Sat math Essentials

e
cannot be true. Cross out answer
choice 
e
!
After evaluating the five answer choices, we are
left with answer choices 
b
and 
d
as the possible correct
answer choices. Let’s decide which one is better. Answer
choice 
b
is only possibly true. We know that 
all integers
in set
A
are odd,
which means that the set contains only
odd integers. It could describe a set that contains 
all the
odd integers,
but it could also describe a set that contains
only one odd integer. Answer choice 
d
, on the other
hand, is always true. If
all integers in set
A
are odd,
then
–
T E C H N I Q U E S A N D S T R AT E G I E S
–
3 0

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no matter how many integers are in the set, none of
them are even. So the statement 
If an integer is even, it
is not in set
A must be true. It is the better answer
choice. Answer choice 
d
is correct!
G u e s s i n g o n F i v e - C h o i c e
Q u e s t i o n s : T h e L o n g Ve r s i o n
Because five-choice questions provide you with the
correct answer as one of their five answer choices, it’s
possible for you to guess the correct answer even if you
don’t read the question. You might just get lucky and
pick the correct answer.
So should you guess on the SAT if you don’t know
the answer? Well, it depends. You may have heard that
there’s a “carelessness penalty” on the SAT. What this
means is that careless or random guessing can lower
your score. But that doesn’t mean you shouldn’t guess,
because smart guessing can actually work to your
advantage and help you earn more points on the exam.
Here’s how smart guessing works:
■
On the math questions, you get one point for
each correct answer. For each question you
answer incorrectly, one-fourth of a point is sub-
tracted from your score. If you leave a question
blank you are neither rewarded nor penalized.
■
On the SAT, all multiple-choice questions have
five answer choices. If you guess blindly from
among those five choices, you have a one-in-five
chance of guessing correctly. That means four
times out of five you will probably guess incor-
rectly. In other words, if there are five questions
that you have no clue how to answer, you will
probably guess correctly on only one of them and
receive one point. You will guess incorrectly on
four of them and receive four deductions of one-
fourth point each. 1 – 
1
4
– 
1
4
– 
1
4
– 
1
4
0, so if you
guess blindly, you will probably neither gain nor
lose points in the process.
Why is this important? Well, it means that if you
can rule out even one incorrect answer choice on each
of the five questions, your odds of guessing correctly
improve greatly. So you will receive more points than
you will lose by guessing.
In fact, on many SAT questions, it’s relatively easy
to rule out all but two possible answers. That means you
have a 50% chance of being right and receiving one
whole point. Of course, you also have a 50% chance of
being wrong, but if you choose the wrong answer, you
lose only one-fourth point. So for every two questions
where you can eliminate all but two answer choices,
chances are that you will gain 1 point and lose 
1
4
point,
for a gain of
3
4
points. Therefore, it’s to your advantage
to guess in these situations!
It’s also to your advantage to guess on questions
where you can eliminate only one answer choice. If
you eliminate one answer choice, you will guess from
four choices, so your chances of guessing correctly are
25%. This means that for every four questions where
you can eliminate an answer choice, chances are that
you will gain 1 point on one of the questions and lose
1
4
point on the other three questions, for a total gain of
1
4
point. This may not seem like much, but a 
1
4
point is
better than 0 points, which is what you would get if you
didn’t guess at all.