1. Which of the following must be even?
I. The sum of two odd numbers
II. The sum of an odd and an even number
III. The sum of two even numbers
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2. In the figure below, the shaded region is what fractional part of the area of the circle?
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3. If P₁ = 4 x 0.095 and P₂ = 0.004 x 0.095, which of the following is true?
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4. If x + 3 = x - b, then b =
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5. In the figure below, x + y =
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6. How many numbers between 20 and 50 are each equal to 9 times an integer?
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7. If (r + 1)(1 / r) = 0, what is r?
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8. If x, y, and z are consecutive integers and x + y + z = 270, what is the value of the LEAST of the three integers?
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9. If the average of 2 numbers is 7 and the product of the 2 numbers is 48, then the positive difference between the 2 numbers is
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10. If 3 * 5 * 7 = x and 3 * 5 = y, then x - y is equal to the product of 15 and
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11. In the figure below, a circle with center R has an area of 36π square units and just touches the X-axis and Y axis. What are the coordinates of R?
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12. If 1 / (x + y) = 1, then x =
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13. In △PQR below, QS⊥PR. Which of the following conditions will insure that area △PQS < area △SQR? 
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14. If 3 persons who work at the same rate can do a job together in 5 days, what fractional part of that job can one of these persons do in 1 day?
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15. If the pattern of the first 5 arrows below continues to the right, the 107th arrow would be in which of the following directions?
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16. Which row in the list below contains both the square of an integer and the cube of a different integer?
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17. Jack begins reading at the top of page N and finishes at the bottom of page R. If the pages are numbered and read consecutively and if there are no blank pages, how many pages has he read?
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18. Out of a total of 154 games played, a ball team won 54 more games than it lost. If there were no ties, how many games did the team win?
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19. On a scale drawing, if 4 centimeters represent 16 meters, how many centimeters represent 2 meters 8 centimeters?
(100 centimeters = 1 meter)
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20. If x is k per cent of y, what per cent of y is kx?
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21. The figure below shows a circle with diameter 1. If 22/7 is used as an approximation to π and if the circle rolls a distance 2, what part of a complete rotation does it make?
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22. At a cost of 5 oranges for t cents, how many oranges can be bought for x dollars?
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23. A triangle is obtuse if and only if the degree measure of one of its angles is greater than 90 and less than 180. A certain triangle has sides of length 5, 5, and x. What are all numbers x for which this triangle is obtuse?
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24. In the correct addition problem shown below, A, B, C, and D represent nonzero digits. What is the value of C?
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25. In the figure below, if O is the center of the circle and the length of side AB of right triangle AOB is 6√2, what is the area of the shaded region?
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1. (2³ - 2⁴)(2² - 2) =
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2. In the figure below, if PQ is a line segment, then x =
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3. In the figure below, a belt which runs over five wheels moves in the direction of the arrows. How many of the wheels are turning clockwise?
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4. In the figure below, the length of the minor arc AC is 1/18 of the circumference of the circle with center B. What is the measure of ∠ABC in degrees?
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5. If S is the sum of the remainders when each number in the list below is divided by 6, what is the remainder when S is divided by 6?
30, 31, 32, 33, 34, 35
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6. The average of positive numbers x, y, and z is what per cent of their sum?
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7. If 70 tickets to a play were bought for a total of $50.00 and if tickets cost $1.00 for adults and $0.50 for children, how many children's tickets were bought?
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8.
A. 1/2 + 1/3
B. 1/4 + 1/5
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9.
A. x²
B. y²
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10. 9 - 3x = 6 12 - 2y = 10
A. x
B. y
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11.
A. √(2) - 1
B. √(3) - 1
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12. In a certain class, every student studies either art or science or both; 12 study only art, 10 study only science, and x study both.
A. Number of students in the class who study art but not science
B. Number of students in the class who study science but not art
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13.
A. The perimeter of a triangle
B. The perimeter of a rectangle
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14. 
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15.
A. The number of articles X can produce per hour if he produces at the rate of 25 articles in 15 minutes
B. The number of articles Y can produce per hour if he produces at the rate of 20 articles in 12 minutes
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16. x > 0
A. √(x + 1)
B. √(x) + 1
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17. k is an integer greater than 1.
A. k²(k-1)²
B. 36
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18. P = (x - 2)(x + 3) Q = (x - 3)(x + 2)
A. Value of P when x = 2
B. Value of Q when x = 2
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19.
A. x
B. y
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20.
A. p + q
B. r + s
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21.
A. x + y
B. 180
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22. A coat that was priced at $36.50 is sold at a 30 per cent discount.
A. Price of the coat after discount
B. $25.55
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23. x < 0 y > 1
A. xy
B. x / y
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24. In a game, a fair coin is to be tossed 10 times and the score will be the number of heads obtained. A. The chances of a score of exactly 7
B. The chances of a score exactly 3
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25.
A. ST
B. RS
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26.
A. Average price per pound of 2 pounds of brand X beef and 3 pounds of brand Y beef
B. Average price per pound of 2 pounds of brand X beef and 1 pound of brand Y beef
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27.x < 0
A. (x + 2)(x + 3)
B. (x + 2)²
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28. If 6t - p = 8 and 4t - 3p = 7, then t + p =
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29. 
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30. If pqrs ≠ 0, which of the following is (are) necessarily true?
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31. In △PQR below, if PQ < RQ < PR, then
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32. A person is paid time and a half for all hours worked in excess of 7.5 hours per day. If the person works 10 hours in one day, by what per cent are his regular wages for the day increased?
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33. A closed rectangular tank 1 meter by 2 meters by 4 meters contains 4 cubic meters of water. When the tank is placed level on its various sides, the water depth changes. What is the greatest possible difference in water depths?
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34. If the average of the degrees measures of two angles of an isosceles triangle is 50, which of the following could be the degree measure of one of the angles of the triangle?
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35. In the highway system illustrated below, one-tenth of the eastbound cars from highway H turn into M; the rest continue on N. One-fifth of the eastbound cars on K come from P; the rest, from M. If traffic on all highways is in the direction of the arrows, what is the ratio of the traffic on H to that on R?
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