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Elementary Functions
EXAMPLE:
If f(x) = 2x + 1 and g(x) = 3x – 2, for what real number k does f(k) = g(k)?
(A) –3
(B) –1
(C) 0
(D) 3
(E) 5
Solution: f(k) = g(k) when 2x + 1 = 3x – 2:
2x + 1 = 3x – 2
–x = –3
x = 3
So the correct answer is (D).
Miscellaneous
EXAMPLE:
All P are M.
No M are S.
Which of the following conclusions can be logically deduced from the statements above?
(A) No S are P.
(B) No M are P.
(C) Some S are P.
(D) Some P are S.
(E) some P are not M.
Solution: A diagram might be useful here. The first statement can be rendered as:
The P–circle contains all things that are Ps, and the M–circle contains all things that are M. Notice that the
P–circle is entirely contained within the M–circle. Now we add the second statement:

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Lesson 8
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w w w . p e t e r s o n s . c o m / a r c o
ARCO
■ SAT II Subject Tests
Notice that there is no overlap between the S–circle and the M–circle. The diagram also shows no overlap
between the P–circle and the S–circle. Thus, answer (A) is deducible.
Unusual Question Structures
Most of the questions that make up the Mathematics Tests have forms similar to those shown above.
There are, however, two special cases. First, some question stems contain “reversers.” A reverser is a word
such as “not” or “except” that turns the question inside–out. For example: