5. While driving on a 500-mile trip, Mr. Smith averages 60 miles per hour for the first t hours. In
terms of t, where t < 8, how many miles remain
to be traveled?
(A) 60t − 500
(B) 500 − 60t
Plug
in Numbers
(C) 20, 000 − t
60
(D) 500 −
t
500
(E)
60t
1. Tom had 2b books for sale at a price of k dollars
each. If y is the number of books he did not sell,
which of the following represents the total dollar
amount he received in sales from the books?
(A) k(2b − y)
6. If
(B) k(y − 2b)
v
r
t
r
= 2 and = , then, for t , 0, =
s
s v
t
(C) ky − 2b
(D) 2b − ky
(A)
(E) 2bk − y
(B)
2. If t represents an odd integer, which of the following expressions represents an even integer?
(C)
(A) t + 2
(D)
(B) 2t − 1
(E)
(C) 3t − 2
1
2
2
t
v
v
2s
2v
s
7. If y = 5x and the value of x is increased by 4, then
the value of y will increase by how much?
(D) 3t + 2
(E) 5t + 1
(A) 1
3. If 0 < x < 1 and 0 < y < 1, which of the following must be true?
(B) 4
(A) xy > 0
(C) 5
(B) xy < 0
x
(C)
<0
y
(D) x − y > 0
(D) 9
(E) 20
8. If e, f , g, and h are consecutive odd integers and
e < f < g < h, then g + h is how much greater
than e + f ?
(E) x − y < 0
4. The cost of 3 sweatshirts is d dollars. At this rate,
what is the cost, in dollars, of 30 sweatshirts?
(A) 2
10d
3
d
(B)
30
30
(C)
d
(D) 10d
(B) 3
(A)
(C) 4
(D) 5
(E) 8
9. If the perimeter of a rectangle is 10 times the
width of the rectangle, then the length of the rectangle is how many times the width?
(E) 30d
Revised 2/2010
1
14. If n is a positive number, which of the following
is equal to 8n?
√
(A) 64n
√
(B) 8n2
√
(C) 16n2
√
(D) 2 4n
√
(E) 4 4n2
10. If n is an even integer greater than 2, what is the
next greater even integer in terms of n?
(A) n + 1
(B) n + 2
(C) n + 3
(D) 2n
(E) n2
11. If the average (arithmetic mean) of 5 consecutive
even integers is n, what is the median of these 5
integers?
15. If p is a prime number greater than 3, which of
the following is NOT a factor of 6p?
(A) p2
(A) 0
(B) 6p
(B) 2
(C) 3p
(C) n
(D) 2p
(D) n − 2
(E) 3
(E) n − 4
16. If x = 2y, y = 4z, 2z = w, and w , 0, then
x
12. If = −1, then x + y =
y
(C) x
1
4
1
(B)
2
(C) 1
(D) y
(D) 2
(E) 2x
(E) 4
x
=
w
(A)
(A) 0
(B) 1
13. If j and k are integers and j + k = 2 j + 4, which
of the following must be true?
17. If x < y, which of the following must be true?
(A) x2 < y2
I. j is even.
(B) −y < −x
II. k is even.
(C) x2 < xy
III. k − j is even.
(D) xy < y2
(E) 2x < y
(A) None
(B) I only
18. The expression
than x?
(C) II only
(D) III only
(E) I, II, and III
2
3x − 1 x + 6
+
is how much more
4
4
19. In a certain shop, items were put in a showcase
and assigned prices for January. Each month after
that, the price was 10 percent less than the price
for the previous month. If the price of an item
was p dollars for January, what was the price for
April?
23. If x is 5 percent of r and r is 20 percent of s, what
percent of s is x?
(A) 1%
(B) 4%
(C) 10%
(A) 0.4p
(D) 40%
(B) 0.6p
(E) 100%
(C) 0.6561p
24. If a and b are positive, then the solution to the
bx
= 1 is x =
equation
a−x
a
(A)
b+1
a+1
(B)
b+1
b−1
(C)
a
b
(D)
a+1
b+1
(E)
a
(D) 0.7p
(E) 0.729p
20. A person slices a pie into k equal pieces and eats
one piece. In terms of k, what percent of the pie
is left?
(A) 100(k − 1) %
100(k − 1)
%
(B)
k
100k
(C)
%
k−1
k−1
(D)
%
100
k−1
(E)
%
100k
25. If m and n are both negative numbers, m is less
than −1 and n is greater than −1, which of the
following gives all possible values of the product
mn?
3
2
21. If x is of y and y is of z, what is the value of
3
5
x
?
z
(A)
(B)
(C)
(D)
(E)
(A) All negative numbers
(B) All negative numbers less than −1
2
5
5
8
9
10
10
9
5
2
(C) All negative numbers greater than −1
(D) All positive numbers
(E) All positive numbers less than 1
x+7
26. If x is an integer and
is an integer, which of
2
the following must be true?
I. x is odd.
II. x is a multiple of 7.
x+5
III.
is an integer.
2
5x3
, what happens to the value of y when
z
both x and z are doubled?
22. If y =
(A) y is not changed.
(A) I only
(B) y is halved.
(B) II only
(C) y is doubled.
(C) III only
(D) y is tripled.
(D) I and II
(E) y is multiplied by 4.
(E) I and III
3
Ratios
31. Three business partners are to share profits of
$24,000 in the ratio 5 : 4 : 3. What is the amount
of the least share?
27. The ratio of 8 to 3 is equal to the ratio of 24 to
what number?
(A) $1,200
(A) 8
(B) $3,000
(B) 9
(C) $6,000
(C) 19
(D) $8,000
(D) 29
(E) $10,000
(E) 64
32. If the ratio of two positive integers is 3 to 2, which
of the following statements about these integers
CANNOT be true?
1
28. A recipe calls for 7 tablespoons of milk. This
3
amount is equivalent to how many teaspoons of
milk? (3 teaspoons = 1 tablespoon)
(A) Their sum is an odd integer.
(A) 2
(B) Their sum is an even integer.
(B) 10
(C) Their product is divisible by 6.
(C) 16
(D) Their product is an even integer.
(D) 22
(E) Their product is an odd integer.
(E) 30
33. If the ratio of q to r is 4 to 5, which of the following could be true?
29. Five of the 12 members of a club are girls and the
rest are boys. What is the ratio of boys to girls in
the club? (Answer as a fraction.)
O
A
4
5
5
(B) q = 2, r =
2
(C) q = 5, r = 6
(A) q = 0, r =
B
(D) q = 15, r = 12
(E) q = 16, r = 25
30. In the figure above, both circles have their centers at point O, and point A lies on segment OB.
If OA = 3 and AB = 2, what is the ratio of the
circumference of the smaller circle to the circumference of the larger circle?
(A)
(B)
(C)
(D)
(E)
2
3
3
5
9
16
1
2
4
9
4
Mean, Median, & Mode
37. If the average (arithmetic mean) of x, 2x − 8,
2x + 2, 3x − 1, and 4x + 1 is 6, what is the value
of the mode of these numbers?
CENTRAL HIGH’S
FIELD HOCKEY RESULTS
Games Played in September
Central
Central
Central
Central
Central
Goals
7
3
3
5
2
Northern
Westfield
Easton
Southern
Bayville
Goals
0
1
2
1
1
38. In a set of eleven different numbers, which of the
following CANNOT affect the value of the median?
Margin of
Victory
(A) Doubling each number
(B) Increasing each number by 10
(C) Increasing the smallest number only
(D) Decreasing the largest number only
(E) Increasing the largest number only
39. If the average (arithmetic mean) of three different
positive integers is 70, what is the greatest possible value of one of the integers?
34. Central High’s field hockey team was undefeated
in September, as shown in the table above. A
team’s margin of victory for a single game is defined as the number of goals it made minus the
number of goals made by the losing team. What
is the median of the missing values in the column
labeled Margin of Victory?
xº
(A) 1
vº
(B) 2
yº
(C) 3
uº
wº
(D) 4
40. In the triangles above, what is the average (arithmetic mean) of u, v, w, x, and y?
(E) 5
35. In a certain club, the median age of the members
is 11. Which of the following must be true?
(A) 21
(B) 45
I. The oldest member in the club is at least 1
year older than the youngest.
(C) 50
(D) 52
II. If there is a 10 year old in the club, there is
also a 12 year old.
(E) 54
III. The mode of the members’ ages is 11.
41. The average (arithmetic mean) of nine numbers
is 9. When a tenth number is added, the average
of the ten numbers is also 9. What is the tenth
number?
(A) None
(B) I only
(C) II only
(A) 0
9
(B)
10
10
(C)
9
(D) 9
(D) III only
(E) II and III
36. The average (arithmetic mean) of the test scores
of a class of p students is 70, and the average of
the test scores of a class of n students is 92. When
the scores of both classes are combined, the averp
age score is 86. What is the value of ?
n
(E) 10
5
47. If ∠CAB = ∠CBD and AB = 12, what is the measure of BC?
Triangles and Geometry
Base your answers to the following questions on
the diagram below, in which l k m. Treat each
question as if the information from the previous
question has been discarded.
t
Base your answers to the following questions on
the diagram below (not drawn to scale), in which
triangles ABD and DBC are right triangles. Treat
each question as if the information from the previous question has been discarded.
k
B
zº
A
C
l
yº
B
xº
C
m
wº
A
D
48. Suppose ABD and DBC are isosceles right triangles, and AB = 5. What is the length of BC?
42. Suppose that y = 2x and w = 60 . What is the
value of y?
◦
49. Suppose triangle ABD is isosceles, BC = 10 and
DC = 6. What is the area of triangle ABD?
43. If y = 70◦ and x = 40◦ , what is the value of z?
44. Suppose the triangle formed by A, B, and C is
equilateral (i.e. A = B = C). What is the value of
z?
10
16
45. Suppose instead that A = B (i.e. the triangle
formed by A, B, and C is isosceles), and that
w = 50◦ . What are the values of y and z?
x
y
Base your answers to the following two questions
on the figure below, in which ACD and BCD
are right triangles. Treat each question as if the
information from the previous question has been
discarded.
50. In the figure above, what is the value of x2 + y2 ?
C
C
D
B
yº
A
D
A xº
B
E
51. In the figure above AE ⊥ CE and CD ⊥ CE. If
x = y, the length of AB is 4, and the length of BD
is 8, what is the length of CE?
46. If AC = BC, AC = 5 and CD = 4, what is the
length of AB?
6
Plug in Numbers Packet KEY
1.
2.
3.
4.
5.
6.
7.
8.
9.
A
E
A
D
B
A
E
E
4
10.
11.
12.
13.
14.
15.
16.
17.
18.
B
C
A
D
E
A
E
B
5/4
19.
20.
21.
22.
23.
24.
25.
26.
27.
E
B
A
E
A
A
D
E
B
28.
29.
30.
31.
32.
33.
34.
35.
36.
7
D
7/5
B
C
E
B
B
A
6/16
37.
38.
39.
40.
41.
42.
43.
44.
45.
8
E
207
E
D
80◦
70◦
60◦
80◦ , 50◦
46.
47.
48.
49.
50.
51.
6√
6 2
10
16
356
√
6 2