Challenging SAT problem

<p>I found this math problem on a website claiming to have SAT practice problems. I thought I had it right, but I don't get the answer:</p>

<p>**If V = 12R / (r + R) , then R =</p>

<p>A. Vr / (12 - V)
B. Vr + V /12
C. Vr - 12
D. V / r - 12
E. V (r + 1) /12 </p>

<p>Correct Answer: A</p>

<p>Explanation:</p>

<p>We have to rearrange the equation to make R the subject.
Start by cross multiplying by (r + R); V (r + R) = 12R
Multiply out the bracket Vr + VR = 12R**</p>

<p>I did exactly what they're saying, and I get:
R = Vr + VR/12
How does that become Vr / (12 - V)? </p>

<p>I'm lost.</p>

<p>Thanks to anyone who wants to help.</p>

<ol>
<li>V = 12R / (r + R)</li>
<li>r + R = 12R / V [switch V with r + R]</li>
<li>Vr + VR = 12R [multiple V to the other side]</li>
<li>Vr = 12R - VR [bring VR to other side]</li>
<li>Vr = R (12 - V)</li>
<li>Vr / (12 - V) = R</li>
</ol>

<p>you were going ok but you did not finish the problem after u got R= Vr+VR/12 u had to continue working the problem until there was only one R
R=Vr+VR/12
12R = Vr+VR
12R-VR= Vr
R (12-V)=Vr
R=Vr/(12-V)</p>

<p>You can also simply take for R,r,V a number and do trial and error</p>

<p>Generally I prefer an algebraic approach, but in this question I agree with Deference:</p>

<p>you could notice that
r=0, R=1 --> V=12 quickly eliminates A, C, and D
and
r=-1, R=2 --> V=24 eliminates B.</p>

<p>Of course, choosing "good" numbers is tricky, but if you practice both methods on a lot of SAT questions, you'll get a knack of it.</p>

<p>Just having chided somebody else for rushing through, I myself fell a victim of that sin.</p>

<p>r=0, R=1 --> V=12 does not eliminate A (R is undefined in this answer).</p>

<p>r=-1, R=2 --> V=24 eliminates B AND E!</p>

<p>It does prove though that this question is not designed properly:
set r=0, R=1, V=12 satisfies given equation, but is not valid for the answer A.
Hey, I got an excuse!</p>

<p>R= 3
r= 6
V= 4</p>

<p>Plug into the equations, see which work?</p>

<p>Or we could avoid this entire ordeal, and punch this simple equation into your TI-89/Titanium:</p>

<p>solve(v=(12r)/(x+r),r) where x represents "r" (lower case r)</p>

<p>"solve" responds with the answer (just multiply it by -1 to get ETS's answer)</p>

<p>Took 30 seconds or less (depending on how fast you can punch keys).</p>

<p>:D :D</p>

<p>Right on, Programmer!
This is also another proof that the question is not your typical SAT - you almost never see equations where "solver" would give you an edge (SAT II is a different story).</p>

<p>What the (bleep) - I used solver several times on the last SAT test to great effect</p>

<p>Programmer, I don't see why you need to use stronger language when it's not really warranted (I remember this example of your extreme reaction:
<a href="http://talk.collegeconfidential.com/showthread.php?p=977596#post977596%5B/url%5D"&gt;http://talk.collegeconfidential.com/showthread.php?p=977596#post977596&lt;/a&gt;)&lt;/p>

<p>Would be cool if you could recall those questions you mention and demostrated them here.
There is also another way to gather statistics (pretty quick) - go through the whole Blue Book and find all the questions where solver would give you an advantage.
What's the average per test?</p>

<p>I am a huge fan of TI-89, but why use a jackhammer where you can perfectly do with a swiss knife (any scientific calculator - they work wonders with fractions)?</p>

<p>First, I am quite positive that this problem would NEVER show up on a real SAR because the answer takes too many steps and the steps do not progress in a NATURAL way. Simply stated, it is yet another poor question and it would never pass the ETS' integrity process. I do like the takesat contents, but their tests are no different from the others and are best ignored. </p>

<p>Programmer, when I started working on the SAT, I did what most everyone does: looking for outside "neat" ways to beat the Math SAT. </p>

<p>At that time, there were a couple kids selling a program for the TI-83. The program was much better than the ones that could be downloaded from the TI site. Guess what, I only thought it would be "neat" because I did not know enough about the SAT. The reality is that you can do the entire 10RS book and not find a single problem that is easier solved with ANY calculator. That does not mean that someone who is VERY, VERY good with a TI-89 or TI-83 could not find the answer. It means that one could find a solution as quickly with nothing more than a quick brain. </p>

<p>Even if some problems were to be dumbed down from the former SAT-II, the issue with the calculator is that the time you could save on a problem will probably be saved on the next one, where the solution can be derived by common sense. Oh wait, what if the student can SEE which questions are perfect for a calculator tour de force and and leave the other alone? The answer is that such student probably does not need the calculator in the first place.</p>

<p>From gcf101's past comments, it is obvious that he knows the SAT requirements, knows how a TI works, and knows how to evaluate its impact on the SAT and the Subject Test Math Level 2. On the SAT, the 89 is an absolute overkill that will hurt most everyone, except the occasional TI virtuoso. The situation is entirely reversed on the Subject test that should have been labeled as the TI89 Subject test. </p>

<p>I understand that you invested a large amount of time in writing the programs. I also invested a large amount of time compiling and evaluating the effects of the Barron's list of words , only to realize how ineffective it was.</p>

<p>Ok I'll tone down the language... :(</p>

<p>But what are you trying to say gcf101 - "Would be cool if you could recall those questions you mention and demostrated them here."</p>

<p>Which questions? Sorry</p>

<p>==========</p>

<p>Xiggi - sorry if we don't see eye to eye, but I (and others) have used my own program and it works effectively and efficiently.</p>

<p>Programmer, there is not a simple BEST method to prepare for the SAT. For instance, someone who plays with trig mightbe able to approach a few problems differently and efficiently. However, it is not nevessary to learn or improve trig to do well on the SAT. </p>

<p>IMHO, it is the same issue for the calculator. If you are very good at using it, it may pay dividends to use it on a number of problems. However, should someone buy and learn how to use it FOR the SAT? </p>

<p>I believe that a great way to illustrate our divergent positions would be to use the Official guides and "borrow" a few questions that lends themselves to a TI-89. You could show the TI method and others could post their method. In the end, readers could pick the method they feel the most comfortable with.</p>

<p>That is a wonderful idea Xiggi - I will attempt to pull some problems from Barron's SAT Math Workbook that would be suitable to users of the TI-89 and/or SAT_OS.</p>

<p>I believe you are correct in that people who feel more comfortable with the calculator will be able to use it to their advantage better than those who are not used to the TI way.</p>

<p>Another thing to note is that if one is not able to think in terms of the capabilities of the calculator, it will prove difficult when deciding when the best time is to use it (you would actually lose time thinking about how you could use the calculator to solve the problem). However, if you have had your calculator for a while, read the instruction manual thoroughly (yes, even the TI-89 one), and are comfortable using the functions, then there should be no reason to not use the calculator (if you want to, that is). :)</p>

<p>Thanks for the response Xiggi! :)</p>

<p>Programmer1324 (Post #10):
"I used solver several times on the last SAT test to great effect".</p>

<p>gcf101 (Post #11):
"Would be cool if you could recall those questions you mention and demostrated them here."</p>

<p>Programmer1324 (Post #13):</p>

<h2>"Which questions?"</h2>

<p>Programmer -
I meant questions from the last SAT test that you've tacked with your TI-89 nail gun.</p>

<p>P.S. Thanks for backing down on the firepower of your vocabulary!</p>

<p>P.P.S. Maybe you could find a shorter TI-89 solution to
<a href="http://talk.collegeconfidential.com/showthread.php?t=77794%5B/url%5D"&gt;http://talk.collegeconfidential.com/showthread.php?t=77794&lt;/a>
than one in my post #17, but would you use TI on this question on a real test?</p>

<p>Would be really interesting to know Xiggi's opinion on the best way of answering that question: both plugging in numbers (post #13 in that thread) and doing it algebraically (post #16) require more steps than you would expect on a "normal" SAT question.</p>

<p>gcf101, I went back and solved the problem in various ways.</p>

<p>For me, the most natural -and quickest- way was to use simple algebra. Also, I do not think that this ETS/TCB has "too" many steps. I looked at my first answer and I only scribbled down 4 very short lines, including the correct answer. I would NOT plug numbers for this problem. </p>

<p>IMHO, there is a world of difference between the original question and the SAT test. The first one is a bad SAT question, the second represents ETS at its best. </p>

<p>Last but not least, since this question is a number 19, and if had only 15 seconds to spare, I would have looked at the proposed answers, looked at the negative power of the question, and picked A with 90% confidence. The answer just "felt" like ETS. :)</p>

<p>Thanks Xiggi for providing your take on that question!</p>

<p>It's pretty interesting that you mentioned a "gut feeling" in answering a math question.
Students can rely on this feeling with a high rate of success when working on CR/Wr questions.
It's quite a different story with math questions. It takes a huge amount of practice to be able to start, in Programmer1324's words, see eye to eye with ETS.</p>

<p>Nothing is new here, of course. Intuition is often just a knowledge that has seeped into the subconscious.</p>

<p>Gcf101, allow me to add that it is not solelly a "gut feeling". When looking at the math questions written by ETS, an overwhelming follow a clear pattern: 2 to 3 answers will be blatantly wrong, and at first blush, 2 or 3 answers could be right with one of them usually being a "trick" answer. However, upon closer scrutiny, one answer will emerge as a very clear choice.</p>

<p>I also tend to think that ETS allows for 2 methods to arrive at the right answer: one is the methodical high school way that takes a student step by step to the right answer. Then, ETS also leaves a "shortcut" answer for students who have become quite familiar with the test or have a natural or developed ability to "see" through the problems as if they were puzzles. </p>

<p>Spending time trying to understand how and why ETS picked their correct answers and then added the 4 wrong answers (for MC) has helped me refine that gut feeling.</p>

<p>Xiggi, I'll be honest - I wish I could see how you "felt" the right answer (and blatantly wrong/possible ones) on the question we are discussing.</p>

<p>Is it possible to put that feeling into words (beside what you already explained)?</p>