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MATH COUNTS

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MATHCOUNTS

2004 School Competition

Countdown Round

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?

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?

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?

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 ?

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.

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?

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.

20

15

10

5

Dogs

Cats

Fish

Birds

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?

34.A stair-step exercise machine indicates that Leon burns 180 calories in 12 minutes. At the same rate, how many calories would Leon burn in a 4-minute workout?

36.Four friends are in line for movie tickets. Rick is behind Tom, but ahead of Mark. James and Tom are separated by one person. Who is last in line?

38.Steven is making a scale drawing of his living room. He is using a scale of one-quarter inch to one foot. In the drawing, how many inches will represent the length of a 72-inch long couch? Express your answer as a decimal to the nearest tenth.

42.Rebecca remembered the first six digits of a friend’s 7-digit phone number. If she randomly selects a digit to replace the last digit she can’t remember, what is the probability she will dial the correct number? Express your answer as a common fraction.

44.The categories and percentages for 536 million juvenile books are given in the table. Of these juvenile books, how many books were Nonfiction?

Fiction55%

Nonfiction25%

Educational10%

Other10%

47.A candy company puts 21 candies in each bag. There are only red and blue candies in each bag. For every two red candies in a bag there are five blue candies. How many red candies are in each bag?

50.Joshua flips three coins. What is the probability that they are neither all heads nor all tails? Express your answer as a common fraction.

54.Each bottle of perfume at The Perfume Parlor contains ounces of perfume. How many of these bottles of perfume could be made from 96 ounces of perfume?

57.On average, each American consumes 286 eggs per year. What is the number of years it would take, at this rate, for an American to eat 2000 eggs? Express your answer to the nearest whole number.

59.One fair standard six-sided die is rolled. What is the probability of rolling a number greater than 4? Express your answer as a common fraction.