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## MATH COUNTS

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**MATHCOUNTS**2003 State Competition Countdown Round**3. A number is randomly selected from the first 20 positive**integers. What is the probability that it is divisible by 2, 3 or 4? Express your answer as a common fraction.**4. A tree is now 12 feet tall and grows 18 inches a year.**In how many years will the tree be 36 feet tall?**5. Stacey is standing in a field. She walks 11 meters west,**30 meters north, 4 meters west and finally 22 meters south. How many meters is she from her starting point?**7. Use each of the digits 3, 4, 6, 8 and 9 exactly once to**create the greatest possible five-digit multiple of 6. What is that multiple of 6?**8. The sum of the first and third of three consecutive**integers is 118. What is the value of the second integer?**9. A palindrome is a number that reads the same forward and**backward, such as 1331. What is the palindrome between 500 and 750 that is divisible by 3 and whose digits have a product of 200?**11. A candy bar weighs 4.48 ounces. A person eats half of**the bar with the first bite. If a person eats half of the amount remaining with each subsequent bite, how many bites have been taken when exactly 0.07 ounces remain?**12. Each corner of a cube is cut off to leave an equilateral**triangle as shown. How many faces does the new polyhedron have?**13. Everyone in a class of 30 students takes math**and history. Seven students received an A in history, 13 received an A in math and four received an A in both courses. How many students did not receive an A in either course?**14. What is the eighth term in thearithmetic sequence**Express your answer in simplestform.**15. The diagonals of a regular hexagon have two possible**lengths. What is the ratio of the shorter length to the longer length? Express your answer as a common fraction in simplest radical form.**16. What is the greatest integer value of n such that 3n <**10,000?**17. What is the units digit of the product of the first 100**prime numbers?**19. A regular pentagon is rotated counterclockwise about its**center. What is the minimum number of degrees it must be rotated until it coincides with its original position?**21. Dora has three candles, which will burn for 3, 4 and**5 hours, respectively. If she wants to keep two candles burning at all times, what is the greatest number of hours she can burn the candles?**22. What is the expression for the area of the circle which**has a circumference of C? Express your answer as a rational expression in terms of C and .**23. Mary completes a 15-mile race in 2.5 hours. What is her**average speed in miles per hour?**25. How many digits are in the whole-number representation**of 10100 – 9100?