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Q11. The circle above has center O and diameter AB. The two semicircles have

diameters OA and OB. If the circumference of the circle is 36π, what is the length of thecurved path from A to B through O?

A) 6π B) 9π

C) 18π

D) 24π

E) 36π

x f(x)

0 a

1 24

2 b

Q12. The table above shows some values for the function f . If f is a linear function, whatis the value of a + b?

A) 24

B) 36

C) 48

D) 72

E) Cannot be determined from the information given

Q14. In the xy-plane, the equation of line l is y = 2x + 5 . If line m is the reflection of line l

in the x-axis, what is the equation of line m?

A) y = -2x–

5B) y = -2x + 5

C) y = 2x – 5

D) y = x – 5

E) y = x + 5



C) 25

D) 30

E) 35

Q14. If (a + b)1/2 = (a – b)-1/2, which of the following must be true?

A) b = 0

B) a + b = 1

C) a – b = 1

D) a 2 + b 2 = 1

E) a 2 -- b 2 = 1

Q15. The figure above shows the graphs of y = x 2 and y = a – x 2 for some constant a. If the

length of {Q is equal to 6, what is the value of a?

A) 6

B) 9

C) 12

D) 15

E) 18

Q16. Set X has x members and set Y has y members. Set Z consists of all members that

are in either set X or set Y with the exception of the k common members (k > 0). Whichof the following represents the number of members in set Z?

A) x + y + k

B) x + y – k

C) x + y + 2k

D) x + y – 2k

E) 2x + 2y – 2k



Q14. What is the perimeter of the figure above?

A) 24B) 25

C) 28

D) 30

E) 36

Q18. During a sale, a customer can buy one shirt for x dollars. Each additional shirt the

customer buys costs z dollars less than the first shirt. For example, the cost of the second

shirt is x – z dollars. Which of the following represents the customer’s cost, in dollars, for

n shirts bought during this sale?

A) x + (n–

1)(x–

z)B) x + n(x – z)

C) n(x – z)

D) ( – )

E) (x – z) + –

Q7. If 18√ 18 = r√ t, where r and t are positive integers and r > t, which of the following

could be the value of rt ?

A) 18

B) 36C) 108

D) 162

E) 324



Q8. In the figure above, what is the value of c in terms of a and b?

A) a + 3b – 180

B) 2a + 2b – 180

C) 180 - a – b

D) 360 – a–

bE) 360 – 2a – 3b

Q17. A merchant sells three types of clocks that chime as indicated by the check

marks in the table above. What is the total number of chimes of the inventory of

clocks in the 90-minute period from 7:15 to 8:45?

Q10. Stacy noted that she is both the 12th tallest and the 12th shortest student in

her class. If everyone in the class is of a different height, how many students are

in the class?

A) 22

B) 23

C) 24

D) 25

E) 34

Q11. If the function f is defined by f(x) = x2 + bx + c, where b and c are positive

constants, which of the following could be the graph of f ?



A)

B)

C)

D)

E)

Q12. In the figure above, ABCD is a rectangle with BC = 4 and AB = 6. Points P, Q,

and R are different points on a line (not shown) that is parallel to AD. Points P

and Q are symmetric about line AB and points Q and R are symmetric about line

CD. What is the length of PR?

A) 6

B) 8

C) 10D) 12



E) 20

Q16. If x is an integer greater than 1 and if y = x = 1/x, which of the following

must be true?

I. y ≠ xII. y is an integer

III. xy > x2

A) I only

B) III only

C) I and II only

D) I and III only

E) I, II, and III

Q8. A total of k passengers went on a bus trip. Each of the n buses that were used

to transport the passengers could seat a maximum of x passengers. If one bus

had 3 empty seats and the remaining buses were filled, which of the following

expresses the relationship among n, x, and k ?

A) nx – 3 = k

B) nx + 3 = k

C) n + x + 3 = k

D) nk = x + 3

E) nk = x – 3

Q12. A list of numbers consists of p positive and n negative numbers. If anumber is picked at random from this list, the probability that the number is

positive is 3/5. What is the value of n/p?

A) 3/8

B) 5/8

C) 2/3

D) 3/2

E) 8/3

Q14. For how many ordered pairs of positive integers (x, y) is 2x + 3y < 6?

A) One

B) Two

C) Three

D) Five

E) Seven

Q17. In the xy-plane, line l passes through the origin and is perpendicular to the

line 4x + y = k, where k is a constant. If the two lines intersect at the point (t, t +

1), what is the value of t ?

A) -4/3



B) -5/4

C) 3/4

D) 5/4

E) 4/3

Q19. In the figure above, triangle XYZ is equilateral, with side of length 2. If WY Is

a diameter of the circle with center O, then the area of the circle is

A)√

B)

C)

D) π

E)

Q20. When 15 is divided by the positive integer k , the remainder is 3. For how

many different values of k is this true?

A) One

B) Two

C) Three

D) Four

E) Five

Q15. A measuring cup contains 1/5 of a cup of orange juice. It is then filled to the

1 cup mark with a mixture that contains equal amounts of orange, grapefruit,

and pineapple juices. What fraction of the final mixture is orange juice?

Q9. A regulation for riding a certain amusements park ride requires that a child

be between30 inches and 50 inches tall. Which of the following inequalities can

be used to determine whether or not a child’s height h satisfies the regulation for

this side?

A) |h – 10| < 50B) |h – 20| < 40



C) |h – 30| < 20

D) |h – 40| < 10

E) |h – 45| < 5

Q13. If x, y, and z are positive integers such that the value of x + y is even and the

value of ( x + y) 2 + x + z is odd, which of the following must be true?

A) x is odd

B) x is even

C) If z is even, then x is odd

D) If z is even, then xy is even

E) xy is even

Q16. The pattern shown above is composed of rectangles. This pattern is used

repeatedly to completely cover a rectangular region 12L units long and 10L units

wide. How many rectangles of dimension L by W are needed?

A) 30

B) 36

C) 100

D) 150

E) 180

Q10. How old was a person exactly 1 years ago if exactly x years ago the person

was y years old?

A) y – 1

B) y – x – 1

C) x – y – 1

D) y + x + 1

E) y + x – 1

Q15. When it is noon eastern standard time (EST) in New York City, it is 9:00 A.M.

Pacific standard time (PST) in San Francisco. A plane took off from New York City

at noon EST and arrived in San Francisco at 4:00 P.M PST on the same day. If a

second plane left San Francisco at noon PST and took exactly the same amount oftime for the trip, what was the plane’s arrival time (EST) in New York City?



A) 10:00 P.M EST

B) 9:00 P.M EST

C) 7:00 P.M EST

D) 6:00 P.M EST

E) 4:00 P.M EST

Q18. In the figure above, ABCD is a rectangle. Points A and C lie on the graph of y

= px2, where p is a constant. If the area of ABCD is 4, what is the value of p?

Q14. If 0 x 8 and -1 y 3, which of the following gives the set of all possible values

of xy ?

A) xy = 4

B) 0 ≤ xy ≤ 24C) -1 ≤ xy ≤ 11

D) -1 ≤ xy ≤ 24

E) -8 ≤ xy ≤ 24

Q16. If the nth term of a sequence is given by the expression 2*4n-1, what is the

value of the units digit of the 131st term in the sequence?

A) 0

B) 2

C) 3

D) 6

E) 8

Q18. A circle with center A has its center at (6, -2) and a radius of 4. Which of the

following is the equation of a line tangent to the circle with center A?

A) y = 3x + 2

B) y = 2x + 1

C) y = -x + 5

E) y = -6



Q16. The faces of a cube are numbered with integers from 1 to 6 so that the sum

of the numbers on apposite faces is 7. Thus, 1 is opposite 6, 2 is opposite 5, and 3

is opposite 4. If the cube is thrown on a flat surface so that 4 shows on the top

face, what is the probability that 6 is on the bottom face of the cube?

(a*2) + (a*22) + (b*23) + (b*24) = 42

Q17. If a and b are positive integers, what is the value of ab?

6P

-2P

--------------

4R

Q5. Assume that the above subtraction problem with digits P and R is without

error. If P and R are not equal to each other, how many distinct digits from 0 to 9

could R symbolize?

A) One

B) Four

C) Five

D) Nine

E) Ten

Q18. If (c + 1)2 = -b, where b and c are both real numbers, which of the following

statements could be true?

I. c > 0

II. c = 0

III. c < 0

A) None

B) I only

C) III only

D) I and II only

E) I, II, and III

Q18. The average (arithmetic mean) of 6 distinct numbers is 71. One of these

numbers is -24, and the rest of the numbers are positive. If all of the numbers are

even integers with at least two digits, what is the greatest possible value of any

of the 6 numbers?



Q14. The figure above is a cube. The length of each edge is 10 cm, and point I is

placed at the center of the side. If a line is drawn through the cube from point I to

point J, what is IJ in centimeters?

A) √ 110 (approx. 10.488)

B) √ 150 (approx.. 12.247)

C) √ 162 (approx.. 12.728)

D) √ 175 (approx.. 13.229)

E) √ 184 (approx.. 13.565)

Q11. Let f(x) be defined for any positive integer x greater than 2 as the sum of all

prime numbers less than x .

For example,

F(4) = 2 + 3 = 5 and f(8) = 2 + 3 + 5 + 7 = 17

What is the value of f(81) – f(78)?

A) 2

B) 3

C) 23

D) 57

E) 79

Q17. In a list of 4 positive even numbers, the mean, median, and mode are all

equal. Which of the following CANNOT be done to the list if the mean, median,

and mode are to remain equal?

A) Add one number to the list

B) Add one number to the list that is greater than the mean

C) Add two distinct numbers to the list.D) Add 2 to each number in the list.



E) Remove the first and last numbers from the list.

-7, -5, -3, -1, 0, 1, 3, 5, 7

Q12. How many distinct products can be obtained by multiplying any two

numbers in the list of numbers above?

A) 9

B) 17

C) 19

D) 21

E) 31

Q19. Joe fills his 100 mL mug with b mL of coffee and then ads a mL of cream so

that the mug is totally full. In terms of a, what percent of the mug is filled with

coffee?

A) 100 – a%

B) 110 + a%

C) –

%

D)

%

E) a%

Q10. Three identical cubes, each with edges of length 8, are to be cut into a total

of 384 identical rectangular solids of length 4. If the width and height of each

solid are integers, what is the surface area of each solid?

A) 4

B) 8

C) 12

D) 16

E) 18