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2016 School Competition Countdown Round

MATH COUNTS . 2016 School Competition Countdown Round. Please note that videotaping, photographing, reproducing or publishing the following questions or answers is strictly prohibited. A sample question follows that you are allowed to reproduce. Sample Question.

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2016 School Competition Countdown Round

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  1. MATHCOUNTS 2016 School Competition Countdown Round

  2. Please note that videotaping, photographing, reproducing or publishing the following questions or answers is strictly prohibited. A sample question follows that you are allowed to reproduce.

  3. Sample Question If the price of a stamp is 33¢, what is the maximum number of stamps that could be purchased with $32?

  4. Sample Question Answer: 96 (stamps)

  5. MATHCOUNTS 2016 School Competition Countdown Round

  6. 1. Misha’s favorite number is even. Her favorite number is also non-negative and less than 1. What is Misha’s favorite number?

  7. Answer: 0

  8. 2. A car is averaging 50 miles per hour. If the car maintains this speed, how many minutes less would a 450-mile trip take than a 475-mile trip?

  9. Answer: 30 (minutes)

  10. 3. Three coplanar circles intersect as shown. What is the maximum number of points on the circles that a line passing through all three circles can touch?

  11. Answer: 6 (points)

  12. 4. An equilateral triangle and a square have the same perimeter of 12 inches. What is the ratio of the side length of the triangle to the side length of the square? Express your answer as a common fraction.

  13. Answer:

  14. 5. If 2x + y = 8, what is the value of 4x + 2y?

  15. Answer: 16

  16. 6. Climbing the first flight of stairs takes Jimmy 20 seconds, and each following flight takes 5 seconds more than the preceding one. How many total seconds does it take to climb the first five flights of stairs?

  17. Answer: 150 (seconds)

  18. 7. If a + b = c and b + c = 11 and c = 8, what is the value of a?

  19. Answer: 5

  20. 8. What is the greatest three-digit integer in which the product of the digits is 0?

  21. Answer: 990

  22. 9. Steve will write the list of consecutive integers, starting with 1, at the speed of 5 digits per second. What will be the sum of the final two digits he writes on his list at the end of 10 seconds?

  23. Answer: 12

  24. 10. The fenced area of a yard is a 15-foot by12-foot rectangular region with a 3-foot by 3-foot square cut out, as shown. What is the area of the region within the fence, in square feet? 15’ 12’ 3’ 3’

  25. Answer: 171 (ft2)

  26. 11. When 700 students from Genius M.S. played SCOOZ, 90% of them scored “proficient or above.” What number of students at Genius M.S. did not score “proficient or above?”

  27. Answer: 70 (students)

  28. 12. If the operation Z is defined as a Z b = b + 10a-a2, what is the value of 2 Z 6?

  29. Answer: 22

  30. 13. Aditi can walk 1.7 miles in half an hour. At the same constant speed, how many hours would it take her to walk 17 miles?

  31. Answer: 5 (hours)

  32. 14. A right hexagonal prism has a height of 3 feet and each edge of the hexagonal bases is 6 inches. What is the sum of the areas of the non-hexagonal faces of the prism, in square feet?

  33. Answer: 9 (ft2)

  34. 15. What common fraction is halfway between and on a number line?

  35. Answer:

  36. 16. A rectangular quilt’s length is twice the length of a rectangular picture, and the quilt’s width is three times the width of the same picture. The area of the picture is 2 square feet. What is the area of the quilt, in square feet?

  37. Answer: 12 (ft2)

  38. 17. Each year, starting with 1999, five new state quarter designs were introduced. How many different state quarter designs were introduced by the end of 2005?

  39. Answer: 35 (designs)

  40. 18. In a convex quadrilateral, the measure of the largest angle is twice the measure of the smallest angle, and the other two angles are both right angles. How many degrees are in the largest angle?

  41. Answer: 120 (degrees)

  42. 19. What is the sum of the six positive integer factors of 18?

  43. Answer: 39

  44. 20. Lyndy conducted a survey of the 300 students in her school. She found that 60 students own dogs, while only 30 students own cats. What percent of the students own cats?

  45. Answer: 10 (percent)

  46. 21. Max must take 10 steps to go the same distance as three of his dad’s steps. His dad takes 30 steps to walk down the hall. How many steps must Max take to walk down the same hall?

  47. Answer: 100 (steps)

  48. 22. The area of a rectangle is 80 ft2. If the width is increased by 1 foot and the length is decreased by 1 foot, the new rectangle has area 90 ft2. What is the perimeter of the original rectangle, in feet?

  49. Answer: 42 (feet)

  50. 23. In a round-robin tournament with n teams, the number of games that must be played is . How many teams are in a round-robin tournament in which 55 games are played?

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