


General Math Strategies
In this section we provide some general strategies to get you thinking in
the right direction regarding GRE math. Here’s a preview:
 Change Your Math Mindset
 Use Scratch Paper
 Avoid Careless Mistakes
Change Your Math Mindset
Earlier we told you the good news that the GRE tests only basic math
from junior high or early high school. However, since the concepts tested
are basic and predictable, those wily test makers have to resort to certain
tricks and traps to throw you off; otherwise, most test takers would ace the
section. This fact has one very important ramification:
You need to change the way you’ve typically approached math
questions in the past.
Think about the typical math tests you took in high school. Many were
accompanied by three dreaded and imposing words: SHOW YOUR WORK. This
mandate implies a slogging mentality: You’re taught to do a problem a
certain way, and then required to spit back that exact method to get full
credit.
GRE math, however, rewards cleverness to combat the traps the test
makers set. It doesn’t matter whether you answer the question using a
traditional or untraditional method. It doesn’t matter if you use algebra or
don’t use algebra, draw a diagram or don’t draw a diagram, or simply get
into the ballpark through approximation instead of calculating an answer
precisely. All that matters is whether you answer the question correctly.
Three elements of your new math mindset will be looking for shortcuts,
approximating when possible, and keeping your eyes open for “common trap”
and “leftfield” answer choices. Let’s have a look at each one.
Shortcuts
As discussed above, your high school math experience may have
instilled in you an instinct to jump into math problems with your
sleeves rolled up, ready to slog away. And yes, sometimes that is the
only way, or at least the only way you can see at the moment. Unless you
perform math calculations lightning fast, however, you’ll probably need
to sneak your way around at least some GRE Math problems to get to all
28 questions; that’s simply how the section is constructed. If you find
yourself up against a real monster calculation that you think you need
to work through to get the right answer, think again: Chances are the
question is testing your math reasoning skills—that is, your ability to
spot a more elegant solution that doesn’t require
hacking through the math. Consider, for example, the following problem:
If x = 33.87, what is the value of ?
Is it really likely that they expect you to plug
such an unwieldy number such as 33.87 in for all those
x’s in the equation, especially given the fact that
calculators aren’t allowed on the test? No, of course not, although
that’s exactly what some people will attempt. Not you. Once you change
your math mindset, you’d know instinctively that there must be some sort
of shortcut here, and indeed there is.
If you multiply out the (x + 1) and (3x
+ 15) in the top part of the fraction (the “numerator”), you
get 3x2 + 18x + 15, which cancels out
the entire bottom part (the “denominator”), leaving the simplified value
of the equation at (x – 2). Alternatively, you may have
factored the bottom into (3x + 15)(x +
1) and then canceled out those terms from the numerator, again reducing
the entire fraction to (x – 2). No matter which
shortcut you employ, all that’s left is to substitute the given value
for x into (x – 2) to get 33.87
– 2 = 31.87, and you’re done.
FOIL, factoring quadratic equations, and canceling are the
concepts in play here, and if you need to brush up on them, don’t
worry—we’ll get to these and plenty more bits of math minutiae soon
enough in the following chapter. The point is simply to understand that
many GRE math questions are written with shortcuts in mind, so begin
right now to look for shortcuts as part of your new GRE math
mindset.
Approximating (When Possible)
Another habit that may be ingrained in you from your math
background is to “get the right answer.” Well duh, you
may be saying; this is math, after all, so naturally
you’ll want to solve the problems. Well, yes and no:
yes in Problem Solving and Data Interpretation, but
no in Quantitative Comparison questions where your
job is not necessarily to solve the problems but rather to learn enough
about quantities A and B to compare them. So especially in QCs—but also
in the other question types—approximating values may save time. (Some DI
questions even ask flat out for an approximate answer.)
Let’s see how we might use approximation on a sample QC question:

There’s no doubt that some test takers with an oldfashioned high
school math mentality would wear down their pencils grinding out
calculations to precisely determine the value of each quantity. Then
they could say with complete confidence which column is greater, or if
they’re the same. (Note that with only numbers and no variables in the
question, the answer cannot be D. More on that in chapter
4.) Will this method get the right answer? Maybe, if they don’t botch
the math—a notsounlikely prospect when dealing with awkward numbers
like these. Even if this method does yield the right
answer, it may take a good chunk of time.
Approximating is the way to go. Observe: 48% is pretty close to
50%, or onehalf, so let’s work with that figure instead. Half of 54 is
27, so a little less than half of 54 (remember, the
real figure is 48%, not the full 50%) must be a little less than
27, which is a fine approximation for Column A. Similarly,
11% is awfully close to 10%, an extremely manageable percentage. To take
10% of anything, we simply move the decimal point one place to the left.
The value in Column B is therefore a little more than 27.3, since 11% of
a number is larger than 10% of that same number. Since the quantity in
Column A is less than 27, and the quantity in Column B
is more than 27.3, Column B must be larger than Column
A, which means that choice B is correct.
It would actually take a quick test taker less time to approximate
the two values and settle on choice B than it took us to
explain the method above. And, needless to say, it would take way less
time (with less risk of careless mistakes, to boot) than it would take
to actually do the math.
Common Traps and LeftField Choices
One more element of your new math mindset concerns how you
interact with the answer choices. The test makers prefer that you don’t
stumble upon the right answer accidentally and therefore construct the
choices accordingly. Let’s first discuss “common trap” and “leftfield”
choices individually, and then we’ll get to some examples.
Common Traps.
Remember, the test makers often spice up what would otherwise be
basic problems. That means that you should assume that they go out of
their way to trap unwary test takers into selecting
appealing wrong answer choices, sometimes called
“distractors” since they’re meant to distract you from the correct
choice. What might make a wrong choice appealing? Three main things:
 It repeats a number used in the problem itself.
 It represents a number you derive along the way to the right answer choice.
 It represents the answer that results from a common misunderstanding of the problem.
You’ll see examples in just a bit, but first let’s discuss another
kind of answer choice you should keep on your radar.
LeftField Choices.
“Leftfield” choices are just what they sound like—choices from
way out in left field that simply make no sense in the context of the
question. Say you get a complicated rate/time/distance problem in which
you’re given a whole bunch of information and need to calculate how long
it would take someone to drive from New York to Chicago. (Don’t
worry—we’ll cover this kind of problem in chapter 2 along with every
other essential math concept you need to know.) Say you forgot to divide
by 100 at some point along the way and ended up with an answer of 1,500
hours. It seems ludicrous, but some people take the test with blinders
on, and if they get 1,500, they get 1,500—period. So if that answer
appeared among the choices, they’d choose it. This despite the fact that
traveling even at a reasonably slow rate of 40 miles per hour,
one could drive from New York to California twenty times in
1,500 hours. The answer just doesn’t make sense in the
context of the question—it comes from left field. The test makers
include some leftfield choices to remind you that it’s not just a math
test; it’s also a reasoning test, which means you can
and should quickly eliminate choices that defy common sense.
Let’s now take a look at some traps and leftfield choices in
action. See what you can make of the following question:

If you understand the formula for compound interest and can get
the answer that way, that’s fine, although in this case we can eliminate
choices to get there faster. Choice A repeats a number from
the question, which makes it suspicious to begin with. Moreover, it
contains shades of “left field” since it defies common sense. Does it
sound reasonable that a bank account that receives interest will have
the same amount it started with after two years, given that no
deductions are made from it? No—it has to have more, so choice
A bites the dust on this count as well. And speaking of
leftfield choices, we may as well cut E too: Does it seem
logical that an account would more than double in two
years at an interest rate of 10%? Any experience with an
interestbearing account should suggest that $21,000 is way out of the
ballpark here, leaving only B, C, and
D as contenders.
Ten percent of $10,000 is $1,000. If the problem were based on
simple interest—which no doubt the test makers are hoping some people
will think—then $11,000 would be in the account after one year, and
$12,000 after two years. But neither of these takes into consideration
that the interest is compounded quarterly. B and C are
therefore traps, both written to tempt anyone who falls for this common
misunderstanding. C, $12,000, is what results if you
calculated simple instead of compound interest, while B,
$11,000, represents a number on the way to that wrong answer. The
correct answer is D, which is what we’d get if we plugged
the numbers into the complicated equation for compound interest. In this
case, we didn’t have to.
Intelligent Guessing
Your familiarity with distractors will help lead you to some
quick and easy points, but that’s not the only use of this
knowledge. Some questions are just downright tough, especially if
you’re doing well and land yourself in the deep end of the question
pool. Since in the computeradaptive format you can’t move on to the
next question until you answer the one in front of can never leave
an answer blank. If you get stuck, you still have to pull the
trigger on some choice or another. In those cases, eliminating even
a few common traps or leftfield choices will put the odds in your
favor and allow you to guess intelligently.
Use Scratch Paper
On test day, you’ll receive at least three pieces of blank 8½ × 11
paper. Use them! Don’t try to solve equations in your head—you get no extra
points, and the risk of error is high when you’re doing complex calculations
or working with complicated strings of numbers. Some people even find it
handy to jot down the letters A through E (or
A through D for QC questions) on their scratch
paper for each new question they face, allowing them to cross off choices
they eliminate so they don’t get confused with which ones they chopped and
which ones are still in contention. Try out this strategy to see whether it
works for you.
If you use up your batch of paper, ask for more during the break
between sections. The test center’s proctor will give you more, in batches
of three sheets at a time. You’ll have to hand in your used scratch paper to
the test proctor to get more, and you won’t be able to take the scratch
paper with you when you leave the testing center.
Avoid Careless Mistakes
The bane of test takers at all levels is selecting the wrong answer to
a question they know how to solve. Such mistakes are understandable,
considering the pressure of the test and the timing restrictions which often
force people to work faster than they’d like. But it doesn’t have to be this
way. To avoid careless mistakes, follow these tips:
 Slow down. Although rushing may allow you to answer more questions, a multitude of wrong answers, especially in the beginning of the test, could send your score plummeting. Think through the questions before jumping in to solve them. Taking the necessary time to select the proper approach will help you get off on the right foot before investing tons of time in a fruitless direction.
 Read the question carefully. The test makers have a knack for asking strange or unexpected questions, the kind not usually asked in math class. Make sure that you answer the question asked rather than the question you think they might ask. If you have time, reread the question one last time before making your final selection to make sure you’re giving them what they want. For example, if they give you a question about boys and girls and ask for the number of boys, make sure you don’t accidentally go with the number of girls or the total number of boys and girls, things you very well may determine along the way. As we noted earlier, the test makers like to scatter such traps among the choices to catch the careless. Also pay attention to the units given in the problems: If they give you information in terms of minutes but ask for the answer in hours, you better take notice. In addition, if the test makers want you to round an answer, they’ll instruct you to do so, and when they’re looking for an approximate value (as is sometimes the case in DI questions), they’ll tell you that too. Listen for exactly what they want, and then give it to them.
 Study your practice sets. Don’t gloss over careless errors in your practice problems. Study them! It’s one thing to simply not know how to do a problem, and quite another to think you aced it only to find out otherwise. Figure out where you went wrong. Were you rushing? Did you mix up numbers or fall for a common trap? Perhaps you did all the right math but then selected something other than what they asked for? Determine where your mistake lies and figure out what you need to do to avoid making that same mistake again.
We’ve provided in this chapter an introduction to the GRE Math section
and some general pointers to get you on your way. Now it’s time for the
specifics. By the end of the next four chapters, you’ll have not only a
solid grasp of the math concepts tested on the GRE but also effective
techniques for applying those concepts to all three question types you’ll
face. First up, as promised, is a heaping helping of Math 101. Ready? Then
let’s get to it.
