1' What is the value of

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 230 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?
51
Answer 100
52
26. What is the least positive three-digit
multiple of 24?
53
Answer 120
54
27. The Carters had a 10-foot by 10-foot patio
built at a cost of 2200. How many dollars per
square foot did the patio cost to build?
55
Answer 22 (dollars per square foot)
56
28. Jenna has 1.75 in nickels and dimes. She
has twice as many dimes as nickels. How many
dimes does Jenna have?
57
Answer 14 (dimes)
58
29. What is the decimal equivalent of ?
Expressyour answer to the nearest hundredth.
59
Answer 2.75
60
30. The ratio of the measures of two
complementary angles is 711. What is the
measure, in degrees, of the larger angle?
61
Answer 55 (degrees)
62
31. Simplify . Express your answer as
a common fraction.
63
Answer
64
32. From a one meter piece of yarn, Chris cuts a
31.5 cm piece and a 35.5 cm piece. In
centimeters, how much yarn is left?
65
Answer 33 (centimeters)
66
33. Simplify 7 103 5 102 - 4 101 7
100.
67
Answer 7467
68
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?
69
Answer 60 (calories)
70
35. If f (x) x2 - 1, what is the value of
f (-1)?
71
Answer 0
72
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?
73
Answer Mark
74
37. When the expression 7 4(x 5) - 8(3 - x)
is simplified, what is the value of the
coefficient of the x-term?
75
Answer 12
76
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.
77
Answer 1.5 (inches)
78
39. The ages, in years, of the ten people in the
math club are 12, 12, 12, 12, 13, 13, 13, 14,
14, 39. What is the mode of the ages?
79
Answer 12 (years)
80
40. What is the greatest prime factor of 10!?
81
Answer 7
82
41. Two numbers are in the ratio of 57. Their
sum is 108. What is the lesser number?
83
Answer 45
84
42. Rebecca remembered the first six digits of a
friends 7-digit phone number. If she randomly
selects a digit to replace the last digit she
cant remember, what is the probability she will
dial the correct number? Express your answer as
a common fraction.
85
Answer
86
43. Given . What is thevalue of the
ratio ? Expressyour answer as a common
fraction.
87
Answer
88
44. The categories and percentages for 536
million juvenile books are given in the table.
Of these juvenile books, how many books were
Nonfiction?
Fiction 55 Nonfiction 25 Educational 10 Other
10
89
Answer 134,000,000 (books)
90
45. Twenty-five percent of what number is 12?
91
Answer 48
92
46. What is the number of square centimeters in
the area of a circle with radius 4 cm? Express
your answer is terms of p.
93
Answer 16p (square centimeters)
94
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?
95
Answer 6 (candies)
96
48. How many positive three-digit integers are
multiples of 11?
97
Answer 81 (integers)
98
49. Express the value of as a common fraction.
99
Answer
100
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.
101
Answer
102
51. How many distinct prime factors does 52 - 32
have?
103
Answer 1 (factor)
104
52. How many triangles of any size are in this
figure?
105
Answer 5 (triangles)
106
53. What is 150 of 26?
107
Answer 39
108
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?
109
Answer 512 (bottles)
110
55. In how many ways can a pair of students be
selected from a group of five students?
111
Answer 10 (ways)
112
56. In the formula d rt, what is the value of r
if d 60 and t 4?
113
Answer 15
114
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.
115
Answer 7 (years)
116
58. Of the 80 students at camp, 37.5 of them are
male. What is the number of students at camp who
are female?
117
Answer 50 (students)
118
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.
119
Answer
120
60. There are 16 boys in Mr. Smiths class of 34
students. What is the ratio of boys to girls?
Express your answer as a common fraction.
121
Answer