MATHCOUNTS  2001 Chapter Competition Countdown Round

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Transcript of MATHCOUNTS  2001 Chapter Competition Countdown Round

  • MATHCOUNTS2001 Chapter CompetitionCountdown Round

  • 1. Three coins are flipped. What is the probability that all three coins land heads? Express your answer as a common fraction.

  • Answer:

  • 2. How many positive integers have exactly three digits?

  • Answer: 900 (integers)

  • 3. A bookstore employee is given a 30% discount off the retail price of any book. How many dollars does she pay for a book with a retail price of $40?

  • Answer: 28 (dollars)

  • 4. How many prime numbers are between 20 and 30?

  • Answer: 2 (numbers)

  • 5. The number 12 can be written as the sum of eight consecutive integers. What is the product of these integers?

  • Answer: 0

  • 6. Fifteen is twenty percent of what number?

  • Answer: 75

  • 7. When Monique visited Australia, the American dollar was equivalent to 1 Australian dollars. She purchased a sweater priced at 30 Australian dollars. What was the equivalent number of American dollars?

  • Answer: 20 (dollars)

  • 8. What is the greatest common factor of 32 and 48?

  • Answer: 16

  • 9. What is the sum of the mean and the median of the set {15, 17, 19, 21, 23} ?

  • Answer: 38

  • 10. If x is 125% of y, then what percent of x is 2y?

  • Answer: 160 (percent)

  • 11. When all two-digit positive integers are written, what fraction of the digits written are 3s? Express your answer as a common fraction.

  • Answer:

  • 12. License plates are issued that contain four digits followed by one letter. If the letters O and I cannot be used, how many different license plates are possible?

  • Answer: 240,000 (plates)

  • 13. A bus can hold a maximum of 38 students. What is the minimum number of buses needed to transport 411 students?

  • Answer: 11 (buses)

  • 14. How many terms does the arithmetic sequence 15, 20, 25, 30, ..., 95 have?

  • Answer: 17 (terms)

  • 15. J.C. rode her bike for 1 hours at 12 miles per hour, and then rode for 1 hours at 8 miles per hour. What is the total number of miles she rode?

  • Answer: 33 (miles)

  • 16. What is the number of square centimeters in the surface area of a rectangular prism whose length is 3 cm, whose width is 4 cm, and whose height is 5 cm?

  • Answer: 94 (square centimeters)

  • 17. Find the integer closest to .

  • Answer: 9

  • 18. Twenty-five percent of the entrants in a marathon did not finish the race. If 375 finished, how many entrants were there?

  • Answer: 500 (entrants)

  • 19. How many different two-letter monograms are possible if letters may be repeated?

  • Answer: 676 (monograms)

  • 20. The product of two consecutive odd whole numbers is 255. What is the greater number?

  • Answer: 17

  • 21. For a concert, 72 fans attempted to get tickets. That was 60% more than the number of tickets available. How many tickets were available?

  • Answer: 45 (tickets)

  • 22. How many diagonals does a regular hexagon have?

  • Answer: 9 (diagonals)

  • 23. If the price of a stamp is 33, what is the maximum number of stamps that could be purchased with $32?

  • Answer: 96 (stamps)

  • 24. Set A contains 15 elements, set B contains 12 elements, and the intersection of the sets contains 8 elements. How many elements are in the union of the sets?

  • Answer: 19 (elements)

  • 25. What is the number of edges in a regular hexagonal prism?

  • Answer: 18 (edges)

  • 26. A racer travels 5000 meters in 1 minutes. What is the racers average speed in kilometers per hour?

  • Answer: 180 (kilometers per hour)

  • 27. A plane is flying at an altitude of 22,000 feet when it begins to descend at a constant rate of 2000 feet per minute. What is its altitude, in feet, after 75 seconds?

  • Answer: 19,500 (feet)

  • 28. A woman spent $57 on a skirt and a sweater. If the sweater cost twice as much as the skirt, how many dollars were in the price of the skirt?

  • Answer: 19 (dollars)

  • 29. If 50% of a number is 26, what is 150% of the number?

  • Answer: 78

  • 30. How many eight-pound weights are needed to balance 12 twelve-pound weights?

  • Answer: 18 (weights)

  • 31. What common fraction of a class is boys if 15 of the 40 students are girls?

  • Answer:

  • 32. The ratio of the number of boys to the number of girls in Ms. Moores class is 3:4. There are 56 students in the class. How many students are girls?

  • Answer: 32 (students)

  • 33. What is the number of square meters in the area of a square if the length of a diagonal is 18 meters?

  • Answer: 162 (square meters)

  • 34. Walking at a constant pace, Jill walks 5 miles in 1 hour and 20 minutes. At this rate, how many minutes does it take her to walk 1 mile?

  • Answer: 16 (minutes)

  • 35. What is the number of square centimeters in the area of a square whose perimeter is 12 cm?

  • Answer: 9 (square centimeters)

  • 36. Football tickets cost $13.50 each. What is the maximum number of tickets Jane can buy with $100.00?

  • Answer: 7 (tickets)

  • 37. What is the value of 100 81 + 64 49 + 36 25 + 16 9 + 4 1?

  • Answer: 55

  • 38. The sum of two positive integers is 124. What is the value of the greatest possible quotient of these two integers?

  • Answer: 123

  • 39. What is the probability of rolling a sum of 7 or 11 by tossing two fair dice? Express your answer as a common fraction.

  • Answer:

  • 40. What is the value of 3 3 + 3(3+3) 33?

  • Answer: 0

  • 41. If 9 is added to three times a number, the result is 90. What is five times the number divided by 9?

  • Answer: 15

  • 42. Joes bowling scores were 112, 182 and 142. What does he need to score in his fourth game to get a mean score of 132?

  • Answer: 92

  • 43. After losing 10% of his weight, a wrestler weighed 135 pounds. What was his original weight in pounds?

  • Answer: 150 (pounds)

  • 44. Twice a number is one-halfof 48. What is the number?

  • Answer: 12

  • 45. A map is drawn to a scale of 3/4 in = 100 mi. How many inches are in the line segment used to represent 800 miles?

  • Answer: 6 (inches)

  • 46. In rectangle ABCD with diagonals AC and BD intersecting at E, what is the ratio of the area of BEC to the area of BDC? Express your answer as a common fraction.

  • Answer:

  • 47. What is the range of the set {112, 124, 136, 148, 160} ?

  • Answer: 48

  • 48. The sum of two positive integers is 50 and their difference is 12. What is the value of the positive difference of the squares of the integers?

  • Answer: 600

  • 49. In how many ways can a person enter a room with 5 doorways and leave through a different doorway?

  • Answer: 20 (ways)

  • 50. If , what is the arithmetic mean of and ?m0mm+3mm

    3

  • Answer: 1

  • 51. A worker bee collects enough nectar in its lifetime to make of a pound of honey. How many bees are needed to collect 5 pounds of honey?

  • Answer: 55 (bees)

  • 52. A box is one-third full of marbles. If one-fourth of the marbles are removed, what percent of the box is filled with marbles?

  • Answer: 25 (percent)

  • 53. A pentagonal train is created by adjoining congruent pentagons with sides of 1 unit each. A pentagonal train of 10 pentagons is constructed. What is the number of units in the perimeter of the resulting polygon?

  • Answer: 32 (units)

  • 54. What is the base-ten number represented by the base-eight number 31?

  • Answer: 25

  • 55. Paul plans to rotate the five tires on his new four-wheel truckso that each tire will have the same number of miles when the odometer reads 20,000 miles. How many miles will be on each of the tires?

  • Answer: 16,000 (miles)

  • 56. The value of the determinant

    What is the value of x if2-3x6=-12 ?

  • Answer: 8

  • 57. It takes Bryan one hour to dig a hole that is 1.4 meters wide, 1.5 meters long and 0.5 meters deep. At the same rate, how many hours will it take Bryan to dig a hole that is 2.8 meters wide, 3.0 meters long and 1.0 meters deep?

  • Answer: 8 (hours)

  • 58. The city of Alexandria posted a high temperature of 18o F and a low temperature of 5o F on the same day. By how many degrees did the high temperature exceed the low temperature?

  • Answer: 23 (degrees)

  • 59. Given a b = a2 + 2ab + b2, what is the value of a b when a = 4 and b = 6?

  • Answer: 100

  • 60. A car travels 30 miles per gallon of gasoline. If gasoline costs $1.25 per gallon, how many dollars will it cost to travel 480 miles?

  • Answer: 20 (dollars)

  • 61. From a group of four boys and two girls, two children are selected at random. What is the probability that the second child selected is a girl? Express your answer as a common fraction.