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Kardash-eration!

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Kardash-eration!

Today, let’s do an LSAT preparation clinic on some Logical Reasoning hot topics (all of them by request from you, my attentive, intelligent, and (I’m assuming) highly physically attractive listeners. You guys are the best).

Our program today in three parts:
  1. The Arrow Goes Both Ways (if you know what I mean): An Investigation Into the Bi-Conditional Relationship.
  2. Keeping It In the Family (uh, if you know what I mean?): An Overview of the Relationships Between Analysis Questions.
  3. Strategery (if you... oh, forget it): A Structural, Tactical Approach to the Logical Reasoning Sections of the LSAT.

Part One: The Bi-Conditional.

Let’s begin with an example. Consider this statement (completely fabricated, having no necessary relationship to reality): The Kardashian family will do absolutely anything at all if - but only if - there’s money in it for them.

Notice that the statement is conditional - that is, it contains a necessary condition. Notice also that it’s biconditional - it really indicates two conditions, each of which is necessary for the other, and each of which is sufficient to guarantee the other.

Let’s take these one at a time. We’ll begin with the “if” portion.

Remember, one half of our central claim is that the Kardashians will do anything at all if there’s money in it.

That is, the presence of some amount of money dangling in front of any member of the Kardashian klan is sufficient to induce that member to do anything (like, you know, turning her wedding into a reality show for E! Television). If there’s money involved, Kardashians are certainly not far behind. In other words, money is sufficient to guarantee Kardashian cooperation (Kardash-eration), and Kardashian involvement necessarily obtains if there’s money on the table (if the Kardashians aren’t involved in a project, you can know for certain that there isn’t money to be made by the Kardashians in that project; if there were, they’d be involved!).

Since money is sufficient to guarantee action by the Kardashians, we can safely and correctly symbolize this conditional relationship by placing money on the left hand side of our arrow:

Money → Actions by Kardashians

And we’ll do the contrapositive:

Actions by Kardashians → Money

So, that’s one half.

But there still remains the second half of the statement; not just that the Kardashians will do anything one can imagine if there’s money in it for them, but that the Kardashians will do things only if there’s money in it for them.

That is, in order to get a Kardashian to do anything at all, you must offer her some money. The Kardashians do not do anything unless they’re being paid to so do - that they do things only if there’s money tells us that the offer of money is a necessary condition for any action undertaken by a member of the Kardashian family. Since money is a necessary condition, we know that we’ll correctly symbolize this second relationship by placing money on the right hand side of our arrow:

Actions by Kardashians → Money

and of course the contrapositive always obtains:

Money → Actions by Kardashians

So, in this statement, we have two equal statements peacefully coexisting - that money is sufficient to motivate the Kardashians (they’ll do anything if there’s money), and that money is also, at the same time, necessary to spur the Kardashians into action (they’ll only do things if there’s money involved).

Since the statement indicates two separate relationships, we will, in every occurrence, symbolize both relationships. Some people will tell you to use a double-sided arrow to indicate this relationship, and those people aren’t wrong, per se, but we take a different view.

If all of our work in procedural matters is about developing a sort of muscle memory whereby we don’t have to think about the process (and it is!), and if, in every instance of conditional symbolization we read correctly from left to right - and not ever the other way around (and we do!), then we believe it is in everybody’s best interest to symbolize the bi-conditional the same way we symbolize every other conditional: from left to right, and not the other way around.

To do it correctly, then, we must make two separate symbols, in precisely the same way we did with this example.

So, for any bi-conditional of the type “A if and only if B” (or “A if but only if B” - the conjunction does not matter!), we will always correctly symbolize by writing:

A → B

with contrapositive

B → A

and also

B → A

with contrapositive

A → B

In this way, we’ll accomplish our symbolization both correctly and coherently with all other conditional symbols.

And thus have we finished with part one. Excelsior!

Now, for Part Two: The Family Resemblance in Analysis Questions.

There is a class of questions in the Logical Reasoning sections of the LSAT that asks us to analyze arguments. These questions include the Flaw, Necessary Assumption, Sufficient Assumption, Weaken, Strengthen, Evaluation, and Resolution Questions.

The cool thing? All of those question types are intimately related.

Like this:

The flaw of any argument is the fact that the argument has assumed some information. In order to succeed, an argument must move smoothly, building from one point to the next without gap or interruption. When an argument fails to provide sufficient evidence for its conclusion - when it assumes that some important piece of evidence is true rather than demonstrating that it's true - that argument has failed.

Often, an argument will indicate its flaw on the basis of a shift in language: If an argument begins by saying that Mechanical Engineering majors are astonishingly physically attractive as a group, and that therefore, they must be a successful dating population, then that argument is flawed. The flaw is that it has failed to consider that the physical attractiveness of a group may not indicate its dating prowess. One necessary assumption of this argument is the assumption that the physical attractiveness of a group has some relationship to that group's success in securing dates.

So, identify the shift in language, and you'll have found the shift in logic. That shift is where the assumption lives, and that assumed evidence is the flaw of the argument.

To answer the Sufficient Assumption question, apply that same thinking, but go big! The answer to the Sufficient Assumption question will fill in not only one gap in logic within the argument, but all of the missing pieces. For this reason, expect the right answer to the Sufficient Assumption Question to look just like the answer to the Necessary Assumption Question, if that answer had been taking human growth hormones. It’ll be big, is what I’m saying.

Strengthen and Weaken questions are two sides of a coin. In both instances, we will answer by appeal to the assumption of the argument. You cannot strengthen an argument on this test by showing that the evidence on offer is true. We will correctly stipulate the truth of all the evidence (we have to. In a world where the facts are in question, how can we ever hope to reason properly together? See the US Congress for illustration). So, if the validity of the evidence is not in question, how can we make the argument stronger or weaker?

We can do so because the argument has assumed something. So, to make the argument stronger, we'll assert that the necessary assumption is true. To weaken it, we'll deny the truth of the assumption.

Consider again our Mechanical Engineering majors example:

To strengthen the conclusion, we’d want to indicate that physical attractiveness does matter in dating. Say something like "Typically, the more attractive a person is, the more likely it is she'll be able to get a date." This doesn't prove that the conclusion is true, but it does make it more likely - and that's what we were asked to do.

To weaken this conclusion, attack the assumption: Say something like "Recent studies have indicated that physical attractiveness is a much less important consideration in dating than financial acumen." In this way, you're denying the strength of the connection between attractiveness and dating. This doesn't prove the conclusion is false, but it makes it less likely. That was its job.

Evaluation Questions are rare, but when they occur, they ask you what would be useful to know in evaluating the argument. You know what would be useful to know? Whether or not the necessary assumption is true. The argument is flawed because it left out some information. Want to know how to evaluate it? Find out if the information it left out is true! Expect the right answer to the Evaluation Question to ask its own question - Is the assumption true?

If you say it isn’t - that physical attractiveness just doesn’t help people get dates, then we can evaluate this argument harshly - it would be a stupid argument if that assumption isn’t true. However, if you say that it is true that physically attractive people get more dates, then you can evaluate the argument more positively, because you’ve strengthened it by asserting the necessary assumption.

Finally, we have our Resolution Questions. These are really only tangentially related to all of the foregoing. They ask us to resolve a paradox, and that paradox usually isn’t contained within an argument at all. Instead, we’re given two seemingly contentious ideas, and asked to bridge them. The job here is similar to that of the Necessary Assumption answer - the right answer will be some key missing piece of evidence that will help us to make sense of the apparent contradiction of the passage. Again, though, this demand is not as tightly bound to the others as all of its analysis cousins are to one another. Similar, but not quite the same.

And that tidy set of relationships brings us to the end of part two!

Soldiering bravely forward, let’s end today’s episode by taking up the question of a strategic approach to the Logical Reasoning section as a whole:

First, let’s start from the knowledge that the first half of a Logical Reasoning section will normally contain about three times as many easy questions as hard questions, and that in the last half of the section, that trend reverses itself.

So, as a whole, the last half of a section is always significantly more difficult than the first half.

Let’s inform our approach to timing accordingly. While we will have, on average, about a minute and twenty-one seconds to answer each question, to expect to answer them each in that time frame would be utter foolishness, and ignores the reality that these questions differ radically in degree of difficulty.

Instead, expect that, to finish a section in time, you’ll spend about 11 to 13 minutes in the first half, and about twice that much time (22 to 24 minutes) answering the remaining questions.

And remember that we said there’d be difficult questions in the first half - expect one or two quite hard questions there - and also that we’d see some easy questions in the last half - expect one or two eminently doable questions there. Since that’s the case, and since every question is worth the same number of points, we’ll maximize our efficiency by going into any section prepared to skip  one or two questions in the first half, to make sure that we get to the easy questions in the last half.

We can always come back and run out of time working on those hard questions we skipped on our first run through a section. Indeed, I’d really rather run out of time working on something hard (that I might not get right anyway) than one something easy (it would suck so much to think “I could have gotten that question right if I’d only had a few more seconds to work”).

Finally, let’s consider a tactical method for our last five minutes in a section.

First, nothing changes! Why would it? What awesome new system are you going to switch to for the last five minutes of the test? If it’s so great, why weren’t you doing that all along?! And you’re not going to switch into doing something worse, right? Right.

So, nothing changes. Nothing except maybe your mindset. Like this:

Do not go into the last five minutes as clean-up time. This is not your chance to answer all of the questions you haven’t gotten to yet.

Instead, the last five minutes of the section should be your time to get three more questions right. Even if you have 6 questions left, it’s better to do three of them and get them all right than to do all 6 and miss half.

The math is partly the reason - if you just guess (D) -for Dave! - on the 3 questions you don’t have time to answer, you might get lucky, and end up with one more point than if you’d answered them half-assed and missed them all.

But the psychology is the more important reason: If you finish the section knowing that you 1) Played your game, having taken some ownership of the test, and 2) Just got 3 questions right, then you head into the next section of the test confident, head high, rather than still moping about the 6 questions you just rushed through and have no idea whether you got any of them right.

And confidence counts for a lot - if nothing else, you’re not trying to work in the next section while your head’s still in the one behind you.

And speaking of heads in behinds, tell us how much we suck (or, even better, how awesome we are!): Check us out online or drop us a line at Info@VelocityLSAT.com, and visit The Forum (http://www.VelocityLSAT.com/Forum) to join the conversation, to share your thoughts on strategy or the Kardashians, or to suggest topics for future conversations.

Until next week, be strong and of good faith, my ninjas.

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