![Page 1: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/1.jpg)
MATHCOUNTS
2001 Chapter Competition
Countdown Round
![Page 2: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/2.jpg)
1. Three coins are flipped. What is the probability that all three coins land heads? Express your answer as a common fraction.
![Page 3: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/3.jpg)
Answer: 1
8
![Page 4: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/4.jpg)
2. How many positive integers have exactly three digits?
![Page 5: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/5.jpg)
Answer: 900 (integers)
![Page 6: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/6.jpg)
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?
![Page 7: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/7.jpg)
Answer: 28 (dollars)
![Page 8: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/8.jpg)
4. How many prime numbers are between 20 and 30?
![Page 9: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/9.jpg)
Answer: 2 (numbers)
![Page 10: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/10.jpg)
5. The number 12 can be written as the sum of eight consecutive integers. What is the product of these integers?
![Page 11: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/11.jpg)
Answer: 0
![Page 12: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/12.jpg)
6. Fifteen is twenty percent of what number?
![Page 13: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/13.jpg)
Answer: 75
![Page 14: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/14.jpg)
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?
12
![Page 15: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/15.jpg)
Answer: 20 (dollars)
![Page 16: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/16.jpg)
8. What is the greatest common factor of 32 and 48?
![Page 17: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/17.jpg)
Answer: 16
![Page 18: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/18.jpg)
9. What is the sum of the mean and the median of the set {15, 17, 19, 21, 23} ?
![Page 19: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/19.jpg)
Answer: 38
![Page 20: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/20.jpg)
10. If x is 125% of y, then what percent of x is 2y?
![Page 21: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/21.jpg)
Answer: 160 (percent)
![Page 22: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/22.jpg)
11. When all two-digit positive integers are written, what fraction of the digits written are 3’s? Express your answer as a common fraction.
![Page 23: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/23.jpg)
Answer: 19
180
![Page 24: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/24.jpg)
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?
![Page 25: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/25.jpg)
Answer: 240,000 (plates)
![Page 26: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/26.jpg)
13. A bus can hold a maximum of 38 students. What is the minimum number of buses needed to transport 411 students?
![Page 27: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/27.jpg)
Answer: 11 (buses)
![Page 28: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/28.jpg)
14. How many terms does the arithmetic sequence 15, 20, 25, 30, ..., 95 have?
![Page 29: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/29.jpg)
Answer: 17 (terms)
![Page 30: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/30.jpg)
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?
12
34
![Page 31: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/31.jpg)
Answer: 33 (miles)
![Page 32: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/32.jpg)
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?
4
53
![Page 33: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/33.jpg)
Answer: 94 (square centimeters)
![Page 34: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/34.jpg)
17. Find the integer closest
to .7003
![Page 35: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/35.jpg)
Answer: 9
![Page 36: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/36.jpg)
18. Twenty-five percent of the entrants in a marathon did not finish the race. If 375 finished, how many entrants were there?
![Page 37: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/37.jpg)
Answer: 500 (entrants)
![Page 38: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/38.jpg)
19. How many different two-letter monograms are possible if letters may be repeated?
![Page 39: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/39.jpg)
Answer: 676 (monograms)
![Page 40: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/40.jpg)
20. The product of two consecutive odd whole numbers is 255. What is the greater number?
![Page 41: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/41.jpg)
Answer: 17
![Page 42: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/42.jpg)
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?
![Page 43: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/43.jpg)
Answer: 45 (tickets)
![Page 44: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/44.jpg)
22. How many diagonals does a regular hexagon have?
![Page 45: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/45.jpg)
Answer: 9 (diagonals)
![Page 46: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/46.jpg)
23. If the price of a stamp is 33¢, what is the maximum number of stamps that could be purchased with $32?
![Page 47: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/47.jpg)
Answer: 96 (stamps)
![Page 48: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/48.jpg)
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?
![Page 49: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/49.jpg)
Answer: 19 (elements)
![Page 50: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/50.jpg)
25. What is the number of edges in a regular hexagonal prism?
![Page 51: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/51.jpg)
Answer: 18 (edges)
![Page 52: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/52.jpg)
26. A racer travels 5000 meters in 1 minutes. What is the racer’s average speed in kilometers per hour?
23
![Page 53: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/53.jpg)
Answer: 180 (kilometers per hour)
![Page 54: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/54.jpg)
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?
![Page 55: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/55.jpg)
Answer: 19,500 (feet)
![Page 56: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/56.jpg)
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?
![Page 57: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/57.jpg)
Answer: 19 (dollars)
![Page 58: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/58.jpg)
29. If 50% of a number is 26, what is 150% of the number?
![Page 59: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/59.jpg)
Answer: 78
![Page 60: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/60.jpg)
30. How many eight-pound weights are needed to balance
12 twelve-pound weights?
![Page 61: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/61.jpg)
Answer: 18 (weights)
![Page 62: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/62.jpg)
31. What common fraction of a class is boys if 15 of the 40 students are girls?
![Page 63: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/63.jpg)
Answer: 5
8
![Page 64: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/64.jpg)
32. The ratio of the number of boys to the number of girls in Ms. Moore’s class is 3:4. There are 56 students in the class. How many students are girls?
![Page 65: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/65.jpg)
Answer: 32 (students)
![Page 66: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/66.jpg)
33. What is the number of square meters in the area of a square if the length of a diagonal is 18 meters?
18 m
![Page 67: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/67.jpg)
Answer: 162 (square meters)
![Page 68: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/68.jpg)
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?
![Page 69: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/69.jpg)
Answer: 16 (minutes)
![Page 70: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/70.jpg)
35. What is the number of square centimeters in the area of a square whose perimeter is 12 cm?
![Page 71: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/71.jpg)
Answer: 9 (square centimeters)
![Page 72: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/72.jpg)
36. Football tickets cost $13.50 each. What is the maximum number of tickets Jane can buy with $100.00?
![Page 73: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/73.jpg)
Answer: 7 (tickets)
![Page 74: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/74.jpg)
37. What is the value of 100 – 81 + 64 – 49 + 36 – 25 + 16 – 9 + 4 – 1?
![Page 75: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/75.jpg)
Answer: 55
![Page 76: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/76.jpg)
38. The sum of two positive integers is 124. What is the value of the greatest possible quotient of these two integers?
![Page 77: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/77.jpg)
Answer: 123
![Page 78: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/78.jpg)
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.
![Page 79: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/79.jpg)
Answer: 2
9
![Page 80: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/80.jpg)
40. What is the value of 3 • 3 + 3(3+3) – 33?
![Page 81: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/81.jpg)
Answer: 0
![Page 82: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/82.jpg)
41. If 9 is added to three times a number, the result is 90. What is five times the number divided by 9?
![Page 83: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/83.jpg)
Answer: 15
![Page 84: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/84.jpg)
42. Joe’s bowling scores were 112, 182 and 142. What does he need to score in his fourth game to get a mean score of 132?
![Page 85: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/85.jpg)
Answer: 92
![Page 86: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/86.jpg)
43. After losing 10% of his weight, a wrestler weighed 135 pounds. What was his original weight in pounds?
![Page 87: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/87.jpg)
Answer: 150 (pounds)
![Page 88: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/88.jpg)
44. Twice a number is one-halfof 48. What is the number?
![Page 89: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/89.jpg)
Answer: 12
![Page 90: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/90.jpg)
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?
![Page 91: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/91.jpg)
Answer: 6 (inches)
![Page 92: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/92.jpg)
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.
A B
CD
E
![Page 93: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/93.jpg)
Answer: 1
2
![Page 94: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/94.jpg)
47. What is the range of the set {112, 124, 136, 148, 160} ?
![Page 95: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/95.jpg)
Answer: 48
![Page 96: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/96.jpg)
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?
![Page 97: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/97.jpg)
Answer: 600
![Page 98: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/98.jpg)
49. In how many ways can a person enter a room with 5 doorways and leave through a different doorway?
![Page 99: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/99.jpg)
Answer: 20 (ways)
![Page 100: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/100.jpg)
50. If , what is the
arithmetic mean of
and ?
m 0mm3
mm– 3
![Page 101: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/101.jpg)
Answer: 1
![Page 102: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/102.jpg)
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?
110
12
![Page 103: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/103.jpg)
Answer: 55 (bees)
![Page 104: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/104.jpg)
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?
![Page 105: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/105.jpg)
Answer: 25 (percent)
![Page 106: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/106.jpg)
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?
![Page 107: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/107.jpg)
Answer: 32 (units)
![Page 108: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/108.jpg)
54. What is the base-ten number represented by the base-eight number 31?
![Page 109: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/109.jpg)
Answer: 25
![Page 110: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/110.jpg)
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?
![Page 111: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/111.jpg)
Answer: 16,000 (miles)
![Page 112: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/112.jpg)
56. The value of the determinant
What is the value of x if
a b
c dad bc.
2 3x 6
![Page 113: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/113.jpg)
Answer: –8
![Page 114: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/114.jpg)
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?
![Page 115: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/115.jpg)
Answer: 8 (hours)
![Page 116: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/116.jpg)
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?
![Page 117: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/117.jpg)
Answer: 23 (degrees)
![Page 118: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/118.jpg)
59. Given a b = a2 + 2ab + b2, what is the value of a b when a = 4 and b = 6?
![Page 119: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/119.jpg)
Answer: 100
![Page 120: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/120.jpg)
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?
![Page 121: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/121.jpg)
Answer: 20 (dollars)
![Page 122: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/122.jpg)
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.
![Page 123: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/123.jpg)
Answer: 1
3
![Page 124: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/124.jpg)
62. The radius of a circle is 6 meters. A square is inscribed in the circle. What is the number of square meters in the area of the square?
6 m
![Page 125: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/125.jpg)
Answer: 72 (square meters)
![Page 126: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/126.jpg)
63. Chan’s bank account contains $450, which is 125% more than it contained at this time last year. How many dollars were in Chan’s bank account last year?
![Page 127: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/127.jpg)
Answer: 200 (dollars)
![Page 128: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/128.jpg)
64. A number x is 5 less than number y. Three times x is 10 less than twice y. What is the value of x – y?
![Page 129: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/129.jpg)
Answer: – 5
![Page 130: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/130.jpg)
65. What is the value of 113 – 3 • 112 + 3 • 11 – 1 ?
![Page 131: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/131.jpg)
Answer: 1000
![Page 132: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/132.jpg)
66. As shown, line k with point P lies in the same plane as circle C. How many circles in the same plane are tangent to k at P and are also tangent to circle C?
C
kP
![Page 133: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/133.jpg)
Answer: 2 (circles)
![Page 134: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/134.jpg)
67. Suppose that bc = 121.What is bc/2 ?
![Page 135: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/135.jpg)
Answer: 11
![Page 136: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/136.jpg)
68. A rectangle has a perimeter of 48 feet. What is the greatest possible number of square feet in the area of the rectangle?
![Page 137: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/137.jpg)
Answer: 144 (square feet)
![Page 138: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/138.jpg)
69. What is the value
of 5252 – 4752 ?
![Page 139: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/139.jpg)
Answer: 50,000
![Page 140: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/140.jpg)
70. How many different integers can be expressed as the sum of two different numbers in the set {1, 2, 3, 4, 5, 6}?
![Page 141: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/141.jpg)
Answer: 9 (integers)
![Page 142: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/142.jpg)
71. Levi had 10,000 points to exchange for prizes. Each prize he selected required half the number of points he had at the time he selected it. How many points did he have left after choosing four prizes?
![Page 143: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/143.jpg)
Answer: 625 (points)
![Page 144: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/144.jpg)
72. What is the remainder when 1 + 2 + 3 + 4 + ... + 9 + 10 is divided by 3?
![Page 145: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/145.jpg)
Answer: 1
![Page 146: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/146.jpg)
73. If a child must choose one of four entrees, one of four side dishes, and one of four drinks from a menu, how many different meals are possible?
![Page 147: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/147.jpg)
Answer: 64 (meals)
![Page 148: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/148.jpg)
74. The price of a radio was discounted 20% on the first day of a sale. The sale price was then discounted an additional 20% on the second day. What percent is the combined discount?
![Page 149: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/149.jpg)
Answer: 36 (percent)
![Page 150: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/150.jpg)
75. What is the number of square inches in the area of a square with side length 12 inches?
![Page 151: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/151.jpg)
Answer: 144 (square inches)
![Page 152: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/152.jpg)
76. Express in simplest form:
3 5 15 .
![Page 153: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/153.jpg)
Answer: 15
![Page 154: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/154.jpg)
77. What day of the week will it be 40 days from Tuesday?
![Page 155: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/155.jpg)
Answer: Sunday
![Page 156: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/156.jpg)
78. The volume of a cube is 343 cubic units. What is the number of square units in the surface area?
![Page 157: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/157.jpg)
Answer: 294 (square units)
![Page 158: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/158.jpg)
79. What is the least common multiple of 14 and 21?
![Page 159: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/159.jpg)
Answer: 42
![Page 160: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/160.jpg)
80. What is the sum of all positive integers t such that 1.2t < 9.6 ?
![Page 161: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/161.jpg)
Answer: 36
![Page 162: MATHCOUNTS 2001 Chapter Competition Countdown Round](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649ebf5503460f94bc9b62/html5/thumbnails/162.jpg)