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12. If the ticket revenue at the Triplex is greater than the ticket revenue at the Village Theater, what is the least possible value of x?
(A) 137
(B) 138
(C) 139
(D) 140
(E) 141
13. How many integers between 100 and 1000 contain only the digits 3, 4 or 5, if any digit may be repeated?
(A) 16
(B) 18
(C) 20
(D) 24
(E) 27
14. If 
, which of the following represents the value of y in terms of x?
(A) 
(B) 
(C) 
(D) 
(E) 
15. The inscribed circle touches square ABCD at points E, F, G, and H, which are all midpoints of their respective sides. If the length of one side of the square is 6, what is the area of the shaded region?
(A) 36 − 9π
(B) 36 − 36π
(C) 24 − 9π
(D) 36π −36
(E) 24 − 9π
16. A chef spends c hours each day at her restaurant, 
hours of which she spends preparing desserts. At this rate, after how many days will the chef have spent 24 hours preparing desserts?
(A) 
(B) 
(C) 
(D) 24 c
(E) 
17. If the rectangles shown below have the same perimeter, what is the value of x?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
18. If b represents a positive integer, which of the following expressions necessarily represents an even integer?
(A) 2 b
(B) b + 2
(C) 2 b + 1
(D) 3 b
(E) 2 b − 1
19. Two lines intersect as shown in the figure below, what is the value of x?
(A) 54
(B) 56
(C) 57
(D) 59
(E) 62
20. If x and y are both positive, which of the following is equivalent to (x 6 y 4) 
(A) 
(B) 
(C) 
(D) 
(E) 
21. Based on the information in the table below, what is the median final exam grade for Mr. Price’s class?
(A) 75
(B) 80
(C) 85
(D) 90
(E) 95
22. If a = b 3, and b is positive, then by what factor does a increase if b is tripled?
(A) 3
(B) 8
(C) 9
(D) 27
(E) 81
23. If f (x) = (x − 2)2 + 4, what is the least possible value of f (x)?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
24. If 20w = 53 × 43, what is the value of w?
(A) 1
(B) 3
(C) 6
(D) 8
(E) 10
25. Which of the following represents the result if the three operations below are performed in sequence?
Step 1: Subtract 5 from x
Step 2: Multiply this difference by 2
Step 3: Add 6 to this product
(A) x – 4
(B) 2 x + 1
(C) 2 x – 4
(D) 2 x – 6
(E) 2 x + 2
26. If 
+ 16 = 79, what is the value of x?
(A) 3
(B) 6
(C) 9
(D) 27
(E) 81
27. Two towns located x miles apart are p centimeters apart on a roadmap that is drawn to scale. How many miles apart are two towns that are p + 5 centimeters apart on this map?
(A) 
(B) 
(C) 
(D) 
(E) 
28. For any positive integer, n, let 
be defined as the integer obtained when each digit in n has been replaced with the corresponding digit in the table below, ignoring any leading zeroes.
For example, 
= 548 and 
= 08 = 8. Which of the following is equivalent to 
+ 
?
(A) 
(B) 
(C) 
(D) 
(E) 
29. Differentiate the function in the below.
(A) 
(B) 
(C) 
(D) 
(E) 
30. Find the integral of the function in the below.
(A) 
(B) 
(C) 
(D) 
(E) 
TEST 24
1. Which of the following integers is 2 greater than a multiple of 7?
(A) 14
(B) 15
(C) 16
(D) 17
(E) 18
2. A store sells oranges for 20 cents each, but for every four oranges you buy, you may buy a fifth for only 5 cents. How many oranges can you buy from this store for $3.40?
(A) 14
(B) 17
(C) 18
(D) 19
(E) 20
3. If r is a positive number and s is a negative number, all of the following must represent positive numbers except
(A) −r + s
(B) r − s
(C) 
(D) rs 2
(E) (rs)2
4. Which of the following expresses the number that is 12 less than the product of 3 and x + 1?
(A) x − 8
(B) x + 37
(C) 3 x − 11
(D) 3 x − 9
(E) 3 x + 15
5. One bag of grass seed covers 5,000 square feet. If each bag costs $25, how much will it cost to buy enough grass seed to cover a square area that is 200 feet by 200 feet?
(A) $25
(B) $100
(C) $200
(D) $1,000
(E) $2,000
6. In the right triangle below, what is the value of w?
(A) 30
(B) 60
(C) 90
(D) 120
(E) 150
7. Three integers have a sum of 7 and a product of 0. If the difference of the greatest number and the least number is 11, then the least of these numbers is
(A) −18
(B) −11
(C) −9
(D) −2
(E) 0
8. Four points lie on a circle. How many different triangles can be drawn with three of these points as vertices?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
9. If a, b, and c are consecutive positive integers such that a < b < c and abc is not a multiple of 4, then which of the following must be true?
(A) a is even
(B) b is even
(C) c is even
(D) a + b + c is odd
(E) abc is odd
10. For which class was the change in percent participation the greatest from 2002 to 2003?
(A) A
(B) B
(C) C
(D) D
(E) E
11. If class B and class E each had 100 students in 2002 and 2003, then, in total, how many more students participated in the fund-raiser from class E than from class B over the 2 years?
(A) 10
(B) 20
(C) 30
(D) 40
(E) 60
12. In 2002, the same number of students participated in the fund-raiser from class C as from class D. If class D contained 120 students in 2002, how many students were there in class C in 2002?
(A) 90
(B) 100
(C) 120
(D) 140
(E) 160
13. If x = −1 is a solution of the equation x 2 = 4 x + c where c is a constant, what is another value of x that satisfies the equation?
(A) -5
(B) -2
(C) 1
(D) 2
(E) 5
14. A three-digit integer is to be formed from the digits listed below. If the first digit must be odd, either the second or the third digit must be 2, and no digit may be repeated, how many such integers are possible?
1, 2, 6, 7, 9
(A) 6
(B) 9
(C) 18
(D) 24
(E) 30
15. If one pound of grain can feed five chickens or two pigs, then ten pounds of grain can feed 20 chickens and how many pigs?
(A) 8
(B) 10
(C) 12
(D) 24
(E) 40
16. Point C is the center of the circle on the figure below. The shaded region has an area of 3π square centimeters. What is the perimeter of the shaded region in centimeters?
(A) 2π + 6
(B) 2π + 9
(C) 2π + 12
(D) 3π + 6
(E) 3π + 12
17. If four apples cost 20 cents, then, at this rate, how much would ten apples cost?
(A) $.40
(B) $.50
(C) $.60
(D) $.70
(E) $.80
18. If 2b = 8, then 3b =
(A) 6
(B) 9
(C) 27
(D) 64
(E) 81
19. How much greater is the average (arithmetic mean) of a, b, and 18 than the average of a, b, and 12?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
20. The first day of a particular month is a Tuesday. What day of the week will it be on the 31st day of the month?
(A) Wednesday
(B) Thursday
(C) Friday
(D) Saturday
(E) Sunday
21. How many integer pairs (m, n) satisfy the statements 0 < m + n < 50 and 
(A) 5
(B) 6
(C) 7
(D) 8
(E) more than 8
22. If y % of 50 is 32, then what is 200% of y?
(A) 16
(B) 32
(C) 64
(D) 128
(E) 256
23. For x > 0, the function g (x) is defined by the equation g (x) = x + x 1/2. What is the value of g (16)?
(A) 16
(B) 20
(C) 24
(D) 64
(E) 272
24. In the figure below, if the slope of 
is −3⁄4, what is the area of Δ ABO?
(A) 54
(B) 72
(C) 96
(D) 108
(E) 192
25. The sequence below continues according to the pattern shown. What is the sum of the first 25 terms of this sequence?
–1, 1, 2, −1, 1, 2, −1, 1, 2...
(A) 15
(B) 16
(C) 18
(D) 19
(E) 21
26. A jar contains only white and blue marbles of identical size and weight. The ratio of the number of white marbles to the number of blue marbles is 4 to b. If the probability of choosing a white marble from the jar at random is 1⁄4, then what is the value of b?
(A) 1
(B) 2
(C) 6
(D) 12
(E) 16
27. The area of a right triangle is 10 square centimeters. If the length of each leg, in centimeters, is a positive integer, then what is the least possible length, in centimeters, of the hypotenuse?
(A) 
(B) 
(C) 
(D) 
(E) 
28. If y is a number less than 0 but greater than −1, which of the following expressions has the greatest value?
(A) 100 y
(B) y 2
(C) y 3
(D) y 4
(E) y 5
29. Differentiate the function in the below.
(A) 
(B) 
(C) 
(D) 
(E) 
30. Find the integral of the function in the below.
(A) 
(B) 
(C) 
(D) 
(E) 
TEST 25
1. If 4 x + 5 = 20, what is the value of 4 x + 8?
(A) 3
(B) 7
(C) 16
(D) 23
(E) 30
2. If one serving of cereal is 
cup, how many servings are in 3 pints of cereal? (1 pint = 2 cups)
(A) 3
(B) 9
(C) 18
(D) 27
(E) 36
3. If the radius of the circle with center O below is 4, what is the length of arc RST?
(A) 2π
(B) 4π
(C) 8π
(D) 12π
(E) 16π
4. In the triangle below, what is the value of x?
(A) 7
(B) 7 
(C) 7 
(D) 14 
(E) 28
5. For x > 0, let ∇ x be defined by the equation ∇ x = 3 x − 3. Which of the following is equivalent to 
?
(A) ∇2
(B) ∇3
(C) ∇6
(D) ∇8
(E) ∇9
6. Stephanie can clean a pool in 1 hour, and Mark can clean the same pool in 1.5 hours. If the rate at which they work together is the sum of their rates working separately, how many minutes should they need to clean the pool if they work together? (1 hour = 60 minutes)
(A) 24 minutes
(B) 36 minutes
(C) 60 minutes
(D) 72 minutes
(E) 100 minutes
7. Which of the following has the greatest value?
(A) (1003)4
(B) (1005)(1006)
(C) (10,000)4
(D) (1002 × 1002)2
(E) (1,000,000)3
8. Line m (not shown) is the reflection of line l over the x -axis. What is the slope of line m?
(A) 3/2
(B) 2/3
(C) 0
(D) −2/3
(E) −3/2
9. If a 2 + b 2 = 4 and ab = 5, what is the value of (a + b)2?
(A) 10
(B) 12
(C) 14
(D) 16
(E) 18
10. The figure below shows the dimensions, in feet, of a stone slab. How many of these slabs are required to construct a rectangular patio 24 feet long and 12 feet wide?
(A) 18
(B) 20
(C) 24
(D) 36
(E) 48
11. $12,000 in winnings for a golf tournament were distributed in the ratio of 7:2:1 to the first, second, and third-place finishers, respectively. How much money did the first-place finisher receive?
(A) $1,200
(B) $1,700
(C) $2,400
(D) $8,400
(E) $10,000
12. If 2 x + 3 y = 7 and 4 x − 5 y = 12, what is the value of 6 x − 2 y?
(A) 5
(B) 8
(C) 15
(D) 17
(E) 19
13. If r and s are positive integers and s + 1 = 2 r, which of the following must be true?
I. s is odd
II. r is even
III. 
is an integer
(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II, and III
14. A bag contains six chips, numbered 1 through 6. If two chips are chosen at random without replacement and the values on those two chips are multiplied, what is the probability that this product will be greater than 20?
(A) 
(B) 
(C) 
(D) 
(E) 
15. In the sequence below, each term after the second is equal to the product of the two pre ceding terms. For example, the third term, −8, is the product of 2 and −4. How many of the first 100 terms of this sequence are negative?
2, -4, -8…
(A) 33
(B) 34
(C) 50
(D) 66
(E) 67
16. In the figure below, points C and D are midpoints of edges of a cube. A triangle is to be drawn with R and S as two of the vertices. Which of the following points should be the third vertex of the triangle if it is to have the largest possible perimeter?
(A) A
(B) B
(C) C
(D) D
(E) E
17. If 3 x + 5 x + 8 x = 32, what is the value of x?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
18. If 
(6 x) = 8, then x =
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
19. If 5 b −10 ≥ 15, which of the following expresses all of the possible values of b?
(A) b ≥ 5
(B) b ≥ 1
(C) b ≥ 9
(D) b ≤ 1
(E) b ≤ 5
20. If t % of 60 is equal to 30% of 50, what is the value of t?
(A) 12
(B) 15
(C) 25
(D) 30
(E) 35
21. If it takes 40 minutes to write h holiday cards, then in terms of h, how many holiday cards can be written at that rate in 8 hours?
(A) 
(B) 8 h
(C) 12 h
(D) 
(E) 
22. Which of the labeled points on the number line below could represent the product −1.5 ×1.25?
(A) A
(B) B
(C) C
(D) D
(E) E
23. If four people share 100 baseball cards and each person must receive a different positive whole number of cards, what is the greatest possible number of cards any one person may have?
(A) 28
(B) 29
(C) 94
(D) 95
(E) 97
24. Which of the following graphs best represents the data presented in the table below?
(A)
(B)
(C)
(D)
(E)
25. If the sum of seven integers is even, at most how many of these integers could be odd?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
26. In a particular year, if January 22 is the fourth Wednesday of the month, what is the date of the fourth Monday in January?
(A) January 20
(B) January 21
(C) January 26
(D) January 27
(E) January 28
27. The graph below shows the number of teachers in Hamden who live in a house, the number of teachers who live in an apartment, and the number of each who use gas or oil heat. Of the teachers who use gas heat, what fraction live in a house?
(A) 
(B) 
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