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18. The correct answer is (C). The problems on this test are arranged in ascending order of difficulty.
Often, what makes a problem more difficult than another problem is that the insight required to solve
the more difficult problem is more subtle. We know from the fact that this problem is situated more
than one third of the way through the test that it is not a give–away. Therefore, you should not make
the mistake of reasoning “3 plus 4 plus 5 is equal to 12, therefore the answer is (B).” If the problem
were that obvious, it would be one of the first few, not number 18. The correct answer is (C). Since the
sum of the lengths of the other three sides is 12, the longest side of integral length that could be used
to close the figure is 11.
19. The correct answer is (A). Let y represent the degree measure of angle BAD. Since ABC is isosce-
les, y = 45. And since the sum of the degree measures of the interior angles of a triangle is 180:
90 + 45 + 20 + x = 180
155 + x = 180
x = 25
20. The correct answer is (E). You can solve this problem by applying the rules for manipulating expo-
nents. When dividing terms of the same base, you subtract exponents. Therefore, the x term is x to the
3 – 2 = 1 power. The y term is y to the 2 – 3 = –1 power, which is 
1
y
. And similarly, the z term is z to
the 1 – 2 = –1 power, which is 
1
z
. Since 
2
8
is 
1
4
, the final result is 
.
Alternatively, you could assume some values for the variables. Use those values to evaluate the
complex expression and derive a value. Then, using the same values, evaluate each answer choice
until you find one that generates the same value. You can make it easy on yourself by assuming small
values that are easy to work with, such as 1. But watch out! Since 1 
× 1 = 1 ÷ 1, you may find that
more than one answer choice seems to be correct. (If you use 1 for x, y, and z, in this problem, you will

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Lesson 8
212
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ARCO
■ SAT II Subject Tests
find that the complex expression has the value 
1
4
but that (C), (D), and (E) all equal 1/4 as well.) If
this happens, or if you anticipate this may happen, use other numbers. Assume, for example, x = 1,
y = 2, and z = 3. The complex expression has the value:
(Don’t do the multiplication. Simplify by cancellation.) Now use the same values in the answer choices:
(A)
4(1)(2)(3) = 24
Wrong!
(B)
Wrong!
(C)
Wrong!
(D)
Wrong!
(E)
Correct!
Yes, substituting numbers is likely to take longer here than using the rules of exponents, but at least
you have an alternative available if you can’t remember what to do.