Am I going crazy? (Math Problem)

Test Preparation SAT Preparation
1

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<a href="http://i.imgur.com/ajL6KFP.jpg%5B/IMG%5D"&gt;http://i.imgur.com/ajL6KFP.jpg

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<p>How can I deduce the length of BC? It may my lack of sleep, but I cannot find a way for finding the length except by assuming certain lengths.</p>

2

<p>Here’s a hint: start drawing line segments. Pretty soon, you will be looking at a bunch of triangles…and you will be able to show that they are equilateral…</p>

3

<p>I believe it’s 20 since E, B and C make an equilateral triangle with sides 4. This means EC = 4.</p>

<p>Sent from my GT-I9300 using Tapatalk 2</p>

4

<p>How can you tell that chords BE and CE are both 4? All we know is that the other sides are 4 but how do you prove that they’re equilateral?</p>

5

<p>triangle BCE is equilateral because the radius of the circle with center E is 4 making an isosceles triangle with BE and CE equaling four</p>

<p>since you know that the other two triangles are equilateral this makes the two adjacent angles to angle BEC each 60 degrees which leaves 60 degrees for angle BEC which then makes it a triangle with 3 60 degree angle and therefore equilateral</p>

<p>therefore BC equals BE equals 4</p>

6

<p>Woahhhh. I completely disregarded the middle circle? Why did I do that? </p>

<p>Lol that was the 1 problem I got wrong on the whole test. These kind of problems can’t be fixed. I have to just be more careful I guess. <em>sigh</em></p>

7

<p>Here’s another quick problem. I got it right through guess and check but is there an algebraic way to do it? </p>

<p>If x and n are positive integers and (x+n)/(4x+n) = 1/3, what is the smallest possible value of x+n?
A) 3
B) 4
C) 6
D) 9
E) 12</p>

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<p>Bump
10char</p>

9

<p>If you cross multiply and then clean up, you land on x=2n. Since they both have to be positive integers, the smallest you can use are n=1, x = 2…</p>

10

<p>Hahaha wow. I need to relax. I am over thinking things wayyyy tooo much.</p>

11

<p>I’m not sure if this is right, but you get the same answer:</p>

<p>Since (x+n)/(4x + n) is 1/3, that means the ratio of any numbers you substitute for x and n in (x+n)/(4x + n) is will be equal to 1/3 as well. 1/3, 2/6, 3/9, 4/12, etc. (x+n) is the numerator, and since 1 and 2 aren’t answer choices, 3 would be the answer.</p>

12

<p>Yea you could do it that way too but I like algebra to make sure.</p>