<p>I just took a practice test; currently, I'm going over the questions I got wrong.
I'm not sure how to solve these ones. I know what the answers are, I just don't know how they were achieved.</p>
<ol>
<li>A square with an area of 1 is divided into two non-overlapping regions, one of which is shaded. If the area of the unshaded region is a, then what percent of the area of the square, in terms of a, is shaded?
A. a%
B. (1-a)%
C. 100a%
D. (100a-100)%
E. (100-100a)%</li>
</ol>
<p>1A</p>
<h1>xB3</h1>
<p>BA</p>
<h1>+60</h1>
<p>6BA</p>
<ol>
<li><p>In the operation above, A and B represent distinct digits. What is the value of A + B?
A. 4
B. 5
C. 9
D. 45
E. 54</p></li>
<li><p>In a right triangle, if twice the length of side AB is equal to 3/2 the length of side AC, what is the ratio of the lengths AC to BC?
A. 1:1
B. 2:3
C. 2:3
D. 4:5
E. 3:2</p></li>
<li><p>Jim's recipe for cranberry-grape juice calls for 4 cups of grape juice every 7 cups of cranberry juice. He wants to make 132 ounces of cranberry-grape juice, but he realizes that he is short by exactly 4 cups of cranberry juice. How many ounces of cranberry juice does he have?
(1 cup = 8 oz)
A. 10
B. 32
C. 52
D. 80
E. 84</p></li>
<li><p>Year | Units Sold
2001 | x
2002 | 896
2003 | 534
2004 | 776
2005 | 652
The table above shows sales of MP3 music players at the local department store. If the median number of units sold is 652, and no two years had the same sales, what is the greatest possible value for X?</p></li>
<li><p>Diagram is at following link: Image</a> - TinyPic - Free Image Hosting, Photo Sharing & Video Hosting
The circle with center O shown in the figure above as an area of 18pi. Isosceles right triangle OAB is inscribed in the circle, and point B lies on the graph:
y = -kx^2.
What is the value of the constant k?</p></li>
</ol>
<ol>
<li><p>Well, I would just use values of a that would be easy to take a percent from, and then plug them into the answer choices to see which one gives you the right percentage value. Like, if the shaded area has an area of 1/2, you would know that the shaded area is 50%, so if you plug in 1/2 to the answer choices, the only one that yields the answer of 50% is C.</p></li>
<li><p>I’m not sure about your formatting on this one, so I can’t really tell what the question is asking. Sorry!</p></li>
<li><p>Take these statements and make them into an equation. 2AB=3/2AC. Divide both sides by 2, and get AB=3/4AC. At this point, you should notice that you’re dealing with a 3-4-5 right triangle, and that AB=3 and AC=4. Therefore, BC=5, and the ratio of AC to BC is 4:5. D</p></li>
<li><p>Okay, so, the way I approached this was to divide the juice up into groups of 88 ounces, each one having 32 ounces of grape juice, and 56 ounces of cranberry juice. In order to make 132 ounces in total, he’ll need to use 1.5 of these groups. Therefore, he would need 84 ounces of cranberry juice. He’s short by 4 cups, or 32 ounces, though, so subtract that from what he has, and the answer is 52. The trickiest thing on this one was probably the units; I worked it all out in cups at first, and got one of the answer choices, however, I’m pretty sure what it’s looking for is C, and not D.</p></li>
<li><p>So, the median of the set is 652, and no two years can have the same number of sales. Well, since we have an odd number of years, we know we won’t have to take the average of two numbers to find the median. We must have exactly two numbers greater than 652 and exactly two numbers less than 652. Since we already have two numbers greater than 652, the next number must be less than 652, so the greatest that it could be is 651.</p></li>
<li><p>So, if the area of the circle is 18pi, we know that the radius of the circle is 3root2. We also know that it is the hypotenuse of the isosceles right triangle, so the length of each side of the triangle is 3. We then plug in the point (3, -3) to the equation y=-kx^2, and I believe that the answer is -1/3.</p></li>
</ol>
<p>Sorry that I couldn’t answer all your questions, but hopefully this helped, and the answers are right. If they’re not, I’d be happy to come back and rework these.</p>
<p>Thank you for the help!
All of the answers you got were right except for question 8.
The answer is actually E for some reason.</p>
<p>As for number 9, the diagram is a little weird, sorry. It’s supposed to be normal column addition and multiplication operations.
The problem is asking you to figure out the value of A and B, essentially.</p>
<p>Oh, I get it now. I was letting a be the shaded region (or whatever region it was asking for. 100a is the percentage of what it’s not asking for, and so if you take 100 (the whole thing) and subtract what it isn’t asking for, you’ll get what it is asking for.</p>