<p>A is definitely the answer for the Italians.</p>
<p>30 / 2 = 15
x + (x + 3) = 15
2x = 12
x = 6</p>
<p>(It does look to me like Monoclide’s reasoning was wrong though).</p>
<p>You can find a related discussion in the vicinity of these posts:
<a href=“http://talk.collegeconfidential.com/sat-act-tests-test-preparation/503773-official-may-3rd-sat-thread-14.html#post1060320855[/url]”>http://talk.collegeconfidential.com/sat-act-tests-test-preparation/503773-official-may-3rd-sat-thread-14.html#post1060320855</a>
and
<a href=“http://talk.collegeconfidential.com/sat-act-tests-test-preparation/503773-official-may-3rd-sat-thread-19.html#post1060353183[/url]”>http://talk.collegeconfidential.com/sat-act-tests-test-preparation/503773-official-may-3rd-sat-thread-19.html#post1060353183</a></p>
<p>There was a discussion a while back on the merits of eyeballing on the SAT.</p>
<h1>20 is a perfect exhibit in favor of that low-brow method.</h1>
<p>On the edge of your answer sheet mark the distance between the vertex of the square and the point of tangency; it equals 1. Slide the answer sheet so the edge would pass through the center of the small circle and one mark would “lie” on the circumeference. Rough estimate: the circle’s diameter = .8, therefore its radius is about .4 - that’s answer D.
10 seconds (just clocked myself).</p>
<h1>12. x-3=y-x—>2x-3=y</h1>
<pre><code> 2x-y=2(x-3)=2(y-x)—>2x-(2x-3)=2x-6—>3=2x-6—>x=9/2
y=2(9/2)-3=6 B
</code></pre>
<h1>20(lower left hand corner)- One side of the square is equal to the 2 diameters of the two large circles combined, or 2+2=4. Since one side of the square is 4, the diagonal of the square is 4 sqrt(2). If we draw the diagonal on the square, we can clearly see that that we need to find the gap between the circle and the corner of the square. In order to do this, make a square with diagonal sqrt(2) and subtract one from the diagonal to find the length of the gap.</h1>
<pre><code> Let’s call the radius of the smaller circle r and then make the following formula:
2(sqrt(2)-1)+4+2r=4sqrt(2)
2sqrt(2)+2+2r=4sqrt(2)
2sqrt(2)=2+2r
r=(2sqrt(2)-2)/2 or sqrt(2)-1 D
</code></pre>
<h1>15. Radius of the 2nd biggest circle is 2 and the radius of the third biggest circle is 5/2.</h1>
<p>Area of shaded area= Area of 3rd biggest circle - Area of 2nd biggest circle
pi(5/2)^(2)-pi(2)^(2)
25pi/4-4pi=25pi-16pi/4=9pi/4 D</p>
<h1>19. xy=x+y and y is greater than 2. We want to know all possible values of x that satisfy the equation.</h1>
<p>xy-y=x
y(x-1)=x
y=x/x-1</p>
<p>Test the answer choices:</p>
<p>A.) x<0, x=-1/2
-1/2/(-3/2)=-1/2<em>2/-3=1/3 No.
B.) 0<x<1, x= 1/2
1/2/-1/2=1/2</em>-2=-1 No.
C.) 0<x<2 , x= 1/2 again, No.
D.) 1<x<2, x=3/2
3/2/(1/2)=3/2*2=3 Yes. This is our answer</p>
<p>Hey guys, I don’t know if you got the proper method for number 19, but here’s quite a simple method:</p>
<p>xy = x + y
xy - y = x
y(x - 1) = x</p>
<p>Therefore:
y = x/(x-1)</p>
<p>Simple as that! Now if you know a little bit about domain and range, you will know that there is a vertical asymptote at x = 1. So x = 1 is one boundary. Then you plug in y = 2:</p>
<p>2 = x/(x - 1)
2x - 2 = x
x = 2</p>
<p>There you go, that’s your other boundary. Since x = 1 is an asymptote, x must be greater than 1. Since we are looking at y is greater than two, x must be smaller than two. So we get:</p>
<p>1 < x < 2
Choice D</p>
<p>If you have a graphic calculator, just graph it and you’ll see the answer straight away.</p>
<p>EDIT: lol, just saw the post above which shows the method I used. Since the second bit of my method is different I’ll keep my post here ;)</p>
<p>Here is the answer to #12:</p>
<p>just set up 3 equations</p>
<p>you have 3 unknowns: x, y, d</p>
<p>d = the equal distance between each tick mark</p>
<p>1) 3+d=x
2) x+d=y
3) y+2d=2x</p>
<p>now solve for d in the first equation:</p>
<p>d=x-3</p>
<p>plug it into the 2nd equation:</p>
<p>x + (x-3) = y
2x - 3 = y</p>
<p>plug in y for the 3rd equation:</p>
<p>2x - 3 + 2d = 2x
-3 + 2d = 0
d=1.5</p>
<p>plug in d into the first equation to solve for x:</p>
<p>3+1.5=x
x=4.5</p>
<p>plug in x and d into the 2nd equation to get y:</p>
<p>4.5 + 1.5 = y
y=6</p>