*For each of the following questions, carefully blacken the appropriate box on the answer sheet with a #2 pencil. Do not fold, bend or write stray marks on either side of the answer sheet. Each correct answer is worth 4 points. Two points are deducted for each incorrect answer. Zero points are given if no box, or more than one box, is marked. Note that wild guessing is apt to lower your score.*

1. Rank the following three numbers in order:
x=2001/2002 y=2002

^{ 1/2002 }z=(-2003)^{2003}.
a. x< y < z b. y < x < z c. y < z <
x d. z < y < x e. z < x < y

2. Today my son is 1/3 of my age. Five years ago he was 1/4
of my age back then. How old is my son now?

a. 12 b. 15 c. 17 d. 20 e.
21

3. For exactly which values of x is |2x-4|< = 6?

a. all x b. 2< = x< = 4 c. 1 < = x < =
5 d. -1 < = x < = 5 e. all x < = 2

4. Which of the following points lies on the line passing
through the points (1,1) and (2,3)?

a. (5,7) b. (7,5) c. (6,11) d.
(-1,5) e. (0,0)

5. Snow White and the seven dwarfs went to work as
carpenters. Each dwarf earned $20. Snow White earned $3.50 more than the
average of the eight. How much did Snow White earn?

a. $21 b. $23.50 c. $24 d. $30
e. $31.50

6. The line y=3-x intersects the parabola y=3x-x

^{2}in two points (x_{ 1},y_{ 1}) and (x_{ 2},y_{ 2}). What is y_{ 1}+y_{ 2}?
a. 2 b. 3 c. 5 d. 6 e. 7

7. Let a and b be the lengths of two legs of a right
triangle and let c be the length of the hypotenuse. Let A be the area of a
circle with radius a, B be the area of a circle with radius b, and C be the
area of a circle with radius c. Which of the following equations must be true?

a. C=A+B b. C=(A+B)/pi c. C

^{ 2}=A^{ 2}+B^{ 2}d. C^{ 2}=(A^{ 2}+B^{ 2})/pi e. C^{ 2}=(A^{ 2}2+B^{ 2})/pi^{ 2}
8. Find x so that log

_{ 2}(2)+log_{ 3}(9)=log_{ 4}(x).
a. 1 b. 3 c. 4 d. 16 e. 64

9. If 7 Muppets can eat 7 cookies in 7 minutes, how many
cookies could 14 Muppets eat in 14 minutes? (Assuming they have an adequate
supply of milk.)

a. 14 b. 21 c. 28 d. 35 e.
42

10. (sin x + cos(-x))

^{ 2}is equal to
a. 1+sin(2x) b. 1 c. 0 d.
1-sin(2x) e. sin(x+pi/2)

11. A bee woke up on a Sunday morning and went directly to
work. It flew straight south for 1 hour to a nice sweet field and spent 30 min
there. Then it went directly west for 3/4 hour to a garden where it stayed for
1 hour. After that it flew the shortest path home. Assuming that the bee flew
with constant speed and that the earth is flat, for how long was the bee away
from home?

a. 4 hours b. 4.5 hours c. 5.2 hours d.
7.2 hours e. 8 hours

12. If the quadratic equation x

^{ 2}+bx+c=0 has exactly one solution r then b/c is equal to
a. -2/r

^{ 2}b. -2/r c. 1 d. 2/r^{ 2}e. 2/r
13. The area of a regular 2002-gon of perimeter 1 is
approximately

a. 1/2 b. 1/3 c. 1/6 d. 1/12
e. 1/24

14. Professor Ding-Dong likes to eat chocolates for an
afternoon snack. On Monday morning he brings in a bag of 5 chocolates, 3 with
red wrappers and 2 with green wrappers. At snack time every day, he reaches
into the bag, pulls one out and eats it. What is the probability that the
chocolate he eats on Friday will have a red wrapper?

a. 1/5 b. 1/3 c. 2/5 d. 1/2
e. 3/5

15. Nine pens cost eleven dollars and x cents, thirteen
pens cost fifteen dollars and y cents. Find (x,y).

a. (13,71) b. (70,37) c. (7,63) d.
(7,99) e. (99,13)

16. The number 2002 is a palindrome since its digits are the
same when read forward or backward. The number 1 is also a palindrome. How many
integers between 1 and 2002 (inclusive) are palindromes?

a. 65 b. 83 c. 99 d. 109 e.
119

17. How many triples of real numbers (x,y,z) are there such
that xy=z, xz=y and yz=x?

a. 2 b. 3 c. 4 d. 5 e. 6

18. Sparrows have two feet, four toes per foot, and one
beak. George says to Martha: ``In that collection of sparrows there are N more
toes than beaks.'' Martha replies: ``No George, I know that you are
wrong." Find a value of N so that Martha's statement must be correct.

a. 21 b. 28 c. 80 d. 350 e.
2002

19. Find the appropriate base b so that the number 95

_{b}in base b is equal to 140 in base 10.
a. 11 b. 15 c. 18 d. 22 e.
135

20. In a certain city there are 7 avenues going north-south
and 4 streets going east-west. How many paths are there that only travel on
roads, start at the southwest corner of the city, end at northeast corner of
the city and have the shortest possible length?

a. 18 b. 21 c. 28 d. 84 e.
330

21. Twelve people are equally spaced around a large circle.
What is the largest number of wires that can be stretched between pairs of
people so that no two wires intersect at any point inside the circle?

a. 11 b. 12 c. 21 d. 23 e.
110

22. A train that is one mile long is moving at a constant
speed. A rabbit, who runs faster than the train, starts at the back of the
train and runs alongside until it reaches the front of the train. At that instant,
it immediately turns around and runs back (at the same rate) until it again
reaches the back of the train. At that instant, the back of the train is now
precisely where the front of the train was when the rabbit started running. In
total, how far did the rabbit run?

a. 1+2

^{ 1/2}miles b. 2 miles c. 1+5^{ 1/2}miles d. 2(5^{ 1/2}-1) miles e. 2 (2^{ 1/2}) miles
23. What is the smallest positive integer a for which there
is an integer c and a right triangle with side lengths a and 17 and hypotenuse
of length c?

a. 1 b. 8 c. 16 d. 39 e.
144

24. Starting January 1 the first dwarf visits Snow White
every day. The second dwarf visits Snow White on January 2 and every second day
therafter. The pattern continues for each of the seven dwarfs (i.e., the
seventh dwarf visits Snow White on January 7 and every seventh day thereafter).
What is the total number of dwarf visits up to and including the first day when
all seven dwarfs visit Snow White?

a. 28 b. 42 c. 105 d. 420
e. 1089

25. Three problems were given to participants of a math
contest. Each participant got 0,1,2, or 3 points for each problem. After the
papers were graded it turned out that no pair of participants received matching
scores for more than one problem. What is the largest possible number of
participants?

a. 8 b. 9 c. 12 d. 16 e. 24

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