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Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Add or subtract.
1)
m - 2
m2- 9m + 20 +2m + 5
m2- 2m - 8
1)
A)
3m + 3
B)
3m + 3
2m2- 11m + 12
C)
3m2- 5m - 29
(m - 4)(m - 5)(m + 2)
D)
3m2- 5m - 29
(m + 4)(m + 5)(m - 2)
2)
8y2+ 20y + 7
9y2-4-5y2- 5
9y2-4
2)
A)
8y + 1
3y +2
B)
3y -2
3y +2
C)
y + 6
3y -2
D)
3y +2
3y -2
Determine the value or values of the variable where the expression is defined.
3)
8
x - 7
3)
A)
all real numbers except x = -7
B)
all real numbers except x =7
C)
all real numbers except x = 0
D)
all real numbers
Add or subtract.
4)
10
8x2-4
8x2
4)
A)
4
3x2
B)
3
C)
3
8x4
D)
3
4x2
Find the least common denominator for the expression.
5)
5
x2+ 10x + 24 -9
x2+ 9x + 20
5)
A)
(x - 6)(x - 4)(x + 5)
B)
(x + 6)(x + 4)
C)
(x + 4)(x + 5)
D)
(x + 6)(x + 4)(x + 5)
Add or subtract.
6)
4x +10
(x +5)(x -6) -3x +5
(x +5)(x -6)
6)
A)
x +15
(x +5)(x -6)
B)
x +5
(x +5)(x -6)
C)
1
x +5
D)
1
x -6
Multiply.
7)
2x2
5·15
x3
7)
A)
6
x
B)
6x2
x3
C)
x
6
D)
30x2
5x3
Add or subtract.
8)
7x + 1
7x - 8 +x + 8
7x - 8
8)
A)
8x + 9
7x - 8
B)
8x - 7
7x - 8
C)
6x - 7
7x - 8
D)
6x + 9
7x - 8
9)
6x - 8
x - 7 -2x + 1
x - 7
9)
A)
4x + 9
x - 7
B)
4x - 9
x - 7
C)
4x - 7
x - 7
D)
4x + 7
x - 7
Solve the equation and check your solution.
10)
9x +1
x +9=1
9
10)
A)
x =- 1
9
B)
x =-9
C)
x = 0
D)
No solution
Find the least common denominator for the expression.
11)
12x +3
9x -13 -20x
9x +13
11)
A)
(9x -13) or (9x +13)
B)
(9x -13)(9x +13)
C)
20x(12x +3)
D)
20x(12x +3)(9x -13)(9x +13)
3
Solve the equation and check your solution.
12)
x +10
x -7=x +8
x -7
12)
A)
x =- 49
2
B)
x =- 62
5
C)
x =7
D)
x =14
11
Add or subtract.
13)
5
8x2+5
8x2
13)
A)
5
B)
5
2x4
C)
4
5x2
D)
5
4x2
Solve the problem.
14)
If the resistance in an electrical circuit is held constant, the amount of current flowing through the
circuit is directly proportional to the amount of voltage applied to the circuit. When 10 volts are
applied to a circuit, 250 milliamperes (mA) of current flow through the circuit. Find the new
current if the voltage is increased to 14 volts.
14)
A)
375 mA
B)
140 mA
C)
336 mA
D)
350 mA
Solve the equation and check your solution.
15)
2
y + 2 -8
y - 2 =10
y2- 4
15)
A)
y =-5
B)
y =10
C)
y =5
D)
y =30
Simplify.
16)
24x2+18x
24x
16)
A)
4x -3
4
B)
x2+18
C)
x2+3
D)
4x +3
4
Divide.
17)
p2-5p + pq -5q
9p2-9q2÷p -5
10p -10q
17)
A)
1
B)
(p -5)2
90(p - q)2
C)
10
9
D)
10(p2-5p + pq -5q)
9(p + q)(p -5)
Solve the problem and answer the question.
18)
A barge takes 4 hours to move (at a constant rate) downstream for 40 miles, helped by a current of
3 miles per hour. If the barge's engines are set at the same pace, find the time of its return trip
against the current.
18)
A)
10 hr
B)
4 hr
C)
7 hr
D)
80 hr
Simplify.
19)
2x -4
x2-4
19)
A)
-2
x +2
B)
2
x +2
C)
2
x -2
D)
-2
x -4
20)
x2-4x +4
x2-4
20)
A)
x -2
x +2
B)
4x
C)
x -2
x -2
D)
x +2
x +2
Add or subtract.
21)
13
q - 2 -4
q - 2
21)
A)
17
q - 2
B)
9
q - 2
C)
13(q - 2)
4(q - 2)
D)
9
q
Solve the equation and check your solution.
22)
x
10 +13
10 =x
9-13
2
22)
A)
x =767
B)
x =116
C)
x =702
D)
x =246
Simplify.
23)
24t -4t2
t3-11t2+30t
23)
A)
20
t3-41
B)
-4
t +5
C)
-4
t -5
D)
4
t -5
Find the least common denominator for the expression.
24)
2
7a2-7
a3
24)
A)
a3
B)
7a2
C)
14a3
D)
7a3
Solve the problem and answer the question.
25)
A grocery store has a display of cans in the shape of a trapezoid as shown. There are a total of 60
cans in the display. If the sum of the number of cans in the top row and the bottom row is 15
8 times
the number of cans in the height of the display, determine the total number of cans in the top and
bottom rows.
25)
A)
64 cans
B)
15 cans
C)
8 cans
D)
120 cans
Simplify.
26)
a2- ab +7a -7b
a +7
26)
A)
1
a +7
B)
a - 2b + 1
C)
a2- ab +7a -7b
a +7
D)
a - b
Solve the equation and check your solution.
27)
x
2x + 2 =-2x
4x + 4 +2x - 3
x + 1
27)
A)
x = -3
B)
x = - 12
5
C)
x =3
2
D)
x = 3
Find the least common denominator for the expression.
28)
7
x2+ 8x + 12 +8
3x + 18
28)
A)
3(x + 2)(x - 6)
B)
3(x + 2)(x + 6)
C)
3(x - 2)(x - 6)
D)
3(x - 2)(x + 6)
Add or subtract.
29)
x
x2+ 3x - 18 -3
x2+ 3x - 18
29)
A)
1
2(x +6)
B)
x +6
C)
x -3
D)
1
x +6
30)
x3-13x2+43x
x(x -4) -x2+3x
x(x -4)
30)
A)
x(x -10)
B)
x -4
C)
x2-14x +40
x -4
D)
x -10
Find the least common denominator for the expression.
31)
6
m2+ 3m+9
m2+ 5m + 6
31)
A)
m(m + 1)(m + 2)
B)
m(m + 3)(m + 2)
C)
m(m + 1)2
D)
(m + 1)2
Find the quantity indicated.
32)
y varies directly as the square of z. If y =72 when z =3, find y when z =5.
32)
A)
120
B)
200
C)
24
D)
15
Solve the problem and answer the question.
33)
A baker can decorate the day's cookie supply four times as fast as his new assistant. If they decorate
all the cookies working together in 12 minutes, how long would it take for each of them to decorate
the cookies working individually?
33)
A)
baker: 60 min
assistant: 240 min
B)
baker: 60 min
assistant: 15 min
C)
baker: 41
4 min
assistant: 17 min
D)
baker: 15 min
assistant: 60 min
Add or subtract.
34)
x
x + 5 +6x +6
5+ x
34)
A)
5x +6
x + 5
B)
x +6
x + 5
C)
7x +6
x + 5
D)
7x
x + 5
9
Simplify.
35)
y3-216
y -6
35)
A)
y3-216
y -6
B)
1
y -6
C)
y2+6y +36
D)
y2-36
Add or subtract.
36)
4
x2- 3x + 2 +5
x2- 1
36)
A)
9x - 6
(x - 1)(x - 2)
B)
6x - 9
(x - 1)(x + 1)(x - 2)
C)
9x - 6
(x - 1)(x + 1)(x - 2)
D)
40x - 6
(x - 1)(x + 1)(x - 2)
Answer true or false.
37)
-2a
9b = - 2a
9b = - -2a
-9b
37)
A)
True
B)
False
Solve the problem and answer the question.
38)
Jim can run 5 miles per hour on level ground on a still day. One windy day, he runs 11 miles with
the wind, and in the same amount of time runs 6 miles against the wind. What is the rate of the
wind?
38)
A)
21
2 mph
B)
18
17 mph
C)
5 mph
D)
17 mph
Simplify.
39)
3x + 3
15x2+ 21x + 6
39)
A)
3x + 5
5x + 21
B)
1
5x + 2
C)
3x + 3
15x2+ 21x + 6
D)
3x
5x + 2
Add or subtract.
40)
x - 6
x2+ 14x + 48 +3x + 1
x2+ 4x - 12
40)
A)
4x - 5
2x2+ 18x + 36
B)
4x - 5
C)
4x2+ 17x + 20
(x + 6)(x + 8)(x - 2)
D)
4x2+ 17x + 20
(x - 6)(x - 8)(x + 2)
41)
8
15a3b-7
18ab2
41)
A)
48b + 35a2
90a3b2
B)
48b - 35a2
90a3b2
C)
48b -7a2
90a3b2
D)
48b - 35a2
90a2b3
Divide.
42)
(y -6)2
7÷7y -42
49
42)
A)
1
y -6
B)
7(y -6)2
7y -42
C)
y -6
D)
(y -6)3
49
Determine if the relationship is direct or inverse variations.
43)
The number of minutes over the amount purchased for your cell phone plan and the amount of
your monthly bill.
43)
A)
Direct
B)
Inverse
Solve the problem.
44)
For a resistor in a direct current circuit that does not vary its resistance, the power that a resistor
must dissipate is directly proportional to the square of the voltage across the resistor. The resistor
must dissipate 1
16 watt of power when the voltage across the resistor is 13 volts. Find the power
that the resistor must dissipate when the voltage across it is 39 volts.
44)
A)
169
16 watts
B)
9
16 watt
C)
13
16 watt
D)
3
16 watt
Multiply.
45)
x2+ 10x + 24
x2+ 8x + 16 ·x2+ 10x + 24
x2+ 12x + 36
45)
A)
1
B)
x + 6
x + 4
C)
x + 4
x + 6
D)
1
x + 6
Simplify.
46)
1
x+ 1
1
x- 1
46)
A)
x
1 -x2
B)
1 + x
1 - x
C)
1
D)
1 -x2
47)
x-1
x2
x-1
x3
47)
A)
x
(x - 1)(x + 1)
B)
x(x2- x + 1)
(x + 1)(x2+ 1)
C)
1
x + 1
D)
x(x2+ x + 1)
(x + 1)(x2+ 1)
Solve the problem and answer the question.
48)
One conveyor belt can move 1000 boxes in 12 minutes. Another can move 1000 boxes in 11
minutes. If another conveyor belt is added and all three are used, the boxes are moved in 3
minutes. How long would it take the third conveyor belt alone to do the same job?
48)
A)
67
132 min
B)
165
67 min
C)
62
7 min
D)
7
44 min
49)
BJ can overhaul a boat's diesel inboard engine in 20 hours. His apprentice takes 60 hours to do the
same job. How long would it take them working together assuming no gain or loss in efficiency?
49)
A)
12 hr
B)
6 hr
C)
15 hr
D)
80 hr
Solve the equation and check your solution.
50)
x
18 + 1
9=x + 8
9
50)
A)
x =-7
B)
x =-15
C)
x =-6
D)
x =-14
51)
3-9
x=7
5
51)
A)
x =- 45
4
B)
x =5
8
C)
x =9
8
D)
x =45
8
Simplify.
52)
1
x+ 1
1
x- 1
52)
A)
x
1 -x2
B)
1
C)
1 -x2
D)
1 + x
1 - x
53)
3x2+9x3
11x +33x2
53)
A)
3+9x3
11x +33
B)
3x
11
C)
3x2+9x3
11x +33x2
D)
3
11
Solve the equation and check your solution.
54)
1 +1
x=72
x2
54)
A)
x =-9, x =8
B)
x =9, x =-8
C)
x =9, x =8
D)
x = - 1
9, x =1
8
14
Simplify.
55)
20x4y
5x6y
55)
A)
4
x10
B)
4
x2
C)
4x2
D)
5
Add or subtract.
56)
6
x7- 9x
56)
A)
6- 9x
x7
B)
9x8- 6
x7
C)
6- 9x6
x7
D)
6- 9x8
x7
Simplify.
57)
3x2- 27
18 - 6x
57)
A)
-x + 3
2
B)
-2(x + 3)
C)
x + 3
2
D)
x2- 9
3 - x
Find the least common denominator for the expression.
58)
3x
x -6+7x
6- x
58)
A)
21x
B)
(x -6)(6- x)
C)
-1
D)
x -6 or 6- x
Solve the equation and check your solution.
59)
3x
5- 9 = x
59)
A)
x = - 45
2
B)
x =5
3
C)
x =2
45
D)
x =- 6
5
Find the quantity indicated.
60)
x varies inversely as y. Find x when y =14 and k =7.
60)
A)
1
2
B)
2
C)
7
2
D)
1
14
61)
y varies directly as z. If y =247 when z =19, find y when z =18.
61)
A)
169
B)
361
C)
234
D)
324
Solve the problem.
62)
The receipts, r, at a concert are directly proportional to the number of people attending the concert,
c. If the receipts for a concert are $21,000 when 600 people attend, determine how many people
attend if the receipts for a concert are $51,000.
62)
A)
14.5714286 people
B)
1457.14286 people
C)
145.714286 people
D)
14,571.4286 people
Simplify.
63)
12k3
4k
63)
A)
3k
B)
3k2
C)
8k2
D)
8
Solve the equation and check your solution.
64)
x -2
x -17 =15
x -17
64)
A)
x =-17
B)
x =34
C)
x =17
D)
No solution
Solve the problem and answer the question.
65)
Glenn and Paula want to dig an irrigation channel for their garden. Together it takes them 1.5 hours
to dig an appropriately sized irrigation channel. If Paula can dig the channel by herself in 2.2 hours,
how long would it take Glenn to dig the channel by himself? (Round your answer to the nearest
tenth of an hour, if necessary.)
65)
A)
0.7 hr
B)
3.7 hr
C)
4.7 hr
D)
3.2 hr
Solve the equation and check your solution.
66)
3+4
x=5
66)
A)
x =1
B)
x =- 2
C)
x =- 1
2
D)
x =2
Add or subtract.
67)
4x +16
6x +24 -3(x +4)
6x +24
67)
A)
x
6x +24
B)
x
6
C)
x +28
6x +24
D)
1
6
68)
8y
x2-y2+8x
y2-x2
68)
A)
8
x - y
B)
y - x
x2 -y2
C)
-8
x + y
D)
8
x + y
69)
5x2-52x
4x2-36x+7x
4x2-36x
69)
A)
5x2-45x
4x2-36x
B)
x2-9x
x2-9x
C)
5
4
D)
5
4x
Solve the equation and check your solution.
70)
x - 4
8=x + 6
4
70)
A)
x =- 16
B)
x =1
2
C)
x =2
D)
x =4
Determine the value or values of the variable where the expression is defined.
71)
x - 3
x2+ 4
71)
A)
all real numbers except x =2, x=-2
B)
all real numbers
C)
all real numbers except x =4
D)
all real numbers except x =-2
Multiply.
72)
5p - 5
p·8p2
7p - 7
72)
A)
35p2+ 70p + 35
8p3
B)
40p
7
C)
40p3- 40p2
7p2- 7p
D)
7
40p
Simplify.
73)
1
3-1
8
1
5-1
6
73)
A)
25
4
B)
4
25
C)
- 5
4
D)
- 4
5
Answer true or false.
74)
-4
-9= - 4
-9= - -4
-9
74)
A)
True
B)
False
B)
Simplify.
75)
x
7
8
x + 8
75)
A)
x(x + 8)
56
B)
56x(x + 8)
C)
8x
7(x + 8)
D)
x + 8
56x
19
Find the least common denominator for the expression.
76)
4
7x +4-7
76)
A)
7x +4
B)
7x
C)
49x +28
D)
28
Solve the equation and check your solution.
77)
1
x + 9 =6
x + 18 --9
x2+ 27x +162
77)
A)
x =-18
B)
x =-9
C)
x =-9, -18
D)
No solution
78)
1
x +7+3
x +4=-3
x2+11x +28
78)
A)
x =4
B)
x = 0
C)
x = -7
D)
No solution
Find the least common denominator for the expression.
79)
8
8a + 64 -4
a2+ 8a
79)
A)
8a(a + 8)
B)
8a2+ 8
C)
8a + 8
D)
8a2+ 64
Simplify.
80)
m2- 25m
25 - m
80)
A)
-(m + 5)
B)
m + 5
C)
m
D)
-m
20
Solve the equation and check your solution.
81)
m -5
7-5m +3
5=4
5
81)
A)
x =- 37
15
B)
x =- 4
5
C)
x =- 16
15
D)
x =37
20
Divide.
82)
27x -27
5÷9x -9
55
82)
A)
11(27x -27)
9x -9
B)
243(x - 1)2
275
C)
33
D)
1
33
Find the least common denominator for the expression.
83)
1
r2+ 14r + 49 -1
r2+ 7r
83)
A)
r(r + 1)(r + 7)
B)
r(r + 7)
C)
r(r + 7)2
D)
(r + 7)2
Multiply.
84)
2z3
4·8
z2
84)
A)
4z
B)
4z2
z3
C)
z
4
D)
4
z
Simplify.
85)
8- m
m - 8
85)
A)
1
B)
-1
C)
0
D)
-m
Solve the equation and check your solution.
86)
12
n-3
6n =1
6
86)
A)
n =3
B)
n =23
24
C)
n =69
D)
n =4
Simplify.
87)
1
6+1
2
1
4+1
7
87)
A)
56
33
B)
7
3
C)
33
56
D)
3
7
Add or subtract.
88)
x
x + 3 +8
x + 3
88)
A)
8x
x2+ 6x +9
B)
8
3
C)
9x
x + 3
D)
x + 8
x + 3
Find the quantity indicated.
89)
x varies inversely as v. If x =48 when v =4, find x when v =24.
89)
A)
6
B)
8
C)
32
D)
16
Multiply.
90)
7y
14y +7·10y +5
2
90)
A)
5y
14
B)
y
2
C)
5
2
D)
5y
2
Find the least common denominator for the expression.
91)
7
t+2
t - 8
91)
A)
t - 8
B)
t
C)
14
D)
t(t - 8)
Add or subtract.
92)
3y2
y - 1 +-3y
y - 1
92)
A)
0
B)
3y(y + 1)
y - 1
C)
3y
y - 1
D)
3y
93)
3
y2- 3y + 2 +5
y2- 1
93)
A)
8y - 7
(y - 1)(y - 2)
B)
7y - 8
(y - 1)(y + 1)(y - 2)
C)
30y - 7
(y - 1)(y + 1)(y - 2)
D)
8y - 7
(y - 1)(y + 1)(y - 2)
94)
2x
x - 6 -x +5
x - 6
94)
A)
3x -5
x - 6
B)
x +5
x - 6
C)
3x +5
x - 6
D)
x -5
x - 6
Solve the equation and check your solution.
95)
2
t=t
5t - 12
95)
A)
t = 4, t = 6
B)
t = 0, t = 36
C)
t = 0
D)
t = 0, t =24
9
Simplify.
96)
6k - 30
20 - 4k
96)
A)
1
B)
3
2
C)
-3
2
D)
-1
Find the least common denominator for the expression.
97)
7
5ab +5
a2b2
97)
A)
35a2b2
B)
5ab
C)
5a2b2
D)
a2b2
Simplify.
98)
7
y
3
y + 8
98)
A)
7(y + 8)
3y
B)
y + 8
21y
C)
21y(y + 8)
D)
3y
7(y + 8)
Solve the problem and answer the question.
99)
One number is 4 times larger than another. The sum of their reciprocals is 5
8. Determine the two
numbers.
99)
A)
2 and 8
B)
2
3 and 8
3
C)
4 and 16
D)
8 and 32
Solve the problem.
100)
The amount of gas that a helicopter uses is directly proportional to the number of hours spent
flying. The helicopter flies for 4 hours and uses 44 gallons of fuel. Find the number of gallons of
fuel that the helicopter uses to fly for 5 hours.
100)
A)
60 gal
B)
20 gal
C)
55 gal
D)
66 gal
Determine the value or values of the variable where the expression is defined.
101)
x - 7
x2- 16
101)
A)
all real numbers except x =7
16
B)
all real numbers except x =16
C)
all real numbers except x =4, x=-4
D)
all real numbers except x =4
Simplify.
102)
x2-25
(x +5)2
102)
A)
x -5
x -5
B)
x +5
x +5
C)
x2-25
x2+25
D)
x -5
x +5
Add or subtract.
103)
x2- 14
x2- 3x - 18 +4+ 3x
18 + 3x -x2
103)
A)
(x -3)(x + 6)
(x +3)(x - 6)
B)
x +3
x - 6
C)
x - 6
x - 6
D)
x - 6
x2- 3x - 18
Find the quantity indicated.
104)
x varies directly as z. Find x when z =9 and k =12.
104)
A)
3
4
B)
4
3
C)
21
D)
108
Add or subtract.
105)
2a + 5b
2-2a - 5b
2
105)
A)
25b
B)
0
C)
5b
D)
2a
Solve the problem.
106)
The distance a bicycle travels, d, is directly proportional to the speed, s, the bicycle is traveling.
Determine the distance travelled if the constant of proportionality, k, is 5 and the speed is 26 mph.
106)
A)
5.20 mi
B)
135.20 mi
C)
10 mi
D)
130 mi
107)
The amount of time it takes a swimmer to swim a race is inversely proportional to the average
speed of the swimmer. A swimmer finishes a race in 60 seconds with an average speed of 5 feet per
second. Find the average speed of the swimmer if it takes 75 seconds to finish the race.
107)
A)
5 ft/sec
B)
3 ft/sec
C)
4 ft/sec
D)
6 ft/sec
Find the least common denominator for the expression.
108)
1
x2- 1 +x - 2
9x3+ 9x2
108)
A)
9x2(x + 1)
B)
9x2(x + 1)2
C)
9x2(x + 1)(x - 1)
D)
9x(x + 1)(x - 1)(x2+ 1)
109)
9
5x2-10x +5+1
20x2-20
109)
A)
20(x -1)(x +1)
B)
100(x -1)2(x +1)
C)
20(x -1)2(x +1)
D)
5(x -1)2(x +1)
Add or subtract.
110)
7
x2-x
6x + 1
110)
A)
7+42x -x2
x2(6x + 1)
B)
7+42x -x2
x(6x + 1)
C)
42x3+7x2
x2(6x + 1)
D)
7+42x -x3
x2(6x + 1)
Divide.
111)
3
5÷ - 1
3
111)
A)
-1
5
B)
9
5
C)
-9
5
D)
5
9
112)
x2-16x +64
7x -56 ÷4x -32
28
112)
A)
1
B)
x2-16x +64
(x -8)2
C)
28
D)
(x -8)2
49
Solve the equation and check your solution.
113)
6x
x +3-18
x -3=6x2+54
x2-9
113)
A)
x =3, -3
B)
x =-3
C)
x =3
D)
No solution
Answer true or false.
114)
3a
8b = - -3a
-8b =-3a
-8b
114)
A)
True
B)
False
Solve the problem and answer the question.
115)
Julie and Eric row their boat (at a constant speed) 48 miles downstream for 6 hours, helped by the
current. Rowing at the same rate, the trip back against the current takes 8 hours. Find the rate of the
current.
115)
A)
7 mph
B)
2 mph
C)
0.5 mph
D)
1 mph
Add or subtract.
116)
8
x2-16 -x2-8
x2-16
116)
A)
0
B)
-1
C)
1
D)
undefined
Find the least common denominator for the expression.
117)
14
x +8+8
x2-64
117)
A)
(x +8)(x -8)2
B)
x +8
C)
x2-64
D)
(x +8)(x2-64)
Add or subtract.
118)
x
x2- 16 -3
x2+ 5x + 4
118)
A)
x2- 2
(x - 4)(x + 4)(x + 1)
B)
x2- 2x + 12
(x - 4)(x + 4)
C)
x2- 2x + 12
(x - 4)(x + 4)(x + 1)
D)
x2+ 2x + 12
(x - 4)(x + 4)(x + 1)
Solve the equation and check your solution.
119)
x
2+9x
6=x
12
119)
A)
x =108
B)
x = 0
C)
x =12
D)
x =54
Simplify.
120)
3x2- 27
18 - 6x
120)
A)
x + 3
2
B)
x2- 9
3 - x
C)
-x + 3
2
D)
-2(x + 3)
Answer Key
Testname: C6
Answer Key
Testname: C6
Answer Key
Testname: C6
