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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 2 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 7 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 16 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 17