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.
One of my students and I recently encountered a problem type that was persistently confounding to him. His math skills were strong, and the math in the problem was quite simple — but nevertheless, it took him a lot of effort to wrap his mind around the questions, which illustrate exactly what we mean when we say that the GRE Quantitative section is a critical thinking test, not a math test.
Here’s what one of these problems might look like:
Every employee at a certain company has either a regular bus pass, which costs $3, or a Deluxe bus pass, which costs $4. If the number of employees is as small as it can possibly be and the total cost of all the bus passes is $49, then how many employees have a regular bus pass?
I call this a “Most” problem, since the key to solving it is that you need to set one of the quantities to be the most it can possibly be. Although the problem requires nothing more than arithmetic and trial and error, it’s challenging when you first encounter it, as lengthy word problems often are.
When you encounter a problem like this, ask yourself this question: Which quantity do I need to max out? This is where the GRE test makers really test your logical reasoning ability: to reach a particular dollar cap, you can either use many cheap items or a few expensive items. So, if we want the number of employees to be as small as possible, we want as many of them as possible to have the Deluxe pass, which is more expensive.
Pause here! If that concept doesn’t make sense, then read the last paragraph over until it does, or write us a note in the comments. If you’re confused at this point, the rest of the problem won’t make any sense either.
Once you realize that to meet the conditions of the problem you need as many Deluxe passes as possible, the math is easy. Here’s a quick recap of the relevant information:
Total cost: $49
Deluxe cost: $4
Regular cost: $3
The most that $4 can fit into $49 is twelve times, so our trial and error should begin there.
If we have 12 Deluxe passes, that’ll put us to 12 x 4 = $48, leaving $1 left over. That doesn’t work.
If we have 11 Deluxe passes, we’ll be at 11 x 4 = $44, leaving $5. That still doesn’t work, since 5 isn’t a multiple of 3.
If we have 10 Deluxe passes, that costs 10 x 4 = $40, with $9 left behind. $9 divides nicely into 3: 9 / 3 = 3. So, there must be 10 Deluxe passes and 3 regular ones.
Click choice (C) and move on — and make sure to duck the trap choice (D), which is the cost of the regular passes, not the number; and (E), which is the number of Deluxe passes, not regular passes.
The pattern on these problems is always the same: first, use critical thinking to deduce which quantity you need to max out; then, start your trial and error at the biggest possible value and work downward until you find one that works. Let us know if you have any questions in the comments, and otherwise, enjoy getting a few extra easy points on Test Day!
Aaron Burr said, ”Never do today what you can put off till tomorrow. Delay may give clearer light as to what is best to be done.” Procrastination gets a bad rap, but it can be a useful tool on the GRE. When you solve algebraic equations containing difficult arithmetic, delay your calculations as long as possible. Here’s a powerful illustration:
18 = 24
A lot of people would start to do 18/3.06 here, and right away the problem would break down. That’s an exhausting computation to make without a calculator, and there’s abundant opportunity for error. Here’s the thing: you don’t actually care what 18/3.06 is. You care what x is. So solve for x first, and then worry about the arithmetic. The first step here is to cross-multiply:
18 * x = 24 * 3.06
Again, some people would reach this step and do 24 * 3.06. But why bother? Finish solving for x first:
x = 24 * 3.06 / 18
Now we see a beautiful thing. As I wrote about here, you should always hunt down the simplest calculations and do them first. In this case, that 3.06 is a real pain, but 24/18 is easy to do: both those numbers are divisible by 6. So you get:
x = 4 * 3.06 / 3
All of a sudden, the arithmetic is done. It so happens that 3 goes nicely into 3, 0, and 6, which are the digits that comprise 3.06. Thus, 3.06 / 3 is just 1.02, and the rest is cake:
x = 4 * 1.02
x = 4.08
Voila! You have the answer, and you never had to do anything painstaking or difficult. Maybe Aaron Burr was joking about procrastination, but his words provide genuine illumination on GRE math.
The new GRE features an on-screen calculator, which is as much a trap as it is a tool. Still, I find that many of my students use the calculator far more than they need to, because they don’t understand arithmetic. To be clear, they can do arithmetic just fine — they just don’t understand it, and this lapse in understanding costs them time and points on the GRE.
Here’s a quick sanity check. How would you do the following:
12 * 14
Were you tempted to make a new fraction, putting 12 * 14 on top and 7 * 3 on bottom? A lot of people do it this way, because they were taught as fifth graders that to multiply two fractions, you “multiply across.” Of course, 12 * 14 is a pain, and dividing that by 21 isn’t any fun either. No wonder most GRE students immediately reach for their calculator.
But you don’t have to do it that way.
In an expression that uses only multiplication and division, you can do the operations in any order you want. So why not simply do the operations in the easiest available order? The above expression offers plenty of options, including:
12 * 14
7 * 3
12 / 7
14 / 3
12 / 3
14 / 7
Some of those are easier than others, aren’t they? Start with them. Yeah, 14 / 7 is easy: that’s just 2. This leaves:
12 * 2
And now you can do 12 / 3, which is 4. This leaves:
4 * 2
And that’s 8. Piece of cake, two seconds.
Using a calculator here would give you plenty of chances to hit the wrong key and get a wrong answer — and for no good reason, since the arithmetic is manageable. Just follow the path of least resistance when it comes to GRE arithmetic.
Perhaps more than any other section of the GRE, reading comprehension is the subject of a lot of mysticism. People seem to think that reading is a “life skill,” and that if you haven’t mastered it by the time you take the GRE, you’re out of luck. Those who have the skill can read the most abstruse of passages and “just get them,” as though struck by divine bolts of understanding. Meanwhile, those less fortunate are doomed to wallow in perpetual ignorance and confusion.
All of this is nonsense. Reading comprehension is a skill, and like all skills, it is statistically impossible that every single person in the world will be equally good at it. The fact that some people are naturally better than others is not a surprise, but a mathematical certainty. Those who are good at reading comprehension aren’t good because heavenly inspiration keeps showering their brains; they’re good because they perform simple, concrete behaviors and notice simple, concrete patterns. Anyone who learns these behaviors and patterns will be just as good at reading comprehension.
In this post, I’d like to share with you the single most important behavior for success in reading comprehension, and offer an easy example to illustrate.
The behavior I’m talking about is prediction. Don’t you hate it when you reach the end of a paragraph and realize, dazedly, that you have no idea what you’ve just read? This happens because you’re reading first, then working backwards to comprehend what you’ve just read. That strategy works fine for Twilight and Harry Potter, but not for serious academic articles. You’ve got to do it backwards: try to understand first, and then read. Once you make a conscious effort to read this way, you’ll be surprised by the extent to which academic writers give away nearly everything they’re about to tell you.
Here’s an easy example. How often have you read passages whose opening lines contain one of these phrases?
Philosophers have long held that…
Traditionally, sociologists have argued that…
It has been commonly believed that…
Many people read over such a phrase with nary a second thought, which is a shame, because these phrases effectively spill all the author’s beans. What it does mean when the author kicks things off with a “traditional,” “long held,” or “commonly believed” point of view? It means the author will challenge it. If the author thought that the view were current and correct, she wouldn’t bother going out of her way to make sure you knew the view was “traditional” and held by somebody else. She’d just present the view as fact.
Readers who notice this simple pattern know what’s coming next. They’re less likely to be caught off guard and more likely to understand the author’s point. By contrast, readers who gloss over this big clue won’t know what to look for, and will therefore be more likely to miss it.