|
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
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 “left-field”
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:
| Column A |
Column B |
| 48% of 54 |
11% of 273 |
(A) The quantity in Column A is greater.
(B) The quantity in Column B is greater.
(C) The two quantities are equal.
(D) The relationship cannot be determined from the information
given.
There’s no doubt that some test takers with an old-fashioned
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 not-so-unlikely 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 one-half, 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
Left-Field 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 “left-field”
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.
Left-Field Choices.
“Left-field” 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 left-field 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 left-field
choices in action. See what you can make of the following
question:
Simone invests $10,000 in a bank account that pays 10%
interest annually. If the interest is compounded quarterly,
how much money will be in the account after two years assuming
that no money is deducted from the account and no money
other than interest and the initial investment is added
to the account?
(A) $10,000.00
(B) $11,000.00
(C) $12,000.00
(D) $12,184.03
(E) $21,435.89
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 left-field 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 interest-bearing 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 computer-adaptive
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 left-field 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.
|
