Lesson 8
220
w w w . p e t e r s o n s . c o m / a r c o
ARCO
■
SAT II Subject Tests
41. The correct answer is (E). A good way to attack this problem is to use Venn or circle diagrams. The
first statement can be represented as follows:
The S circle contains all items that are S’s, and the M circle all those that are M’s. Notice that the S circle
is entirely contained within the M circle. The second statement can be added to the diagram as follows:
The fact that there is no overlap between the P and M circles shows that “No P are M.”
Now we examine
the answer choices. The correct answer is
(E). There is no overlap between the P and S circles.
42. The correct answer is (C). One way of attacking this problem is to use letters. The
formula for
finding the volume of a cube is simply “edge cubed.” Therefore:
V =
e
3
And:
And a cube with an edge one–fourth of that has an edge of:
. And a volume of:
As an alternative strategy, you could assume some numbers. Assume that
the larger cube has an edge
of 4. (Why 4? Because that means the smaller cube has an edge of 1!) The larger cube has a volume
of 4
× 4 × 4 = 64, and the smaller cube a volume of 1 × 1 × 1 = 1. Now, just substitute 64 for
V into the
answer choices, and the one that generates the value 1 is the correct choice.
43. The correct answer is (E). A sketch will make it easier to keep track of the relationships:
Mathematics Level IC/IIC Subject Tests
221
ARCO
■
SAT II Subject Tests
w w w . p e t e r s o n s . c o m / a r c o
Notice
that I have placed side b in relation to
θ to reflect the cosine relation specified in the problem.
I have also
designated the third side as a. The sin
θ, therefore,
is equal to a/c. And we can use the
relationships between the sides
of the right triangle to find a in terms of
b and
c:
a
2
+
b
2
=
c
2
And:
a
2
=
c
2
–
b
2
Therefore:
Substituting this for
a:
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