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EXAMPLE:
If k is a negative integer, then all of the following must be positive integers EXCEPT
(A) –k
(B)
(C) k
2
(D) (–k)
2
(E) –k
2
Solution: Notice the presence of the word “EXCEPT.” It tells us that four of the five expressions must be
positive and that one is negative. We are looking for the EXCEPTION. The correct answer is (E). Since k
is negative, k
2
is positive. Thus, –k
2
must be negative.
When addressing a problem, be sure that you read the question stem carefully. If the question stem
contains a reverser, you may want to circle that word so that you make sure you answer the question asked.
Another special form uses combinations of Roman–numeraled statements to form answer choices:
EXAMPLE:
If x is an odd integer, which of the following must be even?
I.
2x
II.
x + 3
III.
x
2
(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) I, II, and III

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Mathematics Level IC/IIC Subject Tests
195
ARCO
■ SAT II Subject Tests
w w w . p e t e r s o n s . c o m / a r c o
Solution: x is odd, but 2x must be even; and statement I must be part of the correct answer choice. On this
ground, you can eliminate (B)—it does not include statement I. Next, since an odd number plus an odd
number yields an even number, II must be part of the correct choice. And this allows us to eliminate (A)
and (D). The only remaining choices are (C) and (E), and we examine statement III. Since an odd number
multiplied by an odd number yields an odd number, x
2
must be odd. Therefore, statement III should not be