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.
Or how about this one:
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!
Climate change is a very serious issue, but as a resident of Madison, Wisconsin, I sometimes grumble that global warming can’t come soon enough. It wouldn’t be a true Wisconsin winter if we didn’t get at least one blizzard in March, and I found myself last week shoveling desperately through a waist-high mound of heavy, densely packed snow deposited by snowplows at the foot of my driveway. My usual strategy in such situations is “stay in the house until the roommate has to go somewhere first.” Unfortunately, he was out of town, so I had to excavate the driveway myself if I wanted any shot of pulling my car out of the garage.
I get the feeling that many of you view the taking GRE the same way I view shoveling snow: as a chore. Something unpleasant that takes a lot of time and work, that you have no choice about, and that if you were king of the world, you’d never have to deal with.
You might expect that, as a professional GRE teacher, I’d be disappointed that so many of you are as excited to study for the GRE as you are to clean the bathroom. And in some respects, I am. As I wrote recently, I honestly believe that studying for the GRE is a valuable experience, and I’d like for more of my students to be excited by the prospect of becoming smarter and cleverer.
In another light, however, I actually wish that GRE students viewed the test more like a chore. Chores have something going for them: nobody doubts their ability to complete one. As much as I loathe shoveling snow, I knew after a set amount of unpleasant labor, my driveway would be clear and I could pull my car out and move on with my life. We all dread mowing the lawn, folding laundry, and unloading the dishwasher, but we never entertain for even a second the possibility that we won’t be able to bring any of these chores to a successful conclusion. Nobody approaches a loaded dishwasher thinking, “Oh man oh man oh man THIS MIGHT BE THE DISHWASHER THAT ENDS ME.”
By contrast, a staggering number of GRE students fear exactly this: that the GRE will be the end of them. Some of you call the GRE a “chore,” but in actuality you don’t view it as a chore at all. You view it as a trial. You think that, maybe, you won’t succeed. And I know that on some days, the “maybe” tilts dangerously toward a “probably.” Watching my students suffer because they fear their own potential is the most heartbreaking aspect of my job.
Yesterday morning I was lucky enough to TA a practice test for Jesse Evans, one of the best teachers in the whole company. While talking about the despair that shrouds a lot of students who take their first practice test, Jesse uttered a line that I and the other TA’s promptly confessed to each other we were going to steal. The line was this:
“Don’t confuse being uncomfortable with being incapable.”
This was such a simple statement that I was simultaneously blown away by Jesse’s wisdom and stunned that I hadn’t come up with it myself. When you take the GRE, many things about it make you feel uncomfortable: using math you haven’t touched in eight years; reading prose full of words you don’t know; working with question formats you’ve never seen before, and the list goes on. But just because you’re uncomfortable with something doesn’t mean you’ll never be able to do it. If you knew the formulas once, you can learn them again. If you don’t know the meaning of a word, you can memorize it. If a question format seems weird now, it won’t seem weird after you’ve done a hundred problems that use it.
Outside, in the bitter cold, with my nose running and my muscles burning, I felt the keenest discomfort as I hacked through several feet of hard, nasty snow. But I never doubted for a second that someday my ordeal would be over and I’d be able to say, “I did that!” as I got in my car and caromed triumphantly through the gap in the snowdrift. Don’t read too much into your own discomfort on the GRE. Just because you’re uncomfortable doesn’t mean that you’re incapable.
When a GRE quantitative problem features multiple ratios, many of you suffer headaches. This is because the “math” way of solving the problem is brutal, and students who don’t use logic will dive head-first into a morass of ugly substitutions, mistakenly assuming that the GRE is a math test. Here’s the kind of problem I’m talking about:
In a particular mixed candy bag, the ratio of Skittles to M&M’s is 4 to 5, while the ratio of Reese’s Pieces to M&M’s is 9 to 7. What is the ratio of Skittles to Reese’s Pieces?
The “math” way to do this problem is to set up two equations, solve one for M&M’s, and plug that value into the other one. If that sounds painful, that’s because it is. Don’t do this. Make a simple table instead:
S | M | R
4 : 5
7 : 9
Take a moment to confirm that you understand where the numbers above are coming from. They’re just a translation of the information in the word problem.
The question asks for the ratio of S to R. Can you just say it’s 4 to 9? No way. The value connecting them — the M — is different. It’s 5 in one ratio and 7 in the other. So, rewrite the ratios to make the M term the same in both, creating a kind of “bridge.”
Multiply the first ratio by 7: 7×(4:5) = 28:35
Multiply the second ratio by 5: 5×(7:9) = 35:45
Next, check out your new table:
S | M | R
28 : 35
35 : 45
Now you can just “walk across the bridge,” as it were — the ratio of S to R is simply 28:45. Try this technique on your next multiple-ratios problem and let us know how it goes!
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:
¶3 – What if normally-advantaged group made disadvantaged? Impossible to know.
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!
The chat lit up with excitement. I was expecting a positive response, but there was so much enthusiasm that I was taken aback. One student called it “a blessing.” Many others agreed that if they had 15 extra minutes per section, it would be just about the greatest thing that’s ever happened to them: they’d be less stressed, get more problems right, have a higher score; the sun would shine brighter and longer and warmer; a cavalcade of parachuting puppies would rain down from the sky and deliver every child in the world a cupcake made of love and hope; a cadre of unicorns would …
“HANG ON, HANG ON!” I said. “If you had more time to work on each section … what else would happen?”
And then there was silence. For a moment, the class was confused. Nobody saw what I was getting at. I prodded a little more, and finally one student said, “… other people would have more time too?”
Another student caught on. “And the scoring scale would be harder.”
Right. If you had 15 extra minutes per section, that would be terrible! Your competition would get the same bonus you would, so it’d be exactly as hard to get any particular score as it is now, except the test would be 75 minutes longer. Because every student’s score depends entirely on her performance relative to everyone else, a feature that benefits everyone actually benefits no one.
Don’t rail against the strict time limits of the GRE. Don’t fume, saying, “This is stupid. If I had infinite time, I could get all these questions right!” The thing is, if you had infinite time, so would your competition, and you wouldn’t be any better off. Learn to love the clock — it’s an opportunity for you to succeed where others fail.