An arco book arco is a registered trademark of Thomson Learning, Inc., and is used herein under license by Peterson’s. About The Thomson Corporation and Peterson’s

Mathematics Level IC/IIC Subject Tests
217
ARCO
■ SAT II Subject Tests
w w w . p e t e r s o n s . c o m / a r c o
The formula for finding the area of a triangle is 
1
2
× altitude × base. So the areas of the triangles are:
Therefore, the ratio is:
Area 
Area 
∆
∆
BEF
BEG
BG y
BG x
y
y
x
y
=
( )( )
( )
+
( )
=
+
1
2
1
2
And that is the ratio of the areas of the two larger triangles as well.
35. The correct answer is (D). One way to attack this item is to do the indicated operations:
So:
Cross multiply:
c(b + a) = ab
And divide by (b + a)
Alternatively, you could assign some values to a and b. Let a = 1 and b = 2:
That means:
And

---

Lesson 8
218
w w w . p e t e r s o n s . c o m / a r c o
ARCO
■ SAT II Subject Tests
Now substitute the values a = 1 and b = 2 into the choices until you find the one that produces 2/3:
(A)
 
Wrong!
(B)
(1)(2) = 2
Wrong!
(C)
Wrong!
(D)
Right!
(E)
Wrong!
36. The correct answer is (D). This question tests your understanding of the properties of numbers.
First, since the entire expression is less than zero, we know that none of the variables is 0. (Otherwise,
the expression would be equal to and not less than 0.) In addition, we know that y
2
must be positive.
And this means that either x or z—but not both—must be negative! This is what (D) means.
Alternatively, you could assign sets of numbers to x, y, and z, until you manage to eliminate all but one choice.