Sat math Essentials

28.
1
1
1
Seven cards are removed from the deck of
40, leaving 33 cards. There are three cards
remaining that are both a multiple of 4 and
a factor of 40: 4, 20, and 40. The probability
of selecting one of those cards is 
3
3
3
or 
1
1
1
.
29.
4
We are seeking 
D
number of feet away
from the microwave where the amount of
radiation is 
1
1
6
the initial amount. We are
given: radiation varies inversely as the square
of the distance or:
R
1 
D
2
. When 
D
1,
R
1, so we are looking for 
D
when 
R
1
1
6
.
Substituting:
1
1
6
1 
D
2
. Cross multiplying:
(1)(
D
2
) 
(1)(16). Simplifying:
D
2
16, or
D
4 feet.
30.
4
The factors of a number that is whole and
prime are 1 and itself. For this we are given 
x
and 
y
,
x
> 
y
> 1 and 
x
and 
y
are both prime.
Therefore, the factors of
x
are 1 and 
x
, and the
factors of
y
are 1 and 
y
. The factors of the
product 
xy
are 1,
x
,
y
, and 
xy
. For a given 
x
and 
y
under these conditions, there are four
factors for 
xy
, the product of the girls’ favorite
numbers.
–
M AT H P R E T E S T
–
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A l l Te s t s A r e N o t A l i k e
The SAT is not like the tests you are used to taking in school. It may test the same skills and concepts that your
teachers have tested you on, but it tests them in different ways. Therefore, you need to know how to approach the
questions on the SAT so that they don’t surprise you with their tricks.
C H A P T E R
Techniques and
Strategies
The next four chapters will help you review all the mathematics you
need to know for the SAT. However, before you jump ahead, make sure
you first read and understand this chapter thoroughly. It includes tech-
niques and strategies that you can apply to all SAT math questions.
4
2 7

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T h e Tr u t h a b o u t M u l t i p l e -
C h o i c e Q u e s t i o n s
Many students think multiple-choice questions are
easier than other types of questions because, unlike
other types of questions, they provide you with the
correct answer. You just need to figure out which of the
provided answer choices is the correct one. Seems sim-
ple, right? Not necessarily.
There are two types of multiple-choice questions.
The first is the easy one. It asks a question and provides
several answer choices. One of the answer choices is
correct and the rest are obviously wrong. Here is an
example:
Who was the fourteenth president of the United
States? 
a.
Walt Disney
b.
Tom Cruise
c.
Oprah Winfrey
d.
Franklin Pierce
e.
Homer Simpson
Even if you don’t know who was the fourteenth
president, you can still answer the question correctly
because the wrong answers are obviously wrong. Walt
Disney founded the Walt Disney Company, Tom Cruise
is an actor, Oprah Winfrey is a talk show host, and
Homer Simpson is a cartoon character. Answer choice
c
, Franklin Pierce, is therefore correct.
Unfortunately, the SAT does not include this type
of multiple-choice question. Instead, the SAT includes
the other type of multiple-choice question. SAT ques-
tions include one or more answer choices that 
seem
correct
but are actually 
incorrect
. The test writers include
these seemingly correct answer choices to try to trick
you into picking the wrong answer.
Let’s look at how an SAT writer might write a
question about the fourteenth president of the United
States:
Who was the fourteenth president of the United
States?