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Mar
27
2013

# GRE Reading Comp Logic: the Wrong Rabbit Hole

Last year, I wrote a series of entries about the critical reasoning problems that were recently added to the GRE. Since it’s been a while, let’s revisit that question type — and check out another aspect of critical thinking that confounds many of you.

Here’s a type of problem that’s caused no end of consternation to a lot of my students:

Residents of this state are obligated to renew their driver’s license in two circumstances only: if they accumulate six or more points in moving violations, or if they obtain citizenship in another country. Clarice, who is a citizen of only this country, has been involved in only one accident, which added three points to her license. Therefore, Clarice has no reason to renew her driver’s license at this time.

The argument above depends on which of the following assumptions?

I’m not going to show you the answer choices because the essence of this problem needs to be taken care of long before you ever look at a single choice. When I ask my students for the assumption, I invariably hear answers such as the following:

- “The author assumes that Clarice didn’t receive points from sources other than accidents.”

- “The author assumes that Clarice wasn’t already a citizen of some other place.”

- “The author assumes that Clarice didn’t do something else that would make her have to renew her license.”

All of these wrong answers fall for the same trap: thinking in the way that the test makers want you to think. The test makers say, “Hey! Look at these conditions. Clarice didn’t meet any of them. So, there’s no reason for her to renew her license.” And a lot people look at that line of reasoning and say, “Aha! I bet Clarice DID meet one of those conditions, in some sneaky way.” Then they start drumming up clever ways to force poor Clarice to retake her driver’s exam.

This is what I like to call going down the wrong rabbit hole. The test makers show you a rabbit hole, saying basically, “Hey, you! Think about THIS.” And so you think about whatever “this” is, and you think about it really hard, and the problem is that you shouldn’t have even started thinking along those lines in the first place.

Let’s back up a bit.

Consider this argument:

Boris isn’t obligated to exercise. Therefore, there is no reason for Boris to exercise.

There is no law mandating that Boris be kind to his mother. Therefore, he should be a jerk to her.

How do those arguments sound? Terrible, you say?! But why? If I’m not required to do something, doesn’t that mean I have no reason to do it?

Here, again, is the argument about Clarice, but condensed to the essentials:

Clarice isn’t required to renew her driver’s license. Therefore, she has no reason to renew her driver’s license.

It’s tricky to spot the error the first time someone throws you an argument like this, because renewing a driver’s license is boring and lame, so your brain fills in the gap in the argument: “The only reason anyone would ever renew their license was if they had to.” But that’s not necessarily true: that’s an assumption. Maybe Clarice gets a tax credit for renewing her license, or renewing the license will get some of her points taken away, or renewing the license provides some other benefit to something completely unrelated. We don’t know.

Remember this nugget of logical wisdom when you take the GRE: just because a person isn’t required to do something, doesn’t mean that they shouldn’t or they won’t!

Mar
4
2013

One of the most important things to realize about GRE reading comp – nay, the most important thing – is that the details don’t matter. As you read each paragraph of a passage, you need concern yourself with one thing, and one thing only: What the author’s purpose was in writing each paragraph, and his purpose in writing the passage.

You need to take notes while reading passages, but not the type of notes that you’re accustomed to taking – your goal is to make a bare-bones outline that sums up each paragraph in two phrases or fewer.

Here’s a sample passage, one paragraph at a time, and our map of it:

After you read the first sentence, make a quick note about the broad subject matter of the passage:

Topic: Egalia’s Daughters

And once you get to the last sentence or two of the first paragraph, make a note about the passage’s scope –this is just a narrower version of the topic, that tells you what about it specifically interests the author:

Scope: Book’s ending not supported by research

And to sum up the key points from paragraph 1:

¶1 – Book reverses gender roles; ending not based upon research

Now, as you read paragraph two, stop after just the first sentence and predict what the overall paragraph is going to be about:

¶2 – SJT: Even people who are oppressed by a society generally support it

As you scan the rest of the paragraph, did any keywords jump out at you to tell you that the author was doing anything other than explaining this theory? Nope – our note is sufficient, and we can move on to the final paragraph.

Apply the same exercise to the third paragraph: Make a note about what the paragraph’s overall topic seems to be after you’ve read only the first sentence:

Does the rest of the paragraph serve any function other than to prove its leading sentence? You only need to do a quick scan for any new keywords to realize that no, it does not.

Once you’ve read the entire passage, make a note of the author’s primary objective in writing the passage – chances are that you’ll get a question about it. In this case, if we look at our three paragraphs in order, we can see that the author was trying to prove the point that he made about Egalia’s Daughters in the first paragraph:

Purpose: To explain why book’s ending not supported by research.

Now (and not any earlier than now!) we’re ready to go the questions  - having read strategically, we’ve noted information that will allow us to answer virtually every question efficiently. Happy “mapping”, and stay tuned for more reading comp best practices in next week’s entry!

Feb
25
2013

# GRE Reading Comp: Quantitative Vocabulary

When I say “GRE vocabulary,” you might think I mean words like panacea and moribund. But in the past year, I’ve discovered that (aherm) esoteric words aren’t the only ones to give my students headaches. Seemingly (cough) innocuous words like “some,” “many,” and “most” instigate no end of consternation on the new GRE‘s logic-based reading comp problems.

Have a look at what I’m talking about:

Most of Bob’s students are graduate students, and most graduate students at Bob’s university are in a PhD program. Bob owns a hamster, as do many of his students, and most of Bob’s students think he’s a great teacher.

If the statements above are true, which of the following must also be true? Select all that apply.

A) Most of Bob’s students are in a PhD program.

B) Some hamster-owning students think Bob is a great teacher.

C) Some graduate students think Bob is a great teacher.

Let’s examine these statements one by one. First, is it true that most of Bob’s students are in a PhD program? The relevant information is this:

• Most of Bob’s students are grad students
• Most grad students are PhD students

If your intuition is confused, you can pick numbers to make sense of the situation, even though this is a verbal problem!

Suppose that Bob has 5 students. On the GRE (and, for that matter, in real life), the word “most” means “more than half.” So, at minimum 3 of Bob’s students are grad students. Now suppose that there are 1,000 grad students. If “most” of them are getting a PhD, that means there are at least 501 PhD-chasers. This leaves up to 499 students who AREN’T getting a PhD — and Bob’s 3 grad students could easily be among them.

So, no: choice (A) doesn’t have to be true. It could be true, sure, but it doesn’t have to be. Avoid the GRE’s “could be true” answers on “must be true” questions!

Next, check out (B): Some hamster-owning students think Bob is a great teacher. The relevant information this time is this:

• Most of Bob’s students think he’s great
• Many of his students own a hamster

This is cake if you know what “many” means. For some reason, many (cough!) of you think it means “most,” perhaps because both words are four letters long and start with “m.” Not so! “Many” is actually a synonym for “some:” it means, for the precise purposes of the GRE, “at least one.”

(Side note: if you don’t think that’s true — if you think that “many” means “a lot more than one” or some such — consider that “many” is a subjective word that hangs on context. One hair on my head isn’t very many at all, but one cockroach in my soup, I think you’ll agree, is already too “many!”)

So all we’ve got from the stimulus is that at least one of Bob’s students owns a hamster. And that one hamster-owning student could easily be among the few who think Bob sucks. This is another choice that could be true but doesn’t have to be.

On Test Day, there will always be at least one right choice on an “all that apply” question, so if you ever cross out (A) and (B), you know that (C) is right without even checking it. For practice’s sake here, though, let’s give it a look: Some graduate students think Bob is a great teacher.

Well. You know that most of Bob’s students think he’s a great teacher, and you also know that most of Bob’s students are grad students. If Bob has 5 students, that means there has to be a minimum of 3 in each category. Here’s what that could look like:

Student 3: Grad Student, Thinks Bob is Great
Student 4: Thinks Bob is Great
Student 5: Thinks Bob is Great

Notice that despite my best effort to avoid overlap, some overlap was unavoidable: with 3 grad students, 3 fans of Bob, and only 5 total students, at least one student had to be both. So yes: “some” (i.e., at least one) students are both grad students AND think Bob is great.

These problems don’t just test your ability to make good deductions. They also test your ability to not make bad deductions. On Test Day, think everything through, picking numbers if you have to — and before Test Day, ask us in the comments if you’re confused about these or other examples you’ve encountered!

Sep
12
2012

# GRE Reading Comprehension and Critical Reasoning, Part II: The Skittles Case

In this entry, I described the correlation/causation reasoning pattern and how it can help you solve GRE reading comprehension problems. As a follow-up, I’d like to show you a related type of argument and illustrate it with an example.

Whenever a GRE author argues that one thing is the explanation for or the reason for another, the assumption is always the same: that there are no alternative explanations. This idea may seem obvious, but the GRE’s writers have a way of clouding simple ideas with seemingly sophisticated arguments. Consider this one:

On Wednesday of last week, the jar of Skittles in my office was stolen. Since Bob was seen leaving my office just fifteen minutes before I discovered the jar to be missing, he was certainly the person who stole it.

Seems compelling, right? Bob left the office just fifteen minutes before the crime was discovered! He must be the culprit!

Not if you look closely. The argument demonstrates that Bob is a possible explanation for the missing jar, not that Bob is the only possible explanation for the missing jar. Note carefully: just because Bob was in the office at some point, doesn’t mean that other people weren’t. Arguments on the GRE have a tendency to ignore such inconvenient considerations.

All it would take to weaken the argument is any information showing that Bob wasn’t the only person in the office that day. Marco might have been seen leaving the office five minutes before the jar was found stolen — or maybe the jar was already stolen before poor, bewildered Bob entered the office in the first place.

Whenever a GRE author argues that one thing is the cause of/explanation for/reason for another, you’ll find the same assumption every single time: that nothing else in the universe could be the cause/explanation/reason. When you read the answer choices, know that the mere presence of any alternate possibility is enough to weaken the argument, and the elimination of any alternative is enough to strengthen the argument.

Sep
10
2012

# GRE Reading Comprehension and Critical Reasoning, Part I

Reading comprehension makes up about half of the GRE verbal section, but not all reading comp problems are the same. The August 2011 GRE revision introduced short, one-paragraph passages accompanied by questions such as, “Which of the following, if true, would most weaken the argument?” These problems require you to pinpoint an argument’s conclusion, identify its evidence, and figure out the implied — but unstated — assumptions that bind everything together. While they technically fall under the umbrella of “reading comprehension” on the GRE, problems like this are in reality no different than the critical reasoning questions that appear on the GMAT.

If you want to master these logic-based questions, it helps to be familiar with common reasoning patterns. In a series of entries beginning with this one, I’ll teach you several that are handy to know on the GRE.

We’ll start with one that you might already know. At some point in your life you’ve probably heard the phrase, “Correlation does not imply causation.” This is a great one-liner to throw at people who put together such arguments as, “A study found that 99 percent of murderers ate candy as children. Thus, eating candy clearly causes children to grow up to become murderers!” Well, just about everyone eats candy as a kid — it’s probably another aspect of a criminal’s upbringing that causes him or her to grow up that way.

Of course, the GRE won’t give you silly arguments like that. It’ll feed you much more smart- and logical-sounding arguments like this one:

A few years ago, the beaver population of Oak Woods began declining rapidly. An industrial facility near the woods produces a chemical compound that’s been scientifically proven to cause tooth decay in beavers. Since the largest river in Oak Woods runs right behind this facility, the facility is undoubtedly behind the plummeting beaver population.

The GRE test writers craft sciency, smart-sounding arguments in an effort to dull your senses to the awful logic that’s afoot. They also turn your outside knowledge and values against you: if you’re like most people, you’ll feel sympathy for the poor, innocent beavers and shake your fist in rage at the evil, corrupt industrial facility putting profits above the well-being of the environment.

On GRE Test Day, don’t let your emotions cloud your judgment. Sometimes, people we disagree with make logically sound arguments, while people we agree with make logically poor ones. The beaver argument above is every bit as bad as the candy murderer argument before it.

The argument shows that the presence of the industrial facility is correlated with the death of beavers. Does that mean the facility causes the beavers to die? Well, sure — as long as you make approximately 1.2 kajillion assumptions, namely:

• That the facility was already running “a few years ago,” when the beaver population began to decline; and even if it was,
• That the facility is actually dumping the hazardous compound into the river; and even if it is,
• That the beavers in Oak Woods actually drink from the river (as opposed to from a different one); and even if they do,
• That the concentration of the compound in the water, relative to the amount of water the beavers drink, is high enough to actually do damage; and even if it is,
• That tooth decay actually causes beavers to die.

Undermining any of these assumptions would make a smoldering ruin of the argument!

Your takeaway here: Any time a GRE author claims that X caused Y just because X and Y are correlated, examine the evidence carefully. Use logic, not your emotions, to determine whether the correlation/causation claim is a good one — and if you’re reading it in a GRE problem, chances are it isn’t.

For Part II of this series, take a look here.

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