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2019 School Competition Countdown Round

MATH COUNTS . 2019 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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2019 School Competition Countdown Round

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  1. MATHCOUNTS 2019 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 2019 School Competition Countdown Round

  6. 1. What is the units digit when 54 is expressed as an integer?

  7. Answer: 5

  8. 2. What is the quotient when 3 is divided by its reciprocal?

  9. Answer: 9

  10. 3. The complement of angle M has measure 10 degrees. What is the degree measure of angle M?

  11. Answer: 80 (degrees)

  12. 4. Stephen has four blue socks and six gray socks in a drawer. What is the least number of socks he must select, at random, to guarantee having at least two socks of the same color?

  13. Answer: 3 (socks)

  14. 5. In the land of Ink, the money system is unique. One Trinket is equal to 4 Blinkets, and 3 Blinkets are equal to 7 Drinkets. In Trinkets, what is the value of 56 Drinkets?

  15. Answer: 6 (Trinkets)

  16. 6. An integer is tripled, and the result is divided by 2. When the new result is reduced by 1, the final result is 11. What was the original integer?

  17. Answer: 8

  18. 7. The acute angles of a particular isosceles trapezoid each measure 40 degrees. What is the measure, in degrees, of each obtuse angle in the trapezoid?

  19. Answer: 140 (degrees)

  20. 8. How many distinct prime divisors does 56 have?

  21. Answer: 2 (divisors)

  22. 5 2 9. The quotient of two positive integers is and their product is 160. What is the value of the larger of the two integers?

  23. Answer: 20

  24. 10. During a year when Thanksgiving is on Thursday, November 23, on what day of the week does December 23 occur?

  25. Answer: Saturday

  26. 11. A particular convex pentagon has two congruent acute angles. The measure of each of the other interior angles is equal to the sum of the measures of the two acute angles. What is the common measure of the large angles, in degrees?

  27. Answer: 135 (degrees)

  28. 12. Define the operation ☼ as K ☼ L = (K + L)(K − L) for all integers K and L. What is the value of 6 ☼ 5?

  29. Answer: 11

  30. 13. Margaret started a stamp collection. She collected 8 stamps the first day. Each subsequent day she collected 8 more stamps than she collected the previous day. If she collected stamps for 5 consecutive days, what was the average number of stamps she collected per day?

  31. Answer: 24 (stamps)

  32. 14. A 2-cup mixture is flour and cornmeal. If 1 cup of flour is added to the 2-cup mixture, what fraction of the new 3-cup mixture is flour? Express your answer as a common fraction. 1 3 2 3

  33. 5 9 Answer:

  34. 15. What is the value of 8(−6) + 8(10) − 8(4)?

  35. Answer: 0

  36. 16. On a certain farm, each chicken has two feet and each rabbit has four feet. If the combined number of chickens and rabbits on the farm is 100 and there are a total of 260 feet on these animals, how many chickens are there?

  37. Answer: 70 (chickens)

  38. 17. Angie’s class has 2 girls for every 3 boys. If there are 20 students in the class, how many girls are in Angie’s class?

  39. Answer: 8 (girls)

  40. 18. What is the area, in square units, of a rectangle with side lengths 15 and 16 units?

  41. Answer: 240 (units2)

  42. 19. Ivory successfully shot 7 free throws in 15 free-throw attempts. How many additional successful free throws, without a miss, must she make in order to attain a success rate of 75%?

  43. Answer: 17 (free throws)

  44. 20. Jeremiah is riding in a car that is traveling 60 mi/h. At this rate, how many minutes will it take him to travel 20 miles?

  45. Answer: 20 (minutes)

  46. 21. How many unique diagonals can be drawn in a five-sided convex polygon?

  47. Answer: 5 (diagonals)

  48. 22. What is the units digit of 313 + 133?

  49. Answer: 8

  50. 23. What is the smallest integer side length, in units, of a square whose area is numerically greater than its perimeter?

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