Random Good Questions

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 Q11. The circle above has center O and d iameter AB. The two semicircles have diameters OA and OB. If the circumference of the circle is 36π, what is the length of the curved 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, what is 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  5 B) y = -2x + 5 C) y = 2x  5 D) y =  x  5 E) y =  x + 5

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  • 8/13/2019 Random Good Questions


    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 36, what is the length of thecurved path from A to B through O?

    A) 6B) 9C) 18D) 24E) 36

    x f(x)

    0 a

    1 24

    2 b

    Q12. The table above shows some values for the functionf. Iffis 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 lisy = 2x + 5. If line mis 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

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  • 8/13/2019 Random Good Questions


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    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) a2+ b2= 1

    E) a2-- b2= 1

    Q15. The figure above shows the graphs ofy = x2andy = a x2for 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 hasxmembers and set Y hasymembers. Set Z consists of all members that

    are in either set X or set Y with the exception of the kcommon 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

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    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 forxdollars. Each additional shirt the

    customer buys costszdollars less than the first shirt. For example, the cost of the second

    shirt isx zdollars. Which of the following represents the customers cost, in dollars, fornshirts bought during this sale?

    A)x + (n


    z)B)x + n(x z)

    C) n(x z)

    D) ( )

    E) (x z) +

    Q7. If 1818 = rt, where r and t are positive integers and r > t, which of the followingcould be the value of rt?

    A) 18

    B) 36C) 108

    D) 162

    E) 324

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    Q8. In the figure above, what is the value of cin 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 functionfis defined byf(x) = x2 + bx + c, where b and care positive

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

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    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

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    E) 20

    Q16. Ifxis an integer greater than 1 and ify=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 kpassengers went on a bus trip. Each of the nbuses that were used

    to transport the passengers could seat a maximum ofxpassengers. 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 ofppositive 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 lpasses through the origin and is perpendicular to the

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

    1), what is the value of t?

    A) -4/3

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    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






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

    many different values of kis 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 childs height hsatisfies the regulation forthis side?

    A) |h 10| < 50B) |h 20| < 40

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    C) |h30| < 20D) |h40| < 10E) |h45| < 5

    Q13. Ifx, y, andzare positive integers such that the value ofx + yis even and the

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

    A)xis odd

    B)xis even

    C) Ifzis even, thenxis odd

    D) Ifzis even, thenxyis 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 exactlyx 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 planes arrival time (EST) in New York City?

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    A) 10:00 P.MEST

    B) 9:00 P.MEST

    C) 7:00 P.MEST

    D) 6:00 P.MEST

    E) 4:00 P.MEST

    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


    A) xy = 4

    B) 0 xy 24C) -1 xy 11D) -1 xy 24E) -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 131stterm 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

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    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 aand bare positive integers, what is the value of ab?





    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 care 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?

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    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. Letf(x)be defined for any positive integerxgreater than 2 as the sum of all

    prime numbers less thanx.

    For example,

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

    What is the value off(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.

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    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 bmL of coffee and then ads amL of cream so

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


    A) 100 a%B) 110 + a%





    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