Help with Problems from released SAT's

Test Preparation SAT Preparation
1

<ol>
<li>The restoration of the [once bustling] neighborhood, an area [recently marred] by litter and graffiti, is one of the [high praised] [efforts of] the mayor's administration. </li>
</ol>

<p>(The answer is high praised...why? It did sound a little weird when I read it but I thought it was fine.)</p>

<ol>
<li>Though [far] less innovative [as a composer] of vocal and instrumental music, George Philip Telemann was [the most prolific of] either Johann Sebastian Bach or George Frideric Handel.</li>
</ol>

<p>(The answer is the most prolific of...why?)</p>

<ol>
<li>A bookstore has 15,000 books in stock, of which 60 percent are paperback and 40 percent are hardcover. Al the books are either fiction or nonfiction. If 4500 of the books are nonfiction and 2500 of the nonfiction books are paperback, how many of the books are both fiction and hardcover.</li>
</ol>

<p>(I not only spent a while on this problem, I also got it wrong. What is the fastest way to do it?)</p>

<ol>
<li><a href="http://img.photobucket.com/albums/v407/ammad/IMG00224-20110920-1912.jpg%5B/url%5D"&gt;http://img.photobucket.com/albums/v407/ammad/IMG00224-20110920-1912.jpg&lt;/a&gt;&lt;/li>
</ol>

<p>(As you can see, I found that point A is (-4,3). Now they want the slope so I did rise/run which is 3/4 yet the answer is actually 4/3.)</p>

<ol>
<li>[It is] now generally agreed [that] the rings of the planet Saturn [are composed of] [several] billion small ice particles.</li>
</ol>

<p>(This is a level 1 problem and their is no error. What threw me off is the "It is". What is "it" referring too? I didn't know you could start off the sentence like that)</p>

<ol>
<li>In the novel Agnes Gray, Anne Bronte presented a fictionalized account of both she and her sister's bizarre experiences as teachers in the houses of Victorian aristocrats.</li>
</ol>

<p>(A) of both she and her sister's bizarre experiences as teachers
(B) of both her and her sister's bizarre experiences as teachers
(C) of both she and her sister's bizarre experiences teaching</p>

<p>(The answer is B and I got it right however I am a little iffy on when to use "She and her" and "Her and her"...can anyone help me out?)</p>

<p>7.If (x-y)^x = 1 and y^x = 1, where x and y are positive integers, what is the value of x?</p>

<p>(A) 1
(B) 2
(C) 3
(D) 4
(E) 5</p>

<p>(I messed around with this problem on my TI-89 and got it but what is the formal fast way to do it? Answer is B)</p>

<ol>
<li>5, a, b, 5, ...</li>
</ol>

<p>In the sequence above, the first term is 5 and the second term is a. Each term after the second is the product of the two immediately preceding terms. If A<0, what is the 10th term of the sequence?</p>

<p>(A) -5^21
(B) -5^10
(C) 5
(D) 5^10
(E) 5^21</p>

<p>(its e)</p>

<ol>
<li>For which of the following functions is it true that -F(X) = F(-X) for all values of x?</li>
</ol>

<p>(A) F(X) = X + 4
(B) F(X) = X^2 + 4
(C) F(X) = X^3 + 4
(D) F(X) = X^2 + X
(E) F(X) = X^3 + X</p>

<p>(its d)</p>

<ol>
<li>The acoustics of the ancient Greek theater at Epidaurus are [so good that] an actor's words, [even when whispered], are [auditory] to [those sitting] in the last row.</li>
</ol>

<p>(The answer is auditory...what the hell)</p>

<ol>
<li>Though I am [acquainted with] Mr. Bartholomew and have [long known of] his interest in the painting, that he has gone to such lengths [to obtain it] astonishes me.</li>
</ol>

<p>(The answer is to obtain it..why?)</p>

<ol>
<li><p><a href="http://img.photobucket.com/albums/v407/ammad/IMG00218-20110918-0234.jpg%5B/url%5D"&gt;http://img.photobucket.com/albums/v407/ammad/IMG00218-20110918-0234.jpg&lt;/a&gt;&lt;/p&gt;&lt;/li>
<li><p>At North High School, the ski club has 15 members and the debate club has 12 members. If a total of 11 students belong to only one of the two clubs, how many students belong to both clubs?</p></li>
</ol>

<p>(A) 2
(B) 7
(C) 8
(D) 12
(E) 16</p>

<p>It's c</p>

<ol>
<li>If x = 0 and x is inversely proportional to y, which of the following is directly proportional 1/(x^2)?</li>
</ol>

<p>(A) -1/(y^2)
(B) 1/Y^2
(C) 1/Y
(D) Y
(E) Y^2</p>

<ol>
<li><a href="http://img.photobucket.com/albums/v407/ammad/IMG00227-20110921-1501.jpg%5B/url%5D"&gt;http://img.photobucket.com/albums/v407/ammad/IMG00227-20110921-1501.jpg&lt;/a&gt;&lt;/li>
</ol>

<p>(I really hate these problems involving the distance = rate * time formula..the answer is A)</p>

<p>Thanks a lot, I really appreciate it!</p>

2

<p>1) It should by highly praised. (Adverb)
2) It should be more prolific than. (You are only comparing two things at a time. Telemann vs Bach and Telemann vs Handel
5) I don’t know what to tell you…it’s just right!
6) On these types of questions, I always take out the “and” part. She bizarre experiences does not make sense while her bizarre experiences does.</p>

3

<ol>
<li>The acoustics of the ancient Greek theater at Epidaurus are [so good that] an actor’s words, [even when whispered], are [auditory] to [those sitting] in the last row.</li>
</ol>

<p>(The answer is auditory…what the hell)</p>

<p>The answer should be audible</p>

<ol>
<li>Though I am [acquainted with] Mr. Bartholomew and have [long known of] his interest in the painting, that he has gone to such lengths [to obtain it] astonishes me.</li>
</ol>

<p>Really? I would say no error. If I have to be so particular, I would say that it is ambiguous since it can refer to either interest or the painting.</p>

4

<p>Thanks for your speedy replies, they really help.</p>

<p>JefferyJung, you are right. The answer is no error. I chose “to obtain it”. Shouldn’t it be changed to “that he has gone to such lengths in obtaining it astonishes me” instead of “that he has gone to such lengths to obtain it astonishes me”.</p>

5

<p>I’m not too confident in what I’m going to say right now.
I would say that the use of in obtaining tweaks the meaning a little bit. To obtain implies that he went such lengths in order to obtain the painting whereas in obtaining implies a little different meaning.</p>

<p>Since I’m not entirely confident with that question, I’m going to leave that to other CCers who are grammar savvy.</p>

6

<ol>
<li>A bookstore has 15,000 books in stock, of which 60 percent are paperback and 40 percent are hardcover. Al the books are either fiction or nonfiction. If 4500 of the books are nonfiction and 2500 of the nonfiction books are paperback, how many of the books are both fiction and hardcover.</li>
</ol>

<p>(I not only spent a while on this problem, I also got it wrong. What is the fastest way to do it?)</p>

<p>…Paperback…Hardcover…Total
Fiction…6500…4000…10500
Nonfiction…2500…2000…4500
Total…9000…6000…15000</p>

<p>Make a table. It is the safest way. It doesn’t take too much time.</p>

7

<p>For 4, draw a line perpendicular with line l, and let this line be line p. Line p passes through both point A(-4,3), and the origin(0,0). Find the slope.
(y2-y1)/(x2-x1) = (3-0)/(-4-0) = -3/4.
Since line l is perpendicular to line p, find the negative reciprocal of the slope of the line p, and that is 4/3.</p>

<p>Wow…! I think this is a really difficult problem for the SAT…</p>

8

<p>7.If (x-y)^x = 1 and y^x = 1, where x and y are positive integers, what is the value of x?</p>

<p>(A) 1
(B) 2
(C) 3
(D) 4
(E) 5</p>

<p>For this problem, my mind would think, “since y^x=1, y has to be 1 or x has to be 0.” Since x and y are positive integers, x can’t be 0, therefore y is 1. Then, (x-y)^x=1. which means (x-y) must equal 1. Since we know y is 1, x-y(1)=1, x=2.</p>

<p>This would be my thought process. Tell me if any part of this was confusing. I’m not exactly good at math, so I might be giving you the incorrect solution…</p>

9

<p>8) 5, a, b, 5, …</p>

<p>In the sequence above, the first term is 5 and the second term is a. Each term after the second is the product of the two immediately preceding terms. If A<0, what is the 10th term of the sequence?</p>

<p>(A) -5^21
(B) -5^10
(C) 5
(D) 5^10
(E) 5^21</p>

<p>Solve for a:
b= 5a
5=ab
b=5/a and b= 5a
5/a=5a
5=5a^2
1=a^2
Since a<0, a= -1
5, -1, b, 5
5*(-1)= -5
b= -5
5, a, b, 5, 5b, (5^2)(b), (5^3)(b^2), (5^5)(b^3), (5^8)(b^5), <a href=“5%5E13”>b</a>(b^8)**</p>

<p>Since b= -5, (5^13)((-5)^8) = 5^21</p>

10

<ol>
<li>For which of the following functions is it true that -F(X) = F(-X) for all values of x?</li>
</ol>

<p>(A) F(X) = X + 4
(B) F(X) = X^2 + 4
(C) F(X) = X^3 + 4
(D) F(X) = X^2 + X
(E) F(X) = X^3 + X</p>

<p>Plug in numbers…
if x=1…
-(1+4)=(-1+4) nope
.
.
.
Both D and E work.
If x=2
D) -((2^2)+2)=(-2^2)+2
-6=6 nope
E) -((2^3)+2)=(-2^3)-2
-10= -10 YES!</p>

<p>Are you sure D is the correct answer? I got E… :)</p>

11

<ol>
<li><p>D) 90
Is this correct?</p></li>
<li><p>At North High School, the ski club has 15 members and the debate club has 12 members. If a total of 11 students belong to only one of the two clubs, how many students belong to both clubs?</p></li>
</ol>

<p>Ski club- 15
Debate - 12
Total - 27
11 out of 27 belong to one.
16 club members are accounted for by students belonging to both clubs. = 16/2 = 8</p>

12

<p><a href=“I%20really%20hate%20these%20problems%20involving%20the%20distance%20=%20rate%20*%20time%20formula…the%20answer%20is%20A”>quote</a>

[/quote]
</p>

<p>Have some faith. Pay attention to the question and apply the d = rt formula correctly.</p>

<p>Time Down = 2*
Rate Down = 4
D Down = 8</p>

<p>Time Up = 3*
Rate Up = 2
D = 6</p>

<p>Total D = 6 + 8 = 14</p>

<p>D Down
--------- = 8/14 or 4/7
Total D </p>

<p>*This could be 2 and 3, or 2/5 and 3/5 or 2/10 and 3/10 as long as the ratio of time stays constant.</p>

13

<ol>
<li>If x = 0 and x is inversely proportional to y, which of the following is directly proportional 1/(x^2)?</li>
</ol>

<p>(A) -1/(y^2)
(B) 1/Y^2
(C) 1/Y
(D) Y
(E) Y^2</p>

<p>I hope you meant… x is not equal to 0… because if x=0, the problem doesn’t go anywhere.</p>

<p>Inversely proportional: y=k/x
Square both sides: y²=k²/x² (finally found the small 2…)</p>

<p>Since k is constant, let k²=1.
y²=**1/x²<a href=“look%20familiar?”>/b</a>
The answer is (E)</p>

14

<p>The last question was done by the amazing xiggi.</p>

<p>If anything I wrote was confusing for you, PM me or ask me…</p>

15

<p>For number 4, you can also approach the problem with calculus. If you don’t know calculus, disregard the rest of this post.</p>

<p>Your equation is x²+y²=25. You want to find the slope of the line at x=-4. Take the derivative (implicitly) and find the value of y’ (dy/dx) at x=-4 (point A, which is (-4,3)).</p>

<p>f(x)=x²+y²=25</p>

<p>dy/dx: 2x+2y(y’)=0</p>

<p>(dy/dx)|x=-4: 2(-4)+2(3)(y’)=0</p>

<p>2(-4)+2(3)(y’)=0</p>

<p>-8+6y’=0</p>

<p>y’=slope at point A=8/6=4/3=1.33</p>

16

<p>

</p>

<p>What could you say about a triangle with three identical sides? Equilateral triangles have angles of … ?</p>

17

<p>You can use calculus, but SAT is supposed to only test knowledge up to geometry. I don’t feel like I’m solving the problem the right way when I go above and beyond. lol</p>

18

<p>OH NO!! My bad… Yes. Xiggi… you’re right… Sorry the answer is 60.</p>

19

<p>I have reviewed all the solutions you guys posted and now understand them all. Thanks a lot, (Especially Jeffrey for answering almost all haha). Xiggi, I have practiced more and more with the distance formula and have become more comfortable with it now. Thanks for your solution as well.</p>

<p>I still don’t get that equal triangle one with the answer being 60. Can you explain that?</p>

<p>Also, I had a few a more questions…all from QAS again.</p>

<ol>
<li><a href=“http://img.■■■■■■■■■■■■■■■/albums/v407/ammad/IMG00239-20110924-1419.jpg[/url]”>http://img.■■■■■■■■■■■■■■■/albums/v407/ammad/IMG00239-20110924-1419.jpg&lt;/a&gt;&lt;/li&gt;
</ol>

<p>The cone has a volume of 18pi which means the water is 18pi since the cone is fulled to the max. The cylinder has a volume of 54pi. You pour the water into the cylinder so the water would hold 54pi - 18pi = 36pi of the total volume in the cylinder. That is not the answer, they want it in “inches” which screwed me up. The answer is 2. I guess you would do 36pi/54pi * 6 which = 2 but I am not sure I get the logic behind this.</p>

<ol>
<li>Point P lies in plane M. How many circles are there in plane M that have center P and a circumference of 6pi inches?</li>
</ol>

<p>(A) None
(B) One
(C) Two
(D) Four
(E) More than four</p>

<p>I thought this was one of those stupid trick questions where their can be unlimited possibilities. I was wrong, it is B. Why?</p>

<p>Thanks a lot.</p>

20

<p>60 degrees problem. You have three identical diagonals in the cube. They form an equilateral triangle. Each angle is thus 60 degrees.</p>

<p>For the cone, all you do is compare the formula of the cone to the formula of a cylinder. Notice the cone is 1/3 of the cylinder. The water in the cylinder will reach a 1/3 level.</p>