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PMWC Qualifying Test
November 14, 2003
Directions: This test has 15 problems, with a limit of 120 minutes. Show all
your work on the test, and how you obtained your answer. Partial credit
will be given if you do not obtain your answer. Do not worry if you cannot
do all the problems. We are more interested in how you approached
each problem.
1. How many numbers of the form 100a +10b + c can be written
if a >b > c?
Answer: ____________
Work:
1
PMWC Qualifying Test
November 14, 2003
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2. Question. Suppose
(2 3x )
2 2003
= C0 + C1 x + C2 x 2 +…+ C4006 x 4006 where Ci is the x i coefficient
in the expansion of (2 3x 2 )
Answer: ____________
Work:
2003
. Find the value for C0 + C1 + C2 +…+ C4006 .
PMWC Qualifying Test
November 14, 2003
3. One half of the class watched a soccer match on television this weekend. Only
3/8 of the girls watched, but 3/5 of the boys watched the match. What fraction
of the class are girls?
Answer: ___________
Work:
3
PMWC Qualifying Test
November 14, 2003
4. An isosceles trapezoid has base AB = 18 and base CD = 12. Find its area if
diagonal AC = 17.
Answer: _______________
Work:
4
PMWC Qualifying Test
November 14, 2003
5. A store will give a surprise gift with any purchase totaling $ 25 dollars or more.
The store has 6 items you like, with prices of $2, $3, $7, $9, $11 and $24. How
many selections can you make from items you like to qualify for the gift, if you
will not purchase two of the same items?
Answer: ____________
Work:
5
PMWC Qualifying Test
November 14, 2003
6. A and B are tied 20 – 20 in a ping-pong match. The first player to lead by 2
points will win. How many scoring sequences after the 20 – 20 tie will lead to
A winning 30 – 28?
Answer: ____________
Work:
6
PMWC Qualifying Test
November 14, 2003
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7. Pentagon ABCDE has AB = 16 and BC = EA = 10. If EC is parallel to AB with EC
= 28
and AD = BD = 17, what is the area of the pentagon?
Answer: ____________
Work:
PMWC Qualifying Test
November 14, 2003
8. In how many ways can 4 concentric disks of different diameters be stacked in 3
piles A, B and C if no disk may placed on top of a smaller disk. You do not
have to have a disk in every pile.
Answer: ____________
Work:
8
PMWC Qualifying Test
November 14, 2003
9. Points D and E lie on sides AB and BC respectively of triangle ABC. If
AD = 2DB, CE = 3EB and F is the midpoint of CD, what is the ratio of the
area of ADEF to the area of ABC?
Answer: ____________
Work:
9
PMWC Qualifying Test
November 14, 2003
10. Consider a set of all four-digit numbers in which the digits are x, x+2, x+4 and
x+6. What is the probability that a number in the set is a multiple of 5?
Answer: ____________
Work:
10
PMWC Qualifying Test
November 14, 2003
11. Nine identical balls with a radius of 1 unit are packed in a box that has a base
that is 4 units by 4 units and a height of h units. What is the minimum value
of h so that the top of the box can be closed?
Answer: ____________
Work:
11
PMWC Qualifying Test
November 14, 2003
12. How many integers between 1000 and 9999 use exactly 2 different digits?
Answer: ____________
Work:
12
PMWC Qualifying Test
November 14, 2003
13. Team A is favored by odds of 3 to 2 when it plays against Team B. In a series
of games between the two teams, what is the probability that Team B is the first
to win three games?
Answer: ____________
Work:
13
PMWC Qualifying Test
November 14, 2003
14. How many moves are required to transfer the four disks from peg A to peg C
with the following rules: A move consists of transferring a disk between
adjacent pegs, for example, between peg A and peg B, or between pegs B and
C. At no time can a larger disk lie on top of a smaller disk.
Answer: ____________
Work:
14
PMWC Qualifying Test
November 14, 2003
15. At a carnival booth, you are allowed to throw a ball 3 times at a target. You
must hit the target twice in a row to win. You must alternate between throwing
with your right and left hand. You may start with whichever hand you wish.
You hit the target 6/10 of the time with your right hand and 3/10 of the time
with you left hand. What is the probability of winning if you make the best
choice of starting hand?
Answer: ____________
Work:
15
PMWC Qualifying Test
November 14, 2003
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Texas Mathworks
Texas State University – San Marcos
Primary Mathematics World Contest (PMWC)
Qualifying Test
November 13, 2003
COVER SHEET
Name: _______________________________________________________
Street Address:________________________________________________
City:_______________________ State: ________ Zip: ______________
Phone: (______) ___________________________
School: ______________________________________________________
Teacher: _____________________________________________________
Present Grade in School: ________________
Math Courses Taken:
Pre-Algebra_____ Algebra 1 _____ Algebra 2 _____ Geometry _____
Birthdate (Including year): _____- _____ - _____
Social Security Number: ____________________
Are you a U.S. Citizen? Yes_____ No _____
PMWC Qualifying Test
November 14, 2003
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