First off, I’m happy to announce the arrival of my new website: www.acmelsatprep.com At some point (hopefully soon!), this blog will be incorporated into the site – which brings me to my next point. Starting now, those in-depth LSAT tips will appear on the Articles page of that site (they’re in the process of being added). This blog will have more general news and tips about the LSAT and related resources.
I’m happy to have a great topic to launch the “new” blog content – Cambridge LSAT (www.cambridgelsat.com) is in the process of categorizing the LSAT Logic Games, and offering specific game types for sale. I’ve already been recommending this great LSAT resource to my private students, and I’m happy to give it a plug here. If you’ve been doing any sort of LSAT prep, the odds are strong that you’ve found some sections harder than others, and some types of questions harder than others. Most vendors of prep materials offer “whole test” packages, which either leaves you short of the materials you most need, or results in you spending a ton of money on stuff you don’t really need. No longer necessary!!
Cambridge LSAT offers tests (licensed by the Law School Admissions Council) for download, so there’s no shipping cost or time; you can put them on your computer and print them out at your leisure. Better than that, though – you can download individual sections. If you’re fine on Reading Comprehension and Logical Reasoning, but having trouble with Logic Games, you can download a section of Logic Games (choose any section from any past exam, so you can be sure you aren’t getting one you already have) for just $1.75! And it’s getting even better – if you’re having trouble with, say, Grouping Games, soon you’ll be able to download just a batch of Grouping Games. Or Linear Games. Or any other type. This sort of specialization is already in place for Logical Reasoning, by the way – you can get just the question types you need to work on. www.cambridgelsat.com – An outstanding, cost-effective, super-targeted approach to working on past exam questions. Strongly recommended!
If you walked out of the test thinking it went really badly, you may be considering cancelling your score and retaking the LSAT. There’s no one-size-fits-all answer to this big question, but here’s a quick look at some of the relevant considerations:
* Will it set you back a year in your application(s)? Check the deadlines of the schools you’re planning to apply to. If you can retake the LSAT and still get your score back in time to be considered by the schools you’re looking at, one of the major downsides to taking a later test is eliminated.
* If it will set you back a year, how important is that year? How big a hurry are you in to go to law school this year? Are there job or school opportunities for you to take advantage of if you wait a year?
* Be honest – How likely is it that your score will improve? Are you just having post-text anxiety/remorse, or is there a real reason to expect a better score? One of my students recently took the LSAT. As she was checking her work on the first section, which was logic games, she noticed that she had misinterpreted one of the initial conditions, which had almost certainly caused her to mess up several questions. Worse yet, she didn’t have time to re-solve the problems with the correct conditions. Worse YET, because it was the first section, she was stressed about it for the rest of the exam, which resulted in her being distracted, not getting through the other sections, and missing problems. She cancelled her score, and I think it was a good call – I’m sure her re-take will result in a markedly higher score. But if you’re just generally beating yourself up because you’re a perfectionist, or because you’re remembering 2 or 3 questions you should have answered differently, it’s probably not worth it.
* Do you have one or two schools that you’re just dying to get into? If you have a huge preference for a school that’s going to be tough for you to get into, you might need every last LSAT point you can get. If you have a number of schools you’ll be applying to, and you know they’re within your range, and you don’t really care which one you get into, it might be better to just send out your applications. Or if you have a job lined up with your cousin Vinnie; you just need a diploma and a bar card.
Ultimately, the considerations are fairly straightforward – How likely is it that you’ll do better; how important is it that you’ll do better; will the re-take set you back a year; and if so, how critical is that year. Bear in mind that most people who take the LSAT multiple times don’t experience dramatic increases in score. So unless there was a specific reason you think you did poorly, you’re probably not looking at a huge difference in score. On the other hand, if you’re a borderline candidate at School X, even a small difference can be important. Ultimately, it’s an individual system, and your situation may dictate a different answer than someone else’s.
A common thread I’ve seen among students focusing on the Logical Reasoning section is that they often miss questions where the correct answer is one that introduces material not found in the passage – that is to say, it goes “beyond the scope” of the initial reading.
Invariably, these students have done some good prep on their own, or taken a class, and they have learned (correctly) that it’s very common for a wrong answer to introduce new material. In fact, that’s often a good way to eliminate answer choices. But it appears that the sources that have taught students about that concept have taken it a bit too far – there are questions in which the right answer DOES introduce new material. In fact, there are times where a right answer almost HAS TO introduce new material.
It all comes down to the question type. The most common question type in which the advice to avoid new material is spot-on is the “find the conclusion” question. Many, many LSAT questions are of this type, and the conclusion will flow from the premises – which will be given in the passage – so an answer choice that presents new material will be wrong. But there are other question types. For instance, a “find the flaw” question is a GREAT candidate for a correct answer that introduces new material. Consider – one of the more common “flaws” is that the speaker fails to consider an alternative explanation. So of course the “flaw” won’t appear in the passage – the reason the passage is flawed is because it’s not in there! I’m going to update this entry and include some examples from past LSATs so you can see what I mean in practice. But for now, be sure to ask yourself…Is this the kind of question where it makes sense that new material might be a correct answer?
Last add (for a while, anyway) about the contrapositive. If you’ve read the earlier posts (and if you haven’t, you should) on the topic, this should be a review for a short while:
Alex and Bob are two of a group of students, all of whom must take either a math class or an English class. The condition you’re given is, if Alex takes English, the Bob takes math, or, symbolically: A(e) -> B(m). The contrapositive can be diagrammed in the affirmative: If Bob takes English (i.e. “not math”), then Alex takes math (i.e. “not English”): B(e) -> A(m). So:
A(e) ->B(m)
B(e) -> A(m)
That’s the review. Many students mistakenly infer from this that Alex and Bob must be in different classes. But that’s not correct. Notice that there are two conditional relationships – one attaches if Alex takes English, and the other attaches if Bob takes English. There’s nothing there that says they can’t both take math. There will usually be a question or two that will trip you up if you’re not ready for this one. They can’t both be in English, but they could be in math together, or they could be in different classes. Make sure you understand this one; it’s important.
How are you at identifying parts of speech? If you’re looking for a logical reasoning tip, and you know your parts of speech, I’ve got one for you. And it’s all about adverbs.
Quick grammar review: Adverbs are similar to adjectives, except that adjectives modify nouns, and adverbs modify verbs, adjectives, and other adverbs. For instance (adverb in CAPS):
He drove QUICKLY.
Porsches are USUALLY fast.
etc.
Adverbs are used to provide nuance. For instance, in a novel, you might be told that someone said something “pointedly,” or said something “loudly,” which might express anger, for instance. But they’re not critical to telling you exactly what happened. Hemingway said that from Tolstoy, he learned to “distrust” adverbs. The “meat” of the sentence consists of nouns & verbs.
This is especially important in the logical reasoning section of the LSAT. Logic and argument are about nouns & verbs. Who did what? Nuances like adjectives are out of place. And that’s important, because they should stand out like a red thumb. Here’s an example…look at these two arguments:
A1: All cats have four legs.
A2: Spot is a cat.
A3: Therefore, Spot has four legs.
Perfectly valid syllogism. If the premises (A1 & A2) are true, the conclusion (A3) MUST be true. You can “Venn diagram” this (Google search if you don’t know Venn Diagrams). The little circle, cats, is completely enclosed by the big circle, things with 4 legs. Now look at this:
B1. Mammals usually cannot fly.
B2. Spot is a mammal.
B3. Therefore, Spot cannot fly.
INvalid. What’s the difference? “usually.” The adverb acts as a qualifier. In this case, it tells you that a small portion of mammals are NOT in the “things that cann0t fly” category. The argument fails, because even though most mammals can’t fly, Spot MIGHT be a bat.
This focus on the adverb comes up in all sorts of Logical Reasoning question types, and in many different ways. In argument B, above, it might be “Find the Flaw” (the speaker over generalizes that something that is usually true must be true in a particular case). Or in an “Unspoken Assumption” question (the speaker assumes that Spot is not one of the group of mammals that can fly). Or in a “strengthen the argument” question (Which of the following would strengthen the author’s argument? ‘Spot is not a bat’).
Adverbs don’t need to be in arguments. So when they ARE in your LSAT argument, very, very often it’s because they’re relevant to the right answer. An easy way to identify most adjectives is that many end in “LY.” Not all of them, but a lot of them. Train yourself to spot them. Somehow, some way, they’re relevant to the right answer. Maybe the right answer is the only one that addresses something the adverb brings up. Maybe the “qualifying” character of the adverb eliminates a wrong answer, when you’ve got it down to two choices. The bottom line, though, is that they serve a purpose, and that purpose usually isn’t necessary to the speaker’s argument — it’s examsmanship. It’s necessary to creating right or wrong answer choices.
I met with a new student last weekend. She’s going to be taking the September 26th LSAT, so I had limited time to work with her, but I had some concerns about how beneficial our session would be. I was pleasantly surprised, though — she not only knew what section she needed help with (Logical Reasoning), she also knew which type of questions gave her trouble. Specifically, the “identify the unspoken assumption” type of question.
Because she had done such a great job of pinpointing her problem area, I was able to focus our session to give her some helpful tips, and we were able to work through a variety of practice test questions specific to her needs.
When you’re first learning about the LSAT, there’s room for general improvement, as it’s all new to you. After you’re familiar with the test, though, and you have a “baseline” — an approximate score that you’re generally around — then your best bet for improvement is focusing on particular weak points. Odds are, you’re leaving a disproportionate number of points on the table in one of the three sections, or in one of a few specific subtypes of questions. There are only so many types of logic games. A solid majority of Logical Reasoning questions are one of four types. Don’t just do practice tests – analyze your results. Where are those extra 5-10 points you’re looking for going to come from? If you can answer that question, you’re a lot more likely to find them.
So, in the two previous points, I’ve highlighted a few of the most important things (for LSAT Logic Games purposes) about the contrapositive. To recap:
1) The basic format is, “If not Q, then not P.”
2) It’s the only valid inference from a conditional (If P then Q)
3) When there are only two possibilities, “If not Q, then not P” can be expressed affirmatively (see post below).
One other thing you have to be aware of…when the Q has an “and” in it, it becomes an “or” when you’re writing “not Q.” That sounds gobbledygookish, so let’s look at some actual statements.
First, let’s take it in general terms. For instance: “If Spot is a cat, then Spot has four legs and meows.” We have a classic conditional (if P then Q) set-up, so we know that “If not Q, then not P” is valid. But to negate “Spot has four legs and meows,” we only need to negate EITHER possibility. So, for instance, if Spot has 4 legs but doesn’t meow, he’s not a cat; maybe he has 4 legs and barks, and he’s a dog. (Yes, he could be a cat with damaged vocal cords, but we assume the premise is true as given).
For diagramming purposes, it’s important to recognize the difference; seeing the “or” that isn’t in the initial statement actually gives you more to diagram. For instance:
“If Bob takes English, then Ken takes Math and Science.” This can be diagrammed (among other ways) as: B(E) –> K(M+S)
The way to diagram the contrapositive is with TWO statements:
K(~M) –> B(~E) AND
K(~S) –> B(~E).
If Bob WERE in English, then Ken would be in BOTH math AND science. So if Ken isn’t in science, Bob’s not in English. Don’t fall into the trap of thinking that BOTH K(~M) AND K(~S) are necessary conditions to keep Bob out of English. EITHER situation suffices.
If you’re not familiar with the tilde (~) in these diagrams, btw, see earlier post(s) of mine; it is used to designate (“not”) in logic, and I find it a handy LSAT abbreviation. Feel free to use whatever works for you, though!
Typically, when students get a handle on the contrapositive, they mistakenly view contrapositives as only able to be expressed in the negative (since they’re “If NOT Q, then NOT P”). However, in some cases, the contrapositive can be expressed in the affirmative, as well. This is important, because sometimes questions or answer choices are expressed in the affirmative, so for accuracy and speed, you have to accurately translate the given statement into its logical equivalent.
The key to when the contrapositive can be expressed in the affirmative is this: The question must be a binary variable; i.e. there must only be 2 options. For instance, let’s say 6 students are each taking 1 class, and that class is either Math or Science. If our statement is, “If Alex takes Math, then Bob takes Science.” Sample diagram:
A(m) –> B(s). Our hypothesis, P, is “Alex takes Math.” Normally, our contrapositive is expressed as a negative. If NOT Q, then NOT P. But in this case, take a closer look at “NOT Q.” There are only two classes, and everybody’s taking one. “Not Q” = Bob doesn’t take science. But since this is a binary game, “Bob doesn’t take science” = “Bob takes math.” Similarly, “Not P” = “Alex doesn’t take Math,” which = “Alex takes science.” So, our contrapositive, like the conditional, can be written in the affirmative:
B(m) –> A(s).
Again, for this simple re-formulating to be accurate, we must be looking at a binary possibility – Alex takes Math, or Science. Similarly, Bob takes Math, or Science. If there were a third option, say, History, then we’d have to write the more normal expression: ~B(s) –> ~A(m) (If Bob doesn’t take science, Alex doesn’t take math). In this case “doesn’t take science” isn’t equivalent to “takes math” because “takes history” is also an option.
Another situation in which it doesn’t work is in an incomplete grouping game. Say we had 8 students altogether, but only 6 of them were taking classes. Against, “Bob doesn’t take science” isn’t equivalent to “Bob takes math,” because there is a third option — Bob doesn’t take ANY class.
But for the binary possibilities, being able to immediate realize and formulate the contrapositive in the affirmative –
B(m) –> A(s) – is potentially HUGE not necessarily in terms of accuracy (you’d have worked it out anyway, probably), but in terms of time. Questions and answer choices are designed to see if you’ve made the connection, and they’ll be written that simply: “If Bob takes Math which of the following must be true?” And you won’t have a fact pattern that says “Bob takes math.” But you WILL have one that says, “If Alex takes Math, then Bob takes Science.” If you can look at that and diagram “If Bob takes Math, then Alex takes Science” in a few seconds, that’s golden. And I promise, that concept will be on your LSAT, more than once.
I’m open to taking specific questions about LSAT Prep, law school prep, the law school (particularly the 1L) experience (course selection, getting ready for finals, whatever), bar prep, finding a job, starting out as a new lawyer, etc. Please feel free to drop a line.
Philosophy majors can probably skip this one, but for the other 99% of you…if you’re not thoroughly comfortable with the logical implications of conditional statements (“If P, then Q”), then stick around…they’re important on the LSAT, and particularly…the Logic Games.
Surprisingly, there are many levels that pertain to conditionals, so, we’re going to take it from Square 1.
From the Statement Structure “If P, then Q” a few related statements can be constructed. Only one of them, however, is accurate. Let’s use actual statements with meaning, to make it easier to understand. Let’s say I have a drink. My conditional will be “If my drink is a vodka and tonic, then my drink contains alcohol.” We can readily see that this follows the “If P, then Q” structure. P = “my drink is a vodka and tonic” Q = “my drink contains alcohol.”
One possible conclusion to draw from “If P, then Q” is “If Q, then P.” This is not a valid inference. To see why, let’s just put our meaningful content into the formula. If Q, then P translates to, “If my drink contains alcohol, then my drink is a vodka and tonic.” Clearly, though, this does not follow. My drink might be a rum and coke.
Another possibility might be, “If not P, then not Q.” Again, this is not a valid inference. Let’s check it out: “If my drink is not a vodka and tonic, then my drink does not contain alcohol.” But, again, I could have a rum and coke. “Not P” would be satisfied, but “not Q” wouldn’t be true – my rum and coke WOULD contain alcohol.
That leaves “If not Q, then not P.” This is called the “contrapositive,” and it IS true. Check it out: “If my drink does not contain alcohol, then my drink is not a vodka tonic.” That one works.
Very often, a Logic Games question will offer you incorrect answer choices based on drawing one of the faulty conclusions. They want to see if you’ll jump on the wrong conclusions. But the other thing they do is offer correct answer choices based on the contrapositive, and if you don’t spot it right away and allow for it in the diagram, you’ll either miss a correct answer, or spend far too long working it out. Here’s how it plays out in LSAT land. Let’s say we have a grouping game where 8 different students take either a Math class, a Science class, or an English class. One of the clues might be:
“If Alex takes the English class, then Bob takes the Math class.” You might diagram this a number of ways, for instance: A(e) -> B(m) Or If A=e, B=m. Something quick, visual, and understandable (to you). Recognizing it as a conditional, though, you have to note that the contrapositive is true, and you have to get it diagrammed, as well. There are various ways to diagram “not.” I’m partial to the tilde (~), which is the symbol used in formal logic. It’s fine to diagram it in other ways, though. The important thing, though, is to get the contrapositive in your diagram, too, in this case:
~B(m) -> ~A(e), or If B~=m, A~=e. In other words, if Bob doesn’t take the math class, then Art doesn’t take the English class. This is the logical equivalent of the given statement. The reason it’s important to write it out is that you’re guaranteed to get questions that tell you that Bob isn’t in the math class, and you have to be able to immediately rule out answer choices that put Alex in the English class. The question might tell you straight out that Bob doesn’t take English, or it might say, “If Bob is in the science class, which of the following could be true.” Then you have to make the connection: Bob in science = Bob not in math = Alex not in English. And you have to do it fast. If you can lay out the contrapositives at a glance, and reflect them in your diagrams, you’ll be in good shape on a number of questions. If you can’t, then you’re either going to come to faulty conclusions and get some answers wrong, or you’re going to use up valuable time figuring it out on the fly. So learn to:
1) recognize conditional (“if P, then Q”) statements.
2) translate to the contrapositive (“if not Q, then not P”).
3. get the contrapositive diagrammed.
Caveat: Sometimes the Q comes before the P. Just because the standard format is “if P, then Q,” don’t get lazy and assume that the first piece of information is the P, and the second is the Q. It’s the “IF” that defines which part of the sentence is the hypothesis (P), and which is the conclusion (Q). For instance:
“Carl takes Math if David takes Science.” P = “David takes Science” (the part after the “IF”). Q = “Carl takes Math.” The contrapositive is: “If Carl doesn’t take Math, then David doesn’t take science.”
Good practice Logic Game: Prep Test 33 (December 2000), section 4, game 2 (Questions 6-12). Page 177 of “The Next 10 Actual, Official LSAT PrepTests.”
Unfortunately, this post only covers the first layer of thinking you need to have about the contrapositive. Call it “Logic 101 for LSAT” 201 and 301 are more advanced, but they’re tremendously important. Coming soon to an LSAT blog near you.
