CHAPTER 16 / PRACTICE TEST 2 691

17.D a+b=s
a−b=t
Add straight down: 2 a =s+t

Divide by 2:

a+b=s

a−b=t

Subtract straight down: 2 b=s−t

Divide by 2:

Find the

product:

(Chapter 8, Lesson 2: Systems)

18.C y=m^4 =n^3
The answer is in terms of yalone, so find mand nin
terms of y: y=m^4
Take the 4th root: y1/4=m
y=n^3
Take the cube root: y1/3=n
Find the product mn: mn=(y1/4)(y1/3) =y1/3 +1/4
Add exponents: mn=y7/12
(Chapter 11, Lesson 6: Negative and Fractional
Exponents)

19.A This question deals with similar triangles:

Set up ratio:

Cross-multiply: 6x= 48
Divide by 6: x= 8

Area of big triangle =^1 ⁄ 2 (base)(height) =^1 ⁄ 2 (12)(6) = 36
Area of small triangle =^1 ⁄ 2 (base)(height) =^1 ⁄ 2 (8)(4) = 16
Shaded area =area of big triangle −area of small
triangle = 36 − 16 = 20
(Chapter 10, Lesson 6: Similar Figures)
(Chapter 10, Lesson 5: Areas and Perimeters)

20.A Set up a Venn diagram to visualize the
information.

6

12

4

=

x

()()=ab

⎛st st+ s t

⎝⎜

⎞

⎠⎟

⎛ −

⎝⎜

⎞

⎠⎟

=

⎛ −

⎝⎜

⎞

(^224) ⎠⎟
22
b
st

−

2

a

st

=

+

2

Notice that^1 ⁄ 3 the number of sedans must equal^1 ⁄ 5 the

number of convertibles. Say the number of convert-

ible sedans is x.If this is^1 ⁄ 3 the number of sedans, then

there must be 3xsedans in total, and 3x−x= 2 xof

these are notconvertibles. Similarly, if xis^1 ⁄ 5 the num-

ber of convertibles, then there must be 5xconvertibles

altogether, and 5x−x= 4 xof these are notsedans. So

now your diagram can look like this:

So there must be a total of 2x+x+ 4 x= 7 xcars at the

dealership. The only choice that is a multiple of 7 is

(A): 28.

(Chapter 9, Lesson 5: Counting Problems)

Section 4

1.E

Perimeter of a square = 4 s

36 = 4 s

Divide by 4: 9 =s

Area of a square =(s)^2

Area =(9)^2 = 81

(Chapter 10, Lesson 5: Areas and Perimeters)

2.C

Cross-multiply: b= 10 a

Try positive integer values of ato see how many work:

a 123456789

b 10 20 30 40 50 60 70 80 90

There are nine integer pairs that satisfy the equation.

(Chapter 9, Lesson 3: Numerical Reasoning Problems)

3.E The ten bathrooms cost $20 each to clean:

Total cost =$20 × 10 =$200

To clean each bathroom twice would cost:

$200 × 2 =$400

There are 30 offices, and they cost $15 each to clean:

Total cost =$15 × 30 =$450

To clean each office once and each bathroom twice

will cost: $400 +$450 =$850

(Chapter 11, Lesson 5: Data Analysis)

a

b

=

1

10

both

2

3

s

1

3

s

1

5

c

4

5

c

sedans convertibles

x

sedans convertibles

both

2 x 4 x

s s

s

s

6

12

4

x