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MATH COUNTS 

MATH COUNTS . 2001 State Competition Countdown Round. 1. A delivery service increased its fee by 10% and then decreased its fee by 10% a month later. The fee was originally $15. What was the number of dollars in the fee after the decrease? Express your answer to the nearest cent.

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MATH COUNTS 

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  1. MATHCOUNTS 2001 State Competition Countdown Round

  2. 1. A delivery service increased its fee by 10% and then decreased its fee by 10% a month later. The fee was originally $15. What was the number of dollars in the fee after the decrease? Express your answer to the nearest cent.

  3. Answer: 14.85 (dollars)

  4. 2. If 2 inches represents 180 miles on a map, how many miles does 1 inches represent? 1 3 4 8

  5. Answer: 110 (miles)

  6. 3. A rectangular prism, with a square base of side length 6 feet, has a volume of 162 cubic feet. What is the number of feet in the height of the prism? Express your answer as a mixed number. 6 6

  7. Answer: 4 (feet) 1 2

  8. 4. What is the value of 3–1 + 2–2? Express your answer as a common fraction.

  9. Answer: 7/12

  10. 5. Let’s call a prime number a reversible prime if the number formed by reversing its digits is also prime. What is the smallest reversible prime greater than 17?

  11. Answer: 31

  12. 6. On a history exam, Alexia must answer 10 of 12 essay questions. How many different sets of questions can she choose?

  13. Answer: 66 (sets)

  14. 7. A horizontal line through point (–3, 4) and a vertical line through point (–1, –7) are drawn in a coordinate plane. What is the sum of the coordinates of the point of intersection of these two lines?

  15. Answer: 3

  16. 8. The rectangular plot with largest possible area has a perimeter of 86 feet. The plot has whole number dimensions and is enclosed with fencing. How many square feet are in the area of the plot?

  17. Answer: 462 (square feet)

  18. 9. A = {factors of 36}, B = {perfect squares}, andC = {odd numbers greater than 2}. What number is in all three sets?

  19. Answer: 9

  20. 10. Three positive integers have an arithmetic mean of 26 and a median of 27. If the median is 5 less than the largest integer, what is the smallest integer?

  21. Answer: 19

  22. 11. A container of eye drops contains 30 ml. The drops are used three times daily, and each time 0.05 ml is used in each eye. How many days will the container last?

  23. Answer: 100 (days)

  24. 12. What is the value of x for which |2x+3| is not positive? Express your answer as a common fraction.

  25. Answer: – 3 2

  26. 13. Janna’s average score on five 100-point tests was 80. Her score on the sixth test raised her mean score two points. How many points did she score on the sixth test?

  27. Answer: 92 (points)

  28. 14. What is the number of miles per hour in the average speed of a car that travels 210 miles in 3.5 hours?

  29. Answer: 60 (miles per hour)

  30. 15. From St. Louis, MO, Lewis and Clark start on bicycle trips from the same point at the same time. Lewis travels east at8 mph, and Clark travels south at 6 mph. After how many hours are they 60 miles apart?

  31. Answer: 6 (hours)

  32. 16. Four pieces of paper, one of each of the colors red, yellow, blue and green, are randomly selected without replacement. What is the probability that the yellow piece is drawn first and the blue piece is drawn last? Express your answer as a common fraction.

  33. Answer: 1 12

  34. 17. The diameter of a circle is increased so that the circumference increases by 20%. By what percent does the area increase?

  35. Answer: 44 (percent)

  36. 18. For what value of x does 212 = ( )x ? 1 8

  37. Answer: –4

  38. 19. What is the largest of four consecutive multiples of 6 if their mean is 27?

  39. Answer: 36

  40. 20. What is the common fraction equivalent to 0.045 ?

  41. Answer: 1 22

  42. 21. The sum of the digits of a two-digit number is 11. The difference between the number and the number with its digits reversed is 27. What is the sum of the original number and the number with its digits reversed?

  43. Answer: 121

  44. 22. A rectangular wall is being covered with 4-inch by 4-inch square tiles. How many tiles are needed to completely cover a wall that is 5 feet by 7 feet?

  45. Answer: 315 (tiles)

  46. 23. The product of three consecutive integers is 210. What is their sum?

  47. Answer: 18

  48. 24. Six points lie in a plane, no three of which are collinear. How many different triangles can be formed by connecting three of these points?

  49. Answer: 20 (triangles)

  50. 25. How many different integers can be expressed as the sum of two different numbers in the set {9, 12, 15, 18, 21, 24, 27, 30, 33}?

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