LSAT 24: First steps

In my last post [1], I wrote about my plan to work my way through LSAT problems and try to discern best practices to solve them.

For this post, I tackled LSAT test number 24. The test went surprisingly well for me; much better than I would have expected.  I completed it while I was in sort of a strange mood.  I did parts of it on the subway, parts of it in a quiet office, and parts of it on a commuter rail train.  I didn't care about time.  I didn't make any mistakes on the games, but I would not have finished the section if it were timed.  (I'll tackle the games at a later point, and might circle back around and address some of them here.)

Of the four questions I got wrong overall, three were in the Logical Reasoning (arguments) section, and two of them involved formal logic.  By the way, this number wrong is abnormally low.  I usually get about 10 wrong or so.

One last note:  I'm actually not approaching this test completely cold; I have read some LSAT prep books and taken one course.  Thus, it may seem like some of my early answers assume a prior knowledge that I do not explicitly show.  Once I get a critical mass of questions, my plan is to start using the evidence to help determine whether the method I'm using is appropriate or not.

If you'd like to purchase a copy of the exam, you can do so here [2]. 

Question 21, Section 2:

I found this one to be a tricky question, because it seemed to start out with a rather informal set of information, then the question proved to involve a significant amount of formal logic with lots of negation.  I was able to isolate the following items:  that "the laws are impossible to enforce" is an argument that leads to the main argument.  So we know that if there is a law against gambling, then it is impossible to enforce.  "When a law fails to be effective, I should not be a law" is an argument, and the conclusion is that there should be no laws against gambling.  So it's pretty clear that we need some sort of connective from the word "enforce" to the word "effective."  This means that answers A and B are particularly attractive.  When I see the similar wording of the answers, especially with the amount of ‘not's' around (as well as words like ‘All' and ‘No'), I start going back to formalize the relationships.

I symbolized the first statement as LaG → ¬Enforce.
I symbolized the second statement as ¬Effective → ¬Law.

(The ¬ symbolizes the phrase "not", so you would read the last statement as "not-Effective implies not-Law")

Since we know that we're trying to get to ¬LaG, then we know we have to get from Effective to Enforce, because by the contrapositive of the first statement, we know that Enforce → ¬LaG.
Answer choice A requires some manipulation, but if we take the answer and literally convert it, we get ‘No Effective is ¬Enforce.'  Formal logic says that statements of the form "No A is B" become "A → ¬B".  Our statement then becomes Effective → ‘Not' ¬Enforce, which taking the double negation becomes Effective → Enforce.  This is exactly what we're looking for, so it's the correct answer.

I originally picked B, which converts to Enforce → Effective.  Since this is the converse of what we're looking for, it isn't necessarily true.  I should have known this.  Actually, I felt pressed for time and didn't want to go through the hassle of converting A, and this seemed ‘good enough' to get to what I was looking for.  Blech.

STATUS:  RESOLVED VIA FORMAL LOGIC.

Question 19, Section 3:

We see from the words "every" and "some" that we are again in formal logic territory.  Because of the similarity of the wording of the answers, it again feels to me like I need to use some sort of symbolic notation to keep track of exactly what we should be doing here.  The first statement, "Every student who walks to school goes home for lunch" becomes Walk → Home.  The second sentence becomes Part-time → ¬Walk.  I know that the question makes specific use of the words "every" and "some," but I'm going to stay away from that kind of logic for now.

Now, in order to answer this question, we need to make an assumption that binds the two implications together.  Since one deals with Walk and the other deals with ¬Walk, we might need to take the contrapositive of one of the statements.  (Again, I'm assuming a level of knowledge that some of you might not have.  I'm sorry for this; I just didn't want to get bogged down with too much introductory stuff.  I'll cover it later.)  If we take the contrapositive of the first statement, we get ¬Home → ¬Walk.  If we can get ¬Home to Part-time, then we are set.  Is there such an answer?  Yes, it's D.  I had originally picked A, which translates to ¬Part-time → Home.  If I had taken the contrapositive of the second, I would have gotten Walk → ¬Part-time, which when joined with my answer would have given me Walk → Home as well.  Hmm...It looks like the categorical logic does come into play here.

It's pretty clear that in order to do at least some of these questions on the test, we would be aided by formal logic as well as categorical logic (i.e. logic dealing with all, some, etc.)  So let's put a callout here.

Need (1):  Some sort of understanding of formal logic.
Need (2):  Some sort of understanding of categorical logic.

As always, I'd love to get a critical mass of questions that I could go back and reanalyze them after having learned about some formal logic.

STATUS:  UNRESOLVED PENDING CATEGORICAL LOGIC.

Question 18, Section 2:

From the first sentence of this question stem, we can already discern an issue here.  Government funding for the preservation of wetlands has increased by a lot, but the area of wetlands needing protection has only increased by a little.  The next sentence rules out one source of an explanation, which is inflation, and then concludes that the level of funding is still short of what's necessary.

This seems like a great time to bring up mental models.  Whenever I read questions like this, I keep a mental model in my head of what's going on, and I adjust it as each new piece of data comes in.  In fact, I am going to discuss a lot of these answers using mental models.  Here's what I mean:

Let's call this the funding model.  The funding model is very simple:  You have something that you're trying to do, and it costs a certain amount of money to help you do it.  The more money you have, the more you can do; the less money you have, the less you can do.  Sounds pretty straightforward, right?  Well, in this case the funding model seems out of kilter:  We have lots more money, but we've only got a little bit more of stuff to do.  Why do we still need more money?  Well, they rule out the possibility that the cost of doing the same thing has gone up because of inflation, so that knocks out one thing.  They remind us that the amount of stuff to be done was already large, so that knocks out the possibility of us making a claim about the original level of preservation.  So we've got to find an answer that reconciles these two areas.

Here's where my SAT bias kicks in.  Most of the SAT questions can be predicted by being an active reader and thinking actively about the question before one encounters the specific answers.  There are some theories out there about entering the answers with a blank mind and so not being biased, but I have been helped out by my active thinking more often than I've been hurt by it.

So it's time for a hypothesis.  Hypothesis (1):  active thinking, i.e. trying to predict where the question is heading, is bound to help find the right answer in the long run.  It is not guaranteed to find the right answer, and in some cases might lead you astray, but nevertheless is a good thing.  Mental models provide a good way to aid active thinking.

Hypothesis(2):  The funding model is an appropriate way to describe questions when there involves a logical relation between an activity and the money it costs to fund that activity.

Going along with that hypothesis, my first instinct is to come up with an explanation for the issue, no matter how off base, to get my mind working in the right direction.

So my first guess is to say that the reason that funding is inadequate was that there was hardly any funding to begin with.  If there was originally, let's say, 1 unit of funding available for the project but the project needed 100 units of funding, then clearly the recent increase wouldn't be enough.  Now that I'm armed with a reasonable answer, let's see how it plays out:

Answer A could be an answer, although it does not paint things in a very nice light.  When I read it, I was tempted to leave it in until I reread the conclusion of the argument:  "the funding is inadequate and should be augmented."  If the money was there but was just mismanaged, then the level of funding was, in fact, adequate.  At the very least, it raises more issues than it answers, so it cannot be the correct answer.

Answer B was originally the answer I picked.  I think I was desperate for an answer, and picked one that sounded reasonable rather than thinking it through.  This answer says, essentially, that costs of doing the work have gone up.  However, in retrospect, I didn't pay close enough attention to the wording in the problem about inflation.  If the problem says that the increase in funding was at least three times what it was, even factoring in inflation, it makes it pretty hard to justify the necessity of more funding solely on the fact that scientist's salaries have risen.  They would need to have risen by a factor of 3, and more to the point would need to keep rising in order to require more funding.  This is unlikely, or at least allows for an ambiguous outcome (i.e. the salaries might have risen, but not by so much as to explain the entire reason for the funding increase.)

Answer C was another choice I was down to.  In retrospect, the distinction between "wetlands in need of preservation" and "wetlands at serious risk of destruction," was never made explicit in the passage.  Since the government's mission is only the "preservation of wetlands," which is pretty vaguely worded, both of these areas could fall under that description, but they also could not.  This is the danger of thinking too far outside the construct of the prompt and the weird little world the test makers create.

Answer D makes no sense.  There is no distinction made in the passage between scientists and non-scientists.

Answer E is exactly what I was looking for.  Why didn't I see this?  I feel silly.  A possible explanation is the misdirection play contained in this question.  I think this might be important, so I'll put it up for later.

Definition(1):  Misdirection:  The LSAT's process of putting a straightforward answer after several more intricate and complicated answers.  The reason this answer is harder to spot has little to do with the actual validity of the answer itself, but more because the test-taker is still harboring thoughts about the previous complicated answers and therefore doesn't read the straightforward answer correctly.

This provides one vote in favor of my mental-modeling, but I'll have to explain how one goes about formulating mental models later.  

STATUS:  RESOLVED VIA HYPOTHESIS(2){mental model, funding}.

Have a question you'd like to see explained? Have any feedback on what you've read? Please post a comment and let me know.

 

For the past eight years, Charles Williamson [3] hasn’t met a standardized test he didn’t like, helping hundreds of students in everything from the SAT and ACT to the SSAT to the GMAT to AP Calculus. A longtime student of the thought process that defines performance on standardized tests, Charles got off to a good start, receiving a perfect score on his SATs in high school. He then graduated from Brown University, earning bachelor's degrees in computer science and history.  He has long been fascinated by the intersection of education and technology, and when not writing about standardized tests and educational policy, he will be happy to speculate rampantly about how the Internet will affect the ways that we learn.  Charles blogs for the Ivey Files about test preparation.