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WHY ARE YOU HERE?
Some people describe themselves as “bad at math.” These people believe that math is beyond their abilities and have a high level of anxiety about the Math section of the GRE. Maybe you picked up this book because you’re one of these people and the very idea of engaging in a test of your math skills makes you nervous.
Other people are comfortable with math. They feel at home inside the numbers and are confident in their ability to execute on any kind of math problem.
Either way, both kinds of people often have the same misconceptions about the GRE. And both people tend to approach a math question on the GRE the same way. What’s worse is that ETS knows both things, and actively uses them to their advantage on test day.
What Do Most People Think about the GRE?
Most people have a few perceptions about the GRE:
- The GRE is constructed to be fair.
- Knowing the content is enough to get most questions right.
- ETS wants you to get the questions right if you have the knowledge needed.
Unfortunately, none of these is true.
The Truth about the GRE
- The GRE is constructed to make you miss questions you should get right.
- You can completely understand the content behind the question and still get it wrong. In fact, almost all GRE test takers miss some questions this way.
- ETS wants to trick you into getting the question wrong, even if you understand the concepts.
The Anatomy of an Average Test Taker
Those misconceptions are ones of the average test taker. Imagine this scenario. It’s test day. You’ve done all the important things you need to do to succeed—you’ve studied, gotten a good night’s sleep, eaten a good breakfast—and you are ready to go.
Shortly into the test, a math question appears. You read the question, look at the answer choices, think you know the answer, do some quick calculations in your head, select your answer, and move on to the next question.
If this sounds like you, then you have done exactly what ETS wants you to do.
Don’t Be Average
One of the single best lessons you can learn to succeed on the GRE is to not do what ETS wants you to do. ETS writes questions and answer choices designed to trip up the average test taker. The more you know about how ETS constructs questions and answer choices, and about how the average student responds to those questions and answer
choices, the greater your chances of having a successful test day. So, what are the types of things that you can do to not be an average test taker?
THINK LIKE A TEST WRITER
Putting yourself inside the mind of an ETS question writer is a great first step to being able to succeed on the GRE. Let’s imagine a test writer sits down to create a new math question for the GRE and they come up with the following question and correct answer.
The question writer has produced a question with a difficulty level of easy to medium. But, now the test writer must create 4 incorrect answer choices. The test writer could pick values at random, but that is not what test writers do. Instead, test writers try to predict how a student might make a mistake on the problem and use those mistakes to make their correct answer choices.
For instance, a student may have quickly read this problem and not realized that the store is having a clearance on six- packs of gum for $2.70 and assumed that the clearance price was for a single pack of gum. This student will immediately realize that if a clearance price of $2.70 is a discount of 10%, then the original price must be $3.00. So, the test writer will make $3.00 an answer choice.
What if a student misses that the question is asking for the original price of a single pack of gum? Well, that student will divide the clearance price of $2.70 by the six packs of gum, and get an answer of $0.45. So, the test writer will make $0.45 an answer choice.
And for the student who is rushing and therefore sees only the phrase six-packs, $2.70, 10% less per pack , and price of a single pack? Well that student will divide $2.70 by 6 and then subtract 10%, which yields $0.405. The test writer will round up and write $0.41 as an answer choice.
And what about the student who doesn’t quite fully understand how to calculate a savings of 10%? Well, that student may multiply the clearance price of $2.70 by 10% to find $0.27. They may then add $0.27 to $2.70 to yield $2.97.
The completed question, with all five answer choices, looks like this:
○ ○ ○ ○ ○
The test writer has now created a GRE question that includes trap answers for common mistakes that a student might make. The good news for you is that now that you know a little bit about how a test writer constructs wrong answer choices, you can use this knowledge to help you eliminate incorrect answer choices.
Well done.
Turn Algebra into Arithmetic
Later in this book, we will discuss Plugging In, a strategy for turning algebra into arithmetic. The basics of the strategy are that when a problem contains a variable and could be solved using algebra, you should plug in actual numbers for the variables and then solve. A lot of times, this will turn an algebra question into an arithmetic question. We are generally much better at arithmetic than we are at algebra, which works in your favor.
While we’ll discuss this strategy in much more detail later in this book, we felt the need to provide a preamble to it here. Why? Because Plugging In, and all its variations, is one of the most powerful tools in your belt to turn questions that may otherwise be difficult or time-consuming into questions that you can answer with relative ease. You should take extra effort to be very comfortable with this strategy, as it is one of the best ways to ensure that you are not being an average test taker and not doing what ETS wants you to do.
In short, Plugging In is an essential tool to the test taker seeking to not be average.
Be Aware of All Types of Numbers
Part of successfully navigating Plugging In and not being an average student is to show awareness of all kinds of different numbers. What do we mean by that? Consider the following.
If a GRE question gave the variable x and there were no restrictions on what x could be, what number would you plug
in for x? Many test takers will plug in 2, 3, 5, 10, or some other common number. But x could also be −2, −3, 0, , 10
, or any other number you could imagine. Test writers will often rely on test takers to not consider all possible types
of numbers when creating a question that contains variables. The more aware you are of the types of numbers
available to you on any given question, the better chance you have of avoiding choosing one of ETS’s trap answers.
This is not to say that you should ignore the common numbers. You shouldn’t. You should always work with the common numbers first to eliminate as many answer choices as possible. But, after you’ve plugged in a common number, if you still have a couple of answer choices remaining, plugging in a less common number is a good strategy to try to eliminate more answer choices.
Bite-Sized Pieces
Many of the math questions on the GRE read like verbal questions. These word problems are often long and contain a lot of information to process. The average test taker approaches this type of problem by trying to do all the steps at once, finding a shortcut, or trying to keep track of everything in their head. These are bad strategies. Avoid them.
Instead, approach these problems by breaking them into bite-sized pieces. By breaking the question into smaller parts that you can handle individually, you will stay more organized and run less risk of making a careless mistake.
Look at the following example.
At first glance, there is a lot of information in this question. Don’t try to answer the question all at once. Instead, break the question down into bite-sized pieces.
The question begins by stating that point B is 18 miles east of point A , so draw a line with points A and B on the ends and the length labeled 18. Point C is 6 miles west of point B , so draw another line from point B to point C and label the length 6. Point D is halfway between points B and C , so put a point between points B and C and label it D. Because point D is halfway between B and C and the length of BC is 6, the lengths of BD and DC are 3. Point E is halfway between D and B , so put a point between D and B and label it E. The distance between D and B is 3, and E is halfway between them, so the distance from point D to point E is 1.5 miles.
By breaking this question down into bite-sized pieces, it was easy to keep organized and to work your way to the correct answer.
Ballparking
Occasionally, the GRE will present to you a problem that contains strange numbers, such as long decimals or numbers that don’t appear to divide evenly. Many times, those questions will ask for a nonspecific value. When confronted with a question like those, the writers at ETS are hoping that you spend a considerable amount of time working with difficult numbers.
At these times, a good strategy to remember is to use Ballparking. With this technique, a number is designed to make difficult numbers easier to work with by rounding or approximating them to a more favorable number. After ballparking the numbers in a question, the correct answer will be the one that is closest to the value that you determined from your ballparked numbers. At various points throughout this book, we present examples of how to use the technique of ballparking.
PRACTICE
You should take the time to sharpen your GRE math skills if you want to succeed. If you don’t spend much time working with numbers, or if all your numerical calculations are done by calculator or spreadsheet, it is worth your time to go out of your way to become comfortable with numbers again. Here are a couple ways that you can reintroduce numbers into your daily life that are relevant to the GRE.
- Figure out a 15% tip by calculating 10% and adding half again (because 10% plus 5% equals 15%).
- Take a few measurements and find out exactly how much storage space that old armoire has.
- Calculate the exact miles per gallon your car got on that last trip to your sister’s house.
- Figure out what fraction of your monthly budget is taken up by housing expenses, food, utilities, or loan payments.
It also should go without saying that probably the best action you can take is to use the strategies in this book and do the practice problems correctly. While it is true that speed is important when taking the GRE, so is accuracy. You will get faster at employing the techniques we outline here the more familiar you become with them. But you will become faster and more accurate only if you employ the techniques with precision. So, do not feel rushed to work through a
