 pi</p></li>
<li><p>Now, unfortunately, the question isn't asking for the exact value, but is rather looking for an expression for it. I have no clue why the answer is (E). Could someone elucidate on this please, but please in detail steps, so I won't get lost. Thanks in advance!</p></li>
</ul>

2

<p>You’re overthinking.</p>

<p>6/r = x/(r+3); Set up proportions and solve for x.
rx = (6)(r+3)
rx = 6r + 18
x = (6r + 18)/r</p>

3

<p>It’s not really that complicated… haha</p>

<p>Set up a proportion.</p>

<p>r/6 = (r+3)/x; Cross multiply
rx = 6r+18; Divide by r on both sides
x= (6r+18)/r
The answer is E.</p>

4

<p>proportions similar properties</p>

5

<p>Another method- let the angle be z. Because the second circle is extended, the arc of length x is formed by the same angle as the arc of length 6. So the length of arc r is (z/360)(2pi(r+3)) (remember the radius of the larger circle is the sum of the radius of the first circle and the extension, so r+3 ). However, we need to find the unknown, z, in terms of r. So we use the formula for the arc length for the first circle. 6=(z/360)(2pi r) solving for z, z=(6(180))/(pi r)). Plugging z into the first equation, we get x=(6(180))/(pi r))(1/180)(pi(r+3)), so 180 cancels, pi cancels and we are left with (6(r+3))/r = (6r+18)/r -> E</p>

6

<p>Yea, it’s pretty simple. You don’t need to use pi at all.</p>

<p>Just remember the formula L = r * theta, where L is the length of the arc, r is the radius and theta the angle subtended by the arc.</p>

<p>But these arcs subtend the same angle.</p>

<p>so 6=r<em>theta or theta=6/r
and x=(r+3)</em>theta, or theta=x/(r+3)</p>

<p>Equate the two</p>

<p>6/r=x/(r+3)</p>

<p>Cross multiply and solve for x.</p>

7

<p>I got a 750 on math and I also went with the more complicated way (never got the answer). How do you know when to use a proportion?</p>

8

<p>Gruber’s says, there is ALWAYS a way to do every SAT I Math question in less than 30 seconds. Look at a question until it stops being complicated. The long way is never needed.</p>

9

<p>jasonjackson789 your approaches to the questions are right</p>

<ul>
<li><p>Equation of the smaller arc: angle/360 <em>pi 2r = 6–>angle=6</em>180/pir (1)</p></li>
<li><p>Equation for the larger arc: angle/360 * pi * 2(r+3) = angle/360 <em>2</em>r +6 <em>pi–>angle=180x/(r+3)</em>pi (2)</p></li>
</ul>

<p>—> (1)=(2)–> answer E
(I think this is a further step before get the proportion.</p>

10

<p>It’s not using a proportion. It’s solving for the angle x then substituting.</p>

11

<p>Wow, didn’t know it was THAT simple. I always overthink math problems… Anyway, thanks a lot guys for your help! :)</p>