Archive for category LSAT content
Negating Assumptions on the LSAT – Answers
Posted by AileenNielsen in LSAT content on February 22nd, 2010
Alright, here are the answers to the last blog post: Negating Assumptions on the LSAT
Non Exhaustive List of Common Terms and Negations
If you see… Negate with…
All Not all
Some None/no
Most Not most/less than half
Not all All
None At least one/Some
Probably Probably not/Unlikely
Unlikely Likely
Never At least once/Sometimes
Always Not always
Sometimes Never
Without With
With Without
Can you think of others that should be on this list?
Negating Assumptions on the LSAT
Posted by AileenNielsen in LSAT content, LSAT Prep on February 12th, 2010
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Learning to negate answer choices on the LSAT is a key skill if you are really looking to push up your score, for lots of reasons. I tend to think there are two especially important ones. First, assumption questions (and one of the most-related question type, flaw questions) are quite common, and many students find it’s difficult to get all of the most challenging assumption questions correct without using the negation test. Second, negation can be useful for thinking out counterfactuals on inference and strengthen/weaken questions – more on this another time. Today, I’ll be writing about how to negate in general terms. In another blog post, I’ll get into specifics.
An important thing to keep in mind before jumping into this is that negation is not something you should plan to use all the time, even on assumption questions. Use negation to choose between two answer choices if they both seem like close contenders. Your first line of offense for assumption questions should continue to be based on issues of scope and spotting the logical gaps in an argument.
The Basics
You might be wondering what is so difficult about negation, and if you are, I would guess you have not gotten too far into your preparation yet. Often, working with students one-on-one or in a classroom I notice numerous mistakes when students try to negate, and often they don’t even realize they’ve made huge logical changes to the answer choice in the process of negating it. For this reason, I think it’s appropriate to start with a general example that shows in broad, simple terms the mistakes we sometimes make when we negate. Consider,
(1) The cat jumped over the mat.
That would probably be straightforward to negate, right? We could just negate the verb:
The cat did not jump over the mat.
That’s all well and good, but what about this sentence?
(2) A cat jumped over the mat.
Does that get negated the same way? Of course it doesn’t. I’ll talk about why in a second, but more interestingly, I wanted to point out that there are two ways to negate statement (2).
A cat did not jump over the mat
or
No cat jumped over the mat.
Though these two are phrased differently, they actually mean the same thing. Effectively both say that the mat has never seen a cat jumping over it (or should I say that the mat has never been jumped by a cat 
?)
Let’s consider one of these negations:
No cat jumped over the mat
Why can’t I use it to negate statement (1)?
Changing “the” to “no” misreads the meaning of the original in a way that does not simply negate the sentence. Since I used “the” in the original case (1), I was really only writing about a specific cat. I should have only cared about whether that cat had jumped over the mat. If all I wanted to say was that the specific cat did not jump over the mat, I did not need to prove the broad statement above, that no cat, ever, has jumped over that mat. Essentially, trying to negate in the second version I over-negated, a potentially fatal mistake in LSAT practice and law alike. I never want to do more heavy lifting (read negating) than I absolutely must.
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Philosophy
The most important question you should ask yourself when confused about how to negate a particular answer choice is, “What is the minimum I would need to show that disprove the statement above?” This minimum part is very important because often, in difficult cases, students over-negate because they are not paring down to the very minimum.
To see an example of these, consider the following. Imagine your classmate says to you, “I don’t have any friends in this class.” You’d probably respond to this by saying “That’s not true – everyone (or almost everyone here) is your friend.” But that’s a lot more than you’d have to say, and maybe a lot more than you’d want to say, if this classmate was going to ask you to prove your statement. A better idea would be to say more simply, “That’s not true – I’m your friend.” This might sound less promising, but it’s easier to prove, and, importantly, it’s enough to disprove your friend’s statement.
Let’s formalize this a little bit.
(3) No one in this class is my friend.
What do we need to negate here? Well, if we go back to our anecdotal version above, we see that all we need to show to disprove this (and consequently the negation of case (3)) is that
At least one person in this class is my friend.
That is the negation because it would make statement (3) untrue, though it might not comfort the speaker much to have one friend rather than none, but we are concerned with the logical statements above. Now, to give a few versions I might have anticipated a student giving mistakenly, consider each of these:
Everyone in this class is my friend.
No one in this class is not my friend.
I have a lot of friends.
Everyone is my friend.
All of these “overshoot.” Overshooting is bad. Bad on the LSAT because it shows an inability to determine the precise logical negation of a statement, and bad as a lawyer because you make your case more difficult for yourself than you really have to. From here onwards, make parsimony a central feature of your negation process. Also,make sure you can articulate how each one overshoots before you continue reading.
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Complicated Sentences with Multiple Things you Kind of Want to Negate
Now let’s consider the real thing. Consider this answer choice from an assumption question.
(4) Most people who suffer from ordinary mountain sickness recover without any special treatment.
The tricky part about negating this answer choice is that there are many parts of the sentence we could negate. To make it more obvious, I’ve broken it down by idea:
Most people who | suffer from ordinary mountain sickness | recover |without any special treatment.
Let’s break this down by negating each of these in turn and thinking about whether it produces the minimum that, if true, would disprove the original statement (4).
First, let’s negate the first chunk of the sentence, “Most people who.” This is a claim that at least 50% of a group of people do a specific thing. To negate this part, I’d say “less than half of those people”, or “not most.” This sounds a bit awkward, but it conveys the meaning:
#1 Less than half the people who suffer from ordinary mountain sickness recover without any special treatment.
Would this disprove statement (4) if true? It seems it would because it would show that not more than 50% of the group actually gets better without special treatment. This also seems pretty minimal. For example, so long as I could show that fewer than 49% of people got better this way, I would be set.
Let’s look at negating the second part.
#2 Most people who do not suffer from ordinary mountain sickness recover without any special treatment.
If true, would this disprove the original statement (4)? No, absolutely not. If you’ve been studying for the LSAT for some time, you’ll certainly recognize that this has a scope problem. We don’t actually care about people who don’t have ordinary mountain sickness – we care about people who do have the illness. This is definitely not the proper way to negate the statement.
If we negate the third part of the sentence, we have
#3 Most people who suffer from ordinary mountain sickness do not recover without any special treatment.
Like the first version of a negation, this seems as though it would disprove the statement. Here it would do so by talking about the same group of people (most of those who get this illness), but saying that they do not do what the speaker claims they do. Is this minimal? It seems like it, but let’s push on.
Negating the fourth portion of the sentence yields,
#4 Most people who suffer from ordinary mountain sickness recover with special treatment
This one sounds kind of funny, doesn’t it? We know what it means though, so maybe we can rephrase it a bit better as
Most people who suffer from ordinary mountain sickness recover after receiving special treatment
Oh! Now this actually looks a lot like # 3, which in turn looks a lot like #1. Indeed, if we really think about what they mean, they all mean the same thing, which is saying that more than half of people received some kind of special treatment before they get better, which is the opposite of what the answer choice says.
Moreover, it answers our requirement of parsimony too. We don’t need to show that no one can get better without special treatment – all we need to show is that such is not the case.
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Non Exhausted List of Terms and Their Negations
Now that we’ve talked about how to negate an answer choice, it’s also worth thinking about some standard negations that are likely to surface many times on your LSAT. Try to complete as many of these as possible. Feel free to answer in a comment. Answers will be posted in a week or so.
If you see… Negate with…I
All
Some
Most
Not all
None
Probably
Unlikely
Never
Always
Sometimes
Without
With
To be continued…
LSAT Vocabulary
Posted by noah@manhattanlsat.com in LSAT content on February 2nd, 2010
I just saw a good blog post listing vocabulary words that you should have under your belt for the LSAT. Take a look and see if you really know all of them. Thanks for the list, Steve!
LSAT Logical Reasoning Vocabulary Words
June 2007 LSAT Video Explanations
Posted by noah@manhattanlsat.com in LSAT content, Manhattan LSAT Announcements on November 20th, 2009
We’re very excited to announce that we have posted video explanations for the June 2007 LSAT logic games. You can see them here: http://www.atlaslsat.com/logic-games-recordings.cfm or on You Tube – http://www.youtube.com/user/atlaslsat#p/u. Dan and Mike put a lot of time into coming up with truly useful recordings. Granted, we’re much more about teaching — i.e. making students think — than presenting solutions, but when you’re studying, it’s obviously useful to see how someone else solved a game (particularly how one of our super nerdy curriculum developers did it). If you’d like to see explanations for the entire game, check that out on our forums: http://www.atlaslsat.com/forums/
For our students, we’re developing video explanations for some of the toughest games in our course HW. Unfortunately, we have to restrict those to our students in order to respect LSAC’s copyrights.
The June 2007 LSAT is a great way to get your feet wet with the LSAT. However, make sure you take it under timed conditions! If you’d like to get a copy, as well as some of our resources associated with that test (including a spreadsheet that will analyze your answers), take a look here: http://www.atlaslsat.com/lsat-practice-test.cfm
Have fun and good luck!
LSAT Weaken Questions – Logical Reasoning
Posted by dan@atlaslsat.com in LSAT content, LSAT Tips on November 13th, 2009
Weaken questions can operate in a few different ways. Let’s look at some examples.
Sep 09 Exam, Section 4, #2
Here’s the basic logic given in the argument:
You can always keep your hands warm by putting on extra layers of clothing (clothing that keeps the vital organs warm).
THUS, to keep your hands warm in the winter, you never need gloves or mittens.
This argument is a sound argument – no flaws or assumptions. If you have another option for keeping your hands warm, then you never truly need gloves or mittens.
In this case, the correct answer actually attacks the main premise. The correct answer says that sometimes (when it’s really really cold) putting extra layers of clothing on actually is not enough to keep your hands warm. Notice how this contradicts the premise. So, to weaken an argument you can attack a supporting premise.
ANSWER TYPE 1: attack a premise
Sep 09 Exam, Section 4, #10
Here’s the basic logic given in the argument:
Most people don’t eat enough fruits and vegetables to get their daily requirement for vitamins.
THUS, most people need to supplement with vitamin pills.
This argument is NOT a sound argument. It makes a pretty big assumption: People can’t fulfill their daily requirement of vitamins using some other source aside from vitamin pills.
The correct answer could attack this assumption by negating it: People CAN fulfill their daily requirement of vitamins using some other source aside from vitamin pills. This would definitely weaken the argument. However, it’s more likely that the correct answer will be a little tougher to spot. Instead of just outright negating the assumption, it will probably give an example of a source of vitamins other than pills. This is exactly what the correct answer does in this case. It says that many foods that aren’t fruits and vegetables have the vitamins that fruits and vegetables have. This obviously weakens the claim that you would need pills to get those vitamins.
In this case, the correct answer attacks an assumption by introducing a counter premise. In order to see it, you’ve got to be able to spot the assumption first.
ANSWER TYPE 2: attack assumption through counter premise
Jun 09, Section 2, #9
In this case, a single claim is made without any supporting premise:
Reducing meat consumption will not significantly reduce world hunger.
In this case, the answer won’t attack a premise because there isn’t one. It’s hard to attack an assumption because we don’t have a P - C relationship (assumptions usually lie between the premise and conclusion). So, this must be a different type.
Here, the correct answer simply raises a counter premise, an outside fact that seems to indicate that the claim could be wrong: The amount of land needed to raise meat for one person could grow enough grain to feed 10 people. If this were true, maybe, just maybe, we could put a dent in world hunger by eating less meat.
ANSWER TYPE 3: introduce a counter premise.
To see if you’ve got it, take a look at section 3 (LR) of the Sep 09 exam, #24. Which of these three types is it?
Assumptions and Flaws: Focus on the Argument Engine
Posted by dan@atlaslsat.com in LSAT content, LSAT Prep, LSAT Tips on October 13th, 2009
Do you struggle with assumption and flaw questions? Do you often choose answers that seem right, or relevant, but end up being wrong? This may help.
Consider the following argument:
Many respected entrepreneurs assert that insufficient capital, capital required to cover operating expenses in addition to initial start-up costs, is inevitably a factor in the failure of start-up businesses. However, all of the failed start-ups with which I’ve been involved have failed as a result of executives’ lack of expertise in the product or service that the company provides. Thus, insufficient capital is not a factor in causing start-up businesses to fail.
If this were followed by a question that asked you to choose an assumption, this would be a pretty tough question. The average test-taker attempts to memorize, or “learn” the entire argument, and then gets distracted by answer choices that seem relevant to some particular part of the argument that ends up not mattering so much. This leads to wrong answers.
The strong test-taker has a clearer sense for what we’ll call “the argument engine,” and knows that everything else will likely just provide a context for that engine. The correct answer will usually relate or connect the two parts of the engine. The incorrect answers will generally sit outside the engine – irrelevant. So, what’s this engine thing all about?
Let’s turn this argument on its head and start over.
We spend a lot of time deconstructing arguments. Let’s try looking at things in reverse order. Let’s actually construct this argument from the ground up. We’ll start with the conclusion:
Insufficient capital is not a factor in causing start-up businesses to fail.
Now, let’s add a premise to support this conclusion:
All of the failed start-ups with which I’ve been involved have failed as a result of executives’ lack of expertise in the product or service that the company provides. Thus, insufficient capital is not a factor in causing start-up businesses to fail.
To make this argument more LSAT-like, we’ll add an opposing point to the beginning:
Many respected entrepreneurs assert that insufficient capital is inevitably a factor in the failure of start-up businesses. However, all of the failed start-ups with which I’ve been involved have failed as a result of executives’ lack of expertise in the product or service that the company provides. Thus, insufficient capital is not a factor in causing start-up businesses to fail.
Let’s put in some background information, just to add some more language:
Many respected entrepreneurs assert that insufficient capital, capital required to cover operating expenses in addition to initial start-up costs, is inevitably a factor in the failure of start-up businesses. However, all of the failed start-ups with which I’ve been involved have failed as a result of executives’ lack of expertise in the product or service that the company provides. Thus, insufficient capital is not a factor in causing start-up businesses to fail.
Now we have a full argument. Notice that the more we add the more confusing things become. The more words we read, the less we’re able to focus on the things that really matter.
To fight through the confusion, try thinking of the LSAT argument as a car. The engine is the most important part of the car; it makes the car go. The chassis of the car simply provides a frame, or a context, for the engine.
Likewise, the most important part of an LSAT argument, the engine of the argument, is the simple relationship between one supporting premise and one final conclusion: P à C. Everything else, opposing point and background information, simply provides a frame or a context for this simple relationship.
Let’s go back to the example we introduced above. Before we added the opposing point and the background information things were pretty simple, right? We had one simple premise leading to one conclusion:
All of the failed start-ups with which I’ve been involved have failed as a result of executives’ lack of expertise in the product or service that the company provides. Thus, insufficient capital is not a factor in causing start-up businesses to fail.
This is the engine of the argument! We can paraphrase it:
start-ups I’ve seen failed b/c of lack of expertise –> thus, lack of capital not a cause of failure
When we see the engine, or core, of the argument in simple terms, any flaws, gaps, or assumptions become more obvious. In this case, the author assumes that there cannot be more than one reason why a start-up fails.
If you have trouble with assumptions and flaws, try focusing on the engine. Try constructing the argument from the ground up: find the conclusion, find the one premise that directly supports this conclusion, and then recognize that everything else just provides a context for this engine that you’ve just identified.
Once you have your engine, you’ve defined the scope of the argument. The correct answer will generally fall within the scope of the engine.
(ADVANCED NOTE: Sometimes more difficult questions involve a three-part engine: premise –> intermediate conclusion –> conclusion. In a case such as this, you’ll need to examine the logic in two parts. First, look at the premise –> intermediate conclusion relationship. Is there a gap or assumption made in this part of the engine? Next, look at the intermediate conclusion –> conclusion part of the engine and ask yourself the same question. The simple difference here is that there are actually TWO engines at work. You’ll want to check both of them.)
Reading Comprehension: Your Opportunity to Lap the Field
Posted by dan@atlaslsat.com in LSAT content, LSAT Prep on August 18th, 2009
If you’re an LSAT forum poster/reader, you know that the good majority (almost all, in fact) of content-related LSAT posts focus on Logic Games and Logical Reasoning. This makes perfect sense. It’s easy to submit a post about a setup for a tough logic game, and it’s very easy to discuss the underlying logic present in one short LR question. LG and LR questions come in nice, neat packages. They are forum-friendly. Additionally, future LSAT test-takers seem to see and appreciate the immediate impact of a well-designed setup or a clever way to think about a piece of LR logic. The payoff is quick, and often immediate.
Reading comprehension, on the other hand, is messy. In order to have a serious, in-depth discussion about an RC passage, everyone in the conversation needs to be coming directly from a focused read of the passage. It doesn’t work to try to remember back to the passage, or to read a quick summary. For this reason, not many like to talk about it or ask about it. It’s inconvenient. Furthermore, there never seems to be a quick, easy payoff when it comes to RC. There’s not one inference that can be made to change confusion to understanding, there’s no quick gimmick that can be posted concisely to help someone become a better reader. There’s simply no quick fix, no immediate gratification. So why spend time on it? Most people don’t.
These are the people you are competing against. The better you do relative to them, the higher your LSAT score. Make their RC weakness your strength and you’ll put yourself in a position to gain upwards of 4 raw points on the field. Before you decide to make RC your LSAT version of a powerful forehand, you need to be in the right mindset.
1. Focus on the long-term, not the short-term. RC improvement does not come easily, and it certainly doesn’t come immediately. Be prepared for a long, tough slog. It may take 3 weeks, or 5 weeks, or 7 weeks, but if you’re diligent and focused, you CAN make significant improvements over the long-term.
2. Reading comprehension tests your ability to read. Go figure! This may seem obvious, but it’s something that most people don’t want to acknowledge. A lot of test-takers look for shortcuts, skimming techniques, or tricks in order to get better at RC (if they try at all). The problem with these approaches is that they intentionally avoid the part of reading comprehension that really matters: reading! It’s not about whether you read the questions first or the passage first, it’s not about the order in which you take the questions, and it’s not about coming up with some scheme to read only topic sentences and skip the rest to save time. It’s about reading well. You must confront this task head-on. If you are going to improve your RC score, you need to improve (and in many cases change) the way you read.
So, how do you become a better reader? As you evaluate your current reading skills, consider the following statements. Do any of these sound familiar?
1. I have difficulty absorbing all the information in the passage.
2. I have difficulty understanding all the details (especially all the science related details).
3. I have a difficult time deciding what to underline. Or, I end up with 80% of the passage underlined when I’m finished.
4. Reading the passage takes me way too long.
If any one (or more) of these defines your reading, you are most likely having trouble distinguishing the “important” information from the “unimportant” information. You are attempting to absorb everything instead of focusing on what really matters. If you can learn to make this distinction effectively and efficiently, that 4-point advantage will be yours for the taking.
I know what you’re thinking: “Tell me how!” If you’re looking for an easy answer here, you’re falling into the quick-fix trap. It’s going to take more than that. It’s going to take a sustained effort and focus. That said, here are a few ideas to get you started:
1. To figure out what’s “important” information and what’s not, consider the purpose of the LSAT. Why do law schools require you to take the LSAT? One reason: the LSAT is designed to predict how good of a law student you will be. It should not be surprising, then, that most LSAT reading passages are mini representations of the types of reading you will do in law school. Imagine for a second that you are a first-year law student and you’ve been assigned a case to read. Tomorrow, you’ll have to stand in front of your peers and your professor and distill the 100 plus pages of text you’ve read down to a succinct analysis of the case. Clearly, you won’t be able to regurgitate, or even remember for that matter, all 100 plus pages. How will you separate the important information form the unimportant? If you can figure this out, it should help you think about RC passages in a new way.
2. Become an active reader. You can’t read like you watch TV. The LSAT will not present information in commercial form, with a clear, ready-to-digest message. Rather, you’ll achieve success only if you read actively. Research shows that expert readers are active readers. They approach the text with a clear focus and purpose, they constantly evaluate their state of comprehension, and they constantly anticipate what might come next in the text.
So, learn to distinguish between the important and the unimportant information, and then read actively to pursue this information in the text. These are the first few steps on the path to RC success.
Are you ready to commit? Not many LSAT test-takers are, which is what makes RC the lowest hanging fruit on the exam.
Sufficient vs. Necessary Conditions on the LSAT
Posted by noah@manhattanlsat.com in LSAT content, LSAT Prep on July 31st, 2009
“It’s confusing sufficient with necessary” is probably one of the phrases that LSAT students use most frequently. But what does that really mean? If you’re just starting out your LSAT prep, this conditional logic can be a bit confusing. So, here’s a basic lesson.
Let’s start with an example:
If Kate rejects Ethan’s marriage proposal, he’ll move to Wisconsin.
Many LSAT students will immediately want to turn this into letters and arrows, but let’s leave the argument as is for the moment and consider what it means. What happens if Kate rejects Ethan’s proposal? Well, off to Wisconsin he goes. So, Ethan moving to Wisconsin is necessary if she rejects his proposal. What is sufficient to make him move to Wisconsin? A good old-fashioned rejection of his marriage proposal (by Kate) will do just fine. So, her rejecting his marriage proposal is sufficient to make Ethan move to Wisconsin. Is it the only reason he’ll move to Wisconsin? Not as far as we know. He might get a job in Madison, or perhaps he loves really fresh PBRs.
So, what does it mean if he’s moved to Wisconsin? Does it mean that Kate has rejected his proposal? It might, but it doesn’t necessarily mean that. Perhaps she’s moving there with him in holy matrimony. If you think that Ethan moving to Wisconsin means Kate rejected his proposal, you’re confusing sufficient with necessary. Another way to think of this is: you’re illegally treating the effect as a cause. Kate rejecting him is the cause (or “trigger” as I like to think), and Ethan moving to Wisconsin is the effect, result, or, something that is necessary.
More formally: R –> W, (rejection leads to Wisconsin). What else can we infer (prove) from this? We cannot say that W –> R! This is the confusion – or we can say that this is reversed logic. But, there is one other rule we can infer: If Ethan doesn’t end up moving to Wisconsin (not W, or ~ W if you want to get fancy), Kate must not have rejected his proposal. If she had rejected his proposal, then he’d be moving to Wisconsin. So, the other rule we can create is ~ W –>~ R. That’s the contrapositive of the original rule. Reverse the rule and negate (use the opposite of) each side. It’s extremely important to understand what the contrapositive is, how to form it, and how it applies to arguments and logic games.
If you think you have it, figure out the contrapositive of this statement: If Liz didn’t campaign, she didn’t win the election.
Got it? Write it down.
So, the original statement can be represented as ~ C –>~ W , and the contrapositive, which we form by reversing and negating the statement, would be W –> C. That means: if she won, then she campaigned.
The million dollar question: What can we infer if we know that Liz campaigned?
Nothing!
We know is that if she fails to campaign, she definitely (necessarily) will not win. And we know that is she won, she must have campaigned.
A final question, if Liz did not win (the nice way of saying “she lost”), did she not campaign?
If you answered “yes,” you’ve confused necessary and sufficient. But you also cannot say “no”! All we know is 1. that if Liz doesn’t campaign, she will not win, and 2. that if she wins, she must campaigned.
Want more help? Take a look at our LSAT books at http://www.manhattanlsat.com/lsat-books.cfm. You can get this pretty quickly!
