PWN The SAT problems

Test Preparation SAT Preparation
1

<p>Hi guys,</p>

<p>I am solving this exam posted earlier by IceQube Pwn the Sat test,but I have some problems in this test.
Here is the exam
<a href="https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0Bwar2-EatDDSOTQxOTQ4MjktN2Q5ZS00YjE5LTgyNzktNjhhNWI1NTJjMmFm&hl=en%5B/url%5D"&gt;https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0Bwar2-EatDDSOTQxOTQ4MjktN2Q5ZS00YjE5LTgyNzktNjhhNWI1NTJjMmFm&hl=en&lt;/a&gt;&lt;/p>

<p>4)In the figure above,Points A,B,C,and D lie on the circle,N is the center of the circle,and AD is perpendicular to BC. What fraction of the circle is shaded?</p>

<p>12)In the figure above,AB = x,BC = y,and AB and MN are perpendicular to BC. If BN = 0.2y, what is the area of the shaded region, in terms of x and y?</p>

<p>Alright I tried to solve this by doing number,but I failed I said if:</p>

<p>BC = 20;
AB = 22;</p>

<p>BN = 0.2 * 20 = 4;</p>

<p>I broke the shaded figure into a rectangle by doing a line from M to its end which I called MX.</p>

<p>MX = 4 aswell.</p>

<p>Since triangle AMX if you draw another triangle and flipped it oppossite to that small AMX you would find that they are a square,so
AX = 4; AM = 4;</p>

<p>Then 1/2 * 4 * 4 = 8;</p>

<p>Rectangle XMBN = 4 * (22 - 4) = 72 + 8 = 80,but thats wrong I hope someone point out what did I do wrong.</p>

<p>16)Sharon has 20 water balloons in her bucket and Michelle has 3 in hers. Sharon is tossing water balloons to Michelle, who is trying her best to catch them and put them in her bucket. If every 3rd toss result in a dropped and broken balloon,how many tosses have to occur for the two girls have the same number of balloons?</p>

<p>I solved this by substituting numbers and back solving,but I want to know how to solve this algebraically in case if this type of problem come in grid in.</p>

<p>10/3 = 3.333 we remove remainder and get 3,since it goes into 10 only 3 times.</p>

<p>So we have 3 loses 10 - 3 = 7;</p>

<p>Michelle = 3 + 7 = 10;
Sharon = 20 - 10 = 10;</p>

<p>I want to know though how to solve this algebraically.</p>

<p>18)In the figure above,ABCD is a square,and A,B,C,and D are the centers of four congruent circles which touch each other but do not overlap. If the area of ABCD is 1,what is the perimeter of shaded region?</p>

<p>I tried solved this,but there something I did wrong I got 4PI which is circle area + 0.5 * 4,which is obviously not in the answers.</p>

2

<p>For 18, it asks for the perimeter of the shaded region. The radius of each of the four circles is .5 so the perimeter of each circle is 2pi(.5)=1. The perimeter of the shaded region has to be less than the perimeter of the four circles combined, thus the answer is choice A because it’s the only answer choice less than 4pi.</p>

3

<p>@PencilxBoxes </p>

<p>Oh I see I thought I would get of 4 circles combined then add the perimeter of the square,but I see what I did wrong now the I also knew know how can we be sure its 3 atleast in my intuition.</p>

<p>Since that figure consists of 4 squares each side takes quarter of the circle then there is 1 circle all together in that is made of 4 quarters,so 4 * 1/4 = 1;</p>

<p>Then it should be 2 * 4 * 0.5 = 4PI - 1PI = 3PI.</p>

4

<p>Sorry for this post had to do it,so it the question doesn’t go page 2.</p>

5

<p>For number 4, pick a number for the radius, say r=1. Then the circle has area pi(1)2 = pi, and each triangle has area 1/2 (1)(1) = 1/2. So the shaded region has area pi-2(1/2) = pi-1. So the fraction of the circle that is shaded is (area of triangles)/(area of circle) = 1/pi</p>

6

<ol>
<li>I DO NOT recommend doing this algebraically on the SAT, but here’s an algebraic solution anyway:</li>
</ol>

<p>Let x represent the number of tosses:</p>

<p>20-x = 3+2x/3. So 5x/3=17, and x = (17)(3)/5 = 10.2. Since the 10th toss is successful, the answer is 10.</p>

<p>Even if this were a grid in, guessing and checking would be the best way to solve it.</p>

7

<p>Let’s use your numbers for number 12:</p>

<p>y = BC = 20, x = AB = 22. Then BN = .2*20 = 4, and NC = 20-4=16. Using similar triangles, we have MN/16 = 22/20. Cross multiply and divide to get MN = 17.6.</p>

<p>The area of the big triangle is 1/2 (20)(22) = 220. The area of the white triangle is 1/2 (17.6)(16) = 140.8. Thus, the area of the shaded region is 220-140.8 = 79.2. Put a nice big, dark circle around this number. Now plug x=22 and y=20 into all the answer choices. The only choice that gives the correct answer is choice (D).</p>

8

<p>@DrSteve</p>

<p>Thanks alot those questions make perfect sense now :D.</p>

9

<p>Hi guys! Glad you’re enjoying the drill. Someone just alerted me to this discussion, and although it looks like all questions have been resolved, I wanted to echo Dr. Steve and BEG you not to try to solve questions like the water balloon problem algebraically. Doing so is playing right into the hands of the test!</p>