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MATH COUNTS

MATH COUNTS. . 2004 School Competition Countdown Round. 1. Marie owns 103 department stores. Each store has 106 shelves for towels. What is the total number of shelves for towels?. Answer: 10,918 (shelves).

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MATH COUNTS

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  1. MATHCOUNTS  2004 School Competition Countdown Round

  2. 1. Marie owns 103 department stores. Each store has 106 shelves for towels. What is the total number of shelves for towels?

  3. Answer: 10,918 (shelves)

  4. 2. When 5 is subtracted from three times a number, the result is 7. What is the number?

  5. Answer: 4

  6. 3. The Battling Hummingbirds have won 40% of their first 60 games. If they win their next 12 games in a row, what percent of all of their games will they have won?

  7. Answer: 50 (percent)

  8. 4. A 3-foot tall flower-stand casts a 9-foot shadow. At the same time, a nearby tree casts a 51-foot shadow. How many feet tall is the tree?

  9. Answer: 17 (feet)

  10. 5. Two boxes, A and B, contain pennies. In box A, there are nine more pennies than in box B. The total number of pennies in boxes A and B is 41. What is the number of pennies in box A?

  11. Answer: 25 (pennies)

  12. 6. What is the sum of the first five positive odd integers?

  13. Answer: 25

  14. 7. Trae is searching for a treasure on the beach. From point A, he is told to walk two meters north, three meters east, and then two meters north to point B. In meters, what is the length of ?

  15. Answer: 5 (meters)

  16. 8. Mr. Cole is driving at his favorite speed of 55 miles per hour. He is 125 miles from his destination. His goal is to arrive at his destination in two hours. How many miles per hour faster than his preferred speed must he drive to meet his goal? Express your answer as a decimal to the nearest tenth.

  17. Answer: 7.5 (miles per hour)

  18. 9. What number is one hundred less than one thousand thirty-three?

  19. Answer: 933

  20. 10. What is the degree measure of the angle between the hour hand and the minute hand of a clock at exactly 2:30 p.m. on a 12-hour analog clock?

  21. Answer: 105 (degrees)

  22. 11. Katrina can bicycle 50 miles in four hours. At the same speed, how many miles does she bicycle in six hours?

  23. Answer: 75 (miles)

  24. 12. What is the least positive integer that has exactly three distinct factors?

  25. Answer: 4

  26. 13. The cube of what integer is closest to 800?

  27. Answer: 9

  28. 14. In a state senate, there are 24 Democrats, 32 Republicans, and 4 Independents. If one senator is selected at random, what is the probability that the senator is a Republican? Express your answer as a common fraction.

  29. Answer:

  30. 15. The sum of x and y is 11 and the positive difference between x and y is 3. What is the value of the product of x and y?

  31. Answer: 28

  32. 16. The total value of 90 pennies, 20 dimes and 12 quarters is what percent of the value of a ten-dollar bill?

  33. Answer: 59 (percent)

  34. 17. Solve for x: 18 - x = 10 + x.

  35. Answer: 4

  36. 18. An 8 cm by N cm rectangle has a diagonal of length 10 cm. What is the number of centimeters in the perimeter of this rectangle?

  37. Answer: 28 (centimeters)

  38. 19. The histogram shows the numbers of types of the 50 pets reported by the 7th graders in a school. What percent of the pets are cats? 20 15 10 5 Dogs Cats Fish Birds

  39. Answer: 40 (percent)

  40. 20. What is the sum of the reciprocals of the distinct positive factors of 8? Express your answer as a mixed number.

  41. Answer:

  42. 21. What is the number of degrees in the measure of angle ABD in square ABCD?

  43. Answer: 45 (degrees)

  44. 22. What is the units digit of 62004?

  45. Answer: 6

  46. 23. Triangle ABC is isosceles with angle B congruent to angle C. The measure of angle C is four times the measure of angle A. What is the number of degrees in the measure of angle B?

  47. Answer: 80 (degrees)

  48. 24. What integer is closest to ?

  49. Answer: 14

  50. 25. Sixty percent of a number is 40 less than the number. What is the number?

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