A note on question types

In my last post, I was a bit snarky about the tendency of test prep companies to develop complicated taxonomies of, say, argument question types.  I’d like to be a bit more nuanced about that.  I like simple taxonomies, ergo my DESTROY, SUPPORT, DESCRIBE for arguments, and I do think that all of the arguments fit into one of those three broad categories.

HOWEVER.  In the course of your studying, if you start to notice that it helps you to think about “inference” questions differently than “conclusion” questions, that is fantastic.  If it identifies for you a difference that is meaningful to you in what approach you take/traps to look out for, then you know you are studying and learning well.  My only quarrel is when you spend a ton of time (and money) learning someone else’s taxonomy, with nuances that don’t mean a whole lot to you.  Then you stress out a bunch over your inability to see any difference between an inference or a conclusion question, when at the end of the day, there isn’t a difference, and it shouldn’t cause you any stress, because if you weren’t so fucking stressed out, you’d get the right answer.

This applies to other question types as well (RC, LSAT games, math questions on the various math-y tests).

What are you studying for?

I want to post some more worked examples for arguments, but I’ve been chewing over this question for quite a while now, and want to provide some thoughts on what the bulk of test-prep study time should be focused on.

There is a little bit of substantive stuff that is worth making sure you know for each of the tests.  Some math maybe, or logic rules for the LSAT.  This has to be done.  It is also possible to create some things to study for, such as finely grained categories of argument questions.  This is usually a waste of time.  Or you could just do practice questions until the cows come home, hoping for improved results.  The tests are pretty resistant to magical thinking, though.

So what are you studying for?

I like to think of it as taking the decisions out of the test.  You want to absolutely minimize (i.e. get to zero) the moments on the test where you are looking at a question and don’t have a plan for solving it.  This is different from knowing what the right answer is off the bat.  Instead, it is having a process that you know and trust and FOLLOW EVERY SINGLE TIME.  My suspicion for the students who take a test prep class, feel like they are improving, and then get the same fucking score as they have gotten at the start, is that they get into the exam and wing it, rather than relying on a set process.

When you are nervous, you make DUMB decisions.  Big time DUMB.  You are not dumb, but when you are thinking about “ohmygodIhopeIdowellbecause IreallyreallywannagetintoHarvard” you are not at your tip top in thinking through the ins and outs of your approach.  It’s just the way the brain works.  So the way to cope is not to start thinking “ohmygodIbetternotfreakoutbecausethen I’mgoingtomakebaddecisionsandnotgetintoHarvard” but instead to not make decisions when it isn’t safe.  Sort of like not driving drunk.

When you turn the page/click to the next screen, and see a reading comprehension passage, you want to have a tried-and-true process that you don’t question and don’t change on test day.  You are going to read the first question stem, skim for an answer, prove every fucking word of your answer choice is addressed in the passage, rinse and repeat.  You are not suddenly going to decide that maybe reading the passage first would be a good idea.  You aren’t going to go all magical thinking and pick (C) because it just “sounds” like the right answer.  You aren’t going to panic about the time and pick the first plausible answer because “whatifI’mtooslowanddon’tfinishontime bettergofasterorImightnotgetintoHarvard.”

You want to walk into the test with a very clear, realistic idea of what your score is going to be and how you are going to earn it.  Of course there will be some variation and some moments that may call for a bit of creativity or insight, but that is to be kept to a minimum.  If you don’t already know what your score will be, you shouldn’t be taking the test.  If you think you know what your score will be but hope it will be lots better, you DEFINITELY aren’t ready to take the test.  Instead, you want to work systematically through the question types on your test, and figure out your approach, practice it consistently until you would NEVER do it differently, then move on to the next question type.  This is the heart of Test Smashing.  The test should be little smithereens before you walk into the test center.

Arguments: Working an example II

This argument is Q26 in the Critical Reasoning Practice Questions in the 13th Ed. of the GMAT Official Guide.  Let’s work through it in the steps I discuss in this post.

1.  The stem reads: “Which of the following conclusions can most properly be drawn from the information above?” This may sound like it doesn’t fit neatly into my DESTROY, SUPPORT, DESCRIBE framework, but it actually does.  When you are asked to draw a conclusion from an argument, you may not make any assumptions.  This means that the correct answer is an amalgamation of what is in the argument already, and therefore is a DESCRIBE question.

2.  The argument reads:

When a polygraph test is judged inconclusive, this is no reflection on the examinee.  Rather, such a judgment means that the test has failed to show whether the examinee was truthful or untruthful.  Nevertheless, employers will sometimes refuse to hire a job applicant because of an inconclusive polygraph test result.

This is actually all premise (you get to come to a conclusion), though the facts have some discrepancies.

3.  I do not worry about how I happen to know that polygraph testing in general is highly unreliable with lots of false positives.  This is not relevant.

4.  Okay, I don’t need to look for assumptions, I just need to describe.  But it is still useful to simplify the argument to build my description:

(1) Inconclusive = meaningless re applicant.  (2) Inconclusive = bad test.  (3) Inconclusive –> employers turn down applicants.

Which answer choice combines these 3 statements accurately?  Let’s do this by process of elimination.

  • (A) Most examinees with inconclusive polygraph tests are in fact untruthful.  This says that Inconclusive = usually untruthful re applicant.  Contradicts (1).
  • (B) Polygraph tests should not be used by employers in the consideration of job applicants.  This says that Inconclusive + Conclusive results = useless.  We know nothing about Conclusive results.
  • (C) An inconclusive polygraph test result is sometimes unfairly held against the examinee.  We know that Inconclusive = meaningless re applicant (1), and Inconclusive –> bad outcome for applicant.  Since suffering a bad outcome for something that you did not control can be described as unfair, this answer choice is not totally sucky.
  • (D) A polygraph test indicating that an examinee is untruthful can sometimes be mistaken.  The argument tells us nothing about conclusive results. Note Step 3!!!
  • (E) Some employers have refused to consider the results of polygraph tests when evaluating job applicant.  The argument only tells us about how employers use polygraph results, nothing about how they don’t use results.

You should be hyper wary of (C) because of its use of a value-laden word “unfairly.”  Almost always, these answer choices are traps.  But here is an exception worth noting, and you can be confident that it is an exception because the other choices are so badly wrong.

Arguments: Working an example I

This argument is Q2 in the Critical Reasoning Practice Questions in the 13th Ed. of the GMAT Official Guide.  Let’s work through it in the steps I discuss in this post.

1.  The question stem is: “The argument is flawed primarily because the author”.  So, I write down DESTROY on my paper.

2.  The argument is:

Homeowners aged 40 to 50 are more likely to purchase ice cream and are more likely to purchase it in larger amounts than are members of any other demographic group.  The popular belief that teenagers eat more ice cream than adults must, therefore, be false.

The first statement fits in the premise slot, the second in the conclusion slot.  How do I know?  The first sentence is stated as a fact.  The second sentence uses the telltale “therefore” to indicate that it is the conclusion.

3.  I do not indulge in thoughts about how 30-something single females are inclined to eat large quantities of ice cream after romantic missteps!

4.  Since I didn’t write down DESCRIBE, my work is not done.

5, 6.  A shortened, focused summary of the argument:

H buy most X.  Therefore, T do not eat most X.

What is the important shift between premise and conclusion?  buy –> eat.  So I need to find an answer choice that phrases that in a way that DESTROYS the argument.

7.  Looking at the answer choices, A pops out:

fails to distinguish between purchasing and consuming

Since purchasing = buying and consuming = eating, we have a perfect match.

8.  I read again the stem, yes, I am supposed to DESTROY.  A is phrased in a way, “fails to distinguish,” that DESTROYS.

Smash!!!

Arguments

These are the Critical Reasoning questions on the GMAT and the Logical Reasoning questions on the LSAT.  Indeed, the approach to the short reading comprehension passages on the GRE should be approached blending the Arguments and Reading Comprehension question approaches.  There is no equivalent question type on the SAT.

Important:  If you are taking the LSAT, arguments are 50% of the test.  Games and Reading Comprehension are each 25%.  TestSmashing Arguments is the most valuable thing you can do to up your LSAT score.  Not to mention there is a lot of spillover between Arguments and RC.  Games are the strangest (and most fun) part of the LSAT, so they often suck up most of the attention of LSAT studiers.  This is a mistake.  If you can avoid that temptation, you are ahead of the game already.

Okay, ‘nough warm up.  How to smash arguments:

1. Read the question stem first.  A lot of prep companies spend a lot of time categorizing the question types in elaborate ways, and that isn’t a terrible thing to do, but I also think it isn’t the most important thing to worry about.  I would, however, write one of three things down on the test next to the question (or on scratch paper for the GMAT): DESTROY, SUPPORT, DESCRIBE.  Or symbols that are meaningful, like X, (check), ~.  (Spending time writing lots out is not the TestSmasher way, unless it is necessary.)

2.  Read the argument with one main purpose: which bit of the argument fits into which slot?  There are two slots: Premise and Conclusion.  They take the form, Premise: A is X.  Conclusion: Therefore, B must be Y.  In other words, there is a statement of fact (the premise) and then a statement about something else that must also be true (conclusion) because of the original fact.  The order in which these items come is not consistent.  Sometimes the conclusion comes first.  It is very important to know which is which.

3.  Do.  Not.  Ever.  Engage.  The substance of the argument is irrelevant.  The truth in the real world is irrelevant.  This is how people get snookered on arguments.

4.  If you wrote down DESCRIBE on your paper, you are done.  Look at the answer choices and, like in reading comp, prove that every word in your answer choice describes what is happening in whatever part of the argument you have been asked to describe.

5.  Otherwise, you have to figure out the mechanism by which the author of the argument got from Premise to Conclusion.  Unless the argument is:

A is X.  Therefore, A is X.

(and very, very occasionally, you will see an argument that is a tautology like the one above) there is an Assumption involved in the argument.

6.  The key to most argument questions is realizing that there is only a small set of structures to the arguments.  If you can see past the substance and the crappy writing style, you’ll learn that there are maybe 5 or 6 arguments on the tests.  Once you are able to see that, identify the class of argument, know how the correct answer is structured, you have smashed Arguments!!!

Some of the underlying structures are:

A is X.  Therefore, B is X.  Answer choice deals with the question: Is A = B?

A is X.  Therefore, A is Y.  Answer choice deals with the question: Does X imply Y?

There are a handful of these structures, and the prevalence and flavor are somewhat different between the LSAT and GMAT.  You should find a way to characterize the structures in a way that is meaningful to you, and your study time on arguments should be about noting and understanding the structure of arguments.

7.  Which word did you write down?  If you wrote DESTROY, and the argument is such that the answer choice deals with the question of, Is A=B?, then you look for an answer choice that says “B is not the same as A.”  If you wrote SUPPORT, the correct answer would be “B is indeed the same as A,” at least for the purposes of the argument.

8.  Double check that you executed the correct action on the argument.  The other way people get snookered is that they DESTROY instead of SUPPORT or vice versa.  This usually happens when they ask you to DESTROY a sensible argument or SUPPORT a really stupid one.  If you are not engaged with the substance of what you are reading, you won’t make this mistake as much.

Note: One frequent question type is “What assumption does the argument rely upon?”  This sounds DESCRIBE-y, but, since it deals with the assumption it isn’t.  Whether it is DESTROY or SUPPORT depends a bit on your temperament.  TestSmashing makes me snarky, so I like to think of identifying the assumptions as an act of destruction.  Some of you may feel more nurturing than me, and see identifying assumptions as a road to supporting the argument by making it stronger.  So interpret the question in the way that speaks to your perspective, but in the end the answer will always be “the argument assumes A = B” or “the argument assumes that X implies Y.”

How do you know you have smashed Arguments, once and for all?

Well, you’ll get them 100% correct, all the time.  I mean 100%.  Not 80% or 90%.  And, you will start to weird yourself out, since you’ll read the argument, have a pretty good idea of what the correct answer will say, and read the answer choices only to realize you predicted the exact wording of one of the answer choices.  That should scare you, because answer choices that sing to you are often traps, but if you are test smashing arguments in particular, you will know what the right answer should say almost to the word.  Of course, sometimes they will choose a bizarre route to the right answer.  Sort of like “X doesn’t imply Y when aliens invade,” but you should, by now, recognize that indeed it is true that X doesn’t imply Y when aliens invade, this is the form of answer I am looking for, therefore this must be right, bizarro though it may be.

I’ll do some worked examples in subsequent posts.

That math thing

So, unless you are taking the LSAT, you need to know some math.  Perhaps you are taking the LSAT because you want to get an advanced degree but don’t want to know some math, in which case, that is a crappy reason to go to law school.  Maybe you should read this post too.

A lot of people think they don’t like math or that they can’t do math.  Others don’t mind it, but have forgotten everything they used to know and don’t use the skill currently.  For those of you who fit into either of these descriptions, this post is for you.  While the GMAT, GRE, and SAT don’t actually try to test your math skills comprehensively, you do have to be really comfortable with some math.  And for the tiny slice of the discipline that you have to understand, you have to understand it really really well.

But that is okay!  It will serve you really well to learn this stuff!  Particularly if it currently gives you nightmares.  It just sucks to go through life as a professional, competent adult who is scared of math.

The stuff you need to know

The most important three skills for all the math-y tests are estimation, number sense, and basic function manipulation skills.  Estimation is an important TestSmashing skill — it isn’t particularly tested directly.  By number sense, I mean, do you understand zero?   fractions?  negative numbers?  what operations start to behave crazily in which bits of the number line?  Also, what are the differences between even and odd numbers?  Can you factor numbers into their prime factors quickly?  Cope with exponents? That kind of thing.  Unless you like to think about numbers, and be curious about them, this stuff is actually kind of hard to learn — it isn’t really a part of the math curriculum.  You just sort of have to notice it as you go along.  Basic function manipulation — the mechanics of algebra — are also super important.  Can you solve for x?  And not just, do you know how to if you sit down and think about it, but do you automatically start rearranging equations in your head — accurately — every time you see an x?

It also doesn’t hurt to know a few things about triangles.  And the GMAT has a pretty substantial emphasis on combinatorics and probability in the hard questions.  But if math makes you queasy, don’t sweat this stuff.  Focus on estimation, number sense, and function manipulation.  Once you’ve mastered them, then you can start to pick up the less central stuff.

The stuff you don’t need to know

Notation and jargon.  Avoid explanations or manuals that use a lot of either.  It is cognitively taxing and pays no benefits whatsoever on the tests.  (And very little in life, though it can be fun to throw a string of jargon into someone’s face if they aren’t taking you seriously enough.)

How to learn it

The very best self-study guide for learning and cementing the skills you need is Forgotten Algebra by Barbara Lee Bleau.  Units 1-15 are pure gold and on target.  Polynomials are almost never on the tests, so Units 16-22 are not so useful, but Units 23, 25-28, 31 will also help.  The book is great because it breaks everything down into micro-steps, gives lots of examples, has clear explanations and plenty of practice problems.  It is also great in its focus on number sense.  If you do one unit a day, you will be good to go in 2-3 weeks.

If you have found another book that you like, please let me know in the comments section!

How to love it

If you are mathphobic, the problem isn’t so much that you are incapable of learning the mechanical steps in Forgotten Algebra.  It’s that you have blocked your ability through boredom or trauma.  This is common and tragic, and there are books out there that could inspire you past the block.  The very first thing I would do is go read A Mathematician’s Lament.  It won’t take long.  It might make you angry, but the second half of the book, in particular, will pique your brain in a way it may not have been since you were a toddler learning to stand.   Hold on to this sense of joy, excitement.  This is the key to TestSmashing.

I’ll also re-iterate my recommendation of The Myth of Ability: Nurturing Mathematical Talent in Every Child.  It implements Paul Lockhart’s vision, and re-iterates through counter-example how very badly we teach math.  Some of the specific teaching tools he describes are also useful to get you to think about numbers differently, and in a way that will be rewarded by your test.

I know this is a lot of reading, but I think that this is actually time better spent that cranking through GMAT questions if you are mathphobic.  Once you have found the joy, the cranking through GMAT questions will actually be fun and even exciting.

Don’t just take my word for it

I wrote a while ago about how intelligence is not really the issue when taking these tests.  Guess what?  I was right!  The entire concept of intelligence as this immutable, etched-in-stone thing is totally, completely bullshit.  It turns out that studying for the LSAT makes you smarter.  You, dear test smasher, have within your power the option to exercise your brain more, and literally change its structure.  Woohoo!

My favorite quote from the article:

“A lot of people still believe that you are either smart or you are not, and sure, you can practice for a test, but you are not fundamentally changing your brain,” said senior author Silvia Bunge, associate professor in the UC Berkeley Department of Psychology and the Helen Wills Neuroscience Institute. “Our research provides a more positive message. How you perform on one of these tests is not necessarily predictive of your future success, it merely reflects your prior history of cognitive engagement, and potentially how prepared you are at this time to enter a graduate program or a law school, as opposed to how prepared you could ever be.

(My bolding.)  This is really great news for you.  This means that the test you are taking is not a measurement of your sum as a human being for ever and for all.  Instead, it is merely a snapshot of where you are on a particular set of skills at the moment.  This is really great news.

Except.  Now you have to act on it.  If you are performing poorly on your favorite test — or just performing more poorly than you like — you can’t just shake your fist at the sky and go about your life like you always have.  Instead, you have a choice.  You can change how you spend your time, and how you approach problems, and then see your score go up and your view of the world change.  Or, you can stay the same.  Your choice.  Change is really hard, and there is no harm, no foul, if you choose to not change. Life can be rich, wild, and wonderful for people with all levels of cognitive engagement.

But you gotta change your approach if you want to change your score.