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1. What is the greatest prime factor of 99?

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Pokey is 8 days late with each of three books. How much is Pokey's fine in cents? ... 36. At the Marian County Antique Show, 202 tickets were sold on Friday, 357 were ... – PowerPoint PPT presentation

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Title: 1. What is the greatest prime factor of 99?


1
MATHCOUNTS?
2004 Chapter Competition Countdown Round
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1. What is the greatest prime factor of 99?
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Answer 11
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7
2. A small square is entirely contained in a
larger square, as shown. The side length of the
small square is 3 units and the side length of
the larger square is 7 units. What is the number
of square units in the area of the black region?
8
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Answer 40 (square units)
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11
3. Fifty ping-pong-balls are numbered 1, 2, 3,
..., 49, 50. A ball is chosen at random. What
is the probability that the number on the
selected ball is a multiple of 5 or 7 or both?
Express your answer as a common fraction.
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Answer
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15
4. How many zeros are at the end of the product
25 240?
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Answer 3 (zeros)
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19
5. Following the directions of the arrows, how
many different paths are there from A to C?
B
C
A
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Answer 5 (paths)
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23
6. At 230 p.m. during a long drive, Bobbi asks
her parents, Are we there yet? Her mother
responds, We will be there in 7200 seconds. If
Bobbis mother is correct, at what time in the
afternoon will they arrive at their destination?
24
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Answer 430 (p.m.)
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27
7. If 3x 8 5x - 6, what is the value of the
product 10x ?
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29
Answer 70
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31
8. How many prime numbers are between 30 and 40?
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33
Answer 2 (numbers)
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35
9. Triangle ABC is isosceles with angle A
congruent to angle B. The measure of angle C is
30 degrees more than the measure of angle A. What
is the number of degrees in the measure of angle
C?
36
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37
Answer 80 (degrees)
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39
10. In the NBA in 2003, Yao Ming was one of the
tallest players at 75. Earl Boykins was the
shortest player at 55. How many inches taller
than Boykins was Ming?
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41
Answer 24 (inches)
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43
11. Simplify .
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45
Answer 3
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47
12. Robin bought a four-scoop ice cream cone
having a scoop each of vanilla, chocolate,
strawberry and cherry. In how many orders can
the four scoops be stacked on the cone if they
are stacked one on top of the other?
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49
Answer 24 (orders)
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51
13. How many integers n satisfy
?
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Answer 5 (integers)
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55
14. In a 30-year period, what is the maximum
possible number of leap years?
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57
Answer 8 (leap years)
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59
15. Each pirate lied in making the following
statementsLong I stole the map.John Silver
did not steal the map.Silver John stole the
map.Who stole the map?
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Answer Silver
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63
16. What is the least prime factor of 74 - 73 ?
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Answer 2
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67
17. If x 3y2, what is the value of 4x in terms
of y?
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69
Answer 12y2
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71
18. What is the 2004th positive odd integer?
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73
Answer 4007
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75
19. Solve for x 5 - x 8.
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Answer -3
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79
20. What is the greatest two-digit whole number,
the product of whose digits is 8?
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Answer 81
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83
21. The lengths of two sides of a triangle are
33 units and 42 units. The third side also has
an integral length. What is the least possible
number of units in the perimeter of the triangle?
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85
Answer 85 (units)
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87
22. The daily high temperatures in degrees
Celsius for Monday through Friday were 3, -1, -6,
-5 and 2, respectively. What is the arithmetic
mean of these five temperatures? Express your
answer as a decimal to the nearest tenth.
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Answer -1.4 (degrees)
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91
23. Compute . Express your
answer as a common fraction.
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Answer
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95
24. One gallon of paint covers 400 square feet.
If paint is only sold in whole gallons, how many
gallons of paint do you have to buy to paint a
surface of 925 square feet?
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97
Answer 3 (gallons)
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99
25. What is the units digit of the product of all
of the odd integers between 0 and 12?
100
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Answer 5
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103
26. You connect the points (0, 0) and (9, 6) with
a line segment. Starting at (0, 0), you move
of the way along the segment. What is the sum
of the coordinates of the point you land upon?
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Answer 5
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107
27. Each of the six members from the Skateer
University hockey team shakes hands with each of
the six members of the Iceburg Tech team. How
many handshakes take place?
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109
Answer 36 (handshakes)
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111
28. For x gt 0, the area of the triangle with
vertices (0, 0), (x, 0) and (x, 5) is 30 square
units. What is the value of x?
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113
Answer 12
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115
29. The probability that a randomly thrown dart
will land on a target is . What is the
probability that the dart will not land on the
target? Express your answer as a common fraction.
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Answer
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30. What is the value of the 25th term of the
arithmetic sequence 2, 5, 8, ... ?
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Answer 74
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123
31. The fine for an overdue library book is 8
cents per day. Pokey is 8 days late with each of
three books. How much is Pokeys fine in cents?
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Answer 192 (cents)
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127
32. The congruent sides of an isosceles triangle
are each 5 cm long, and the perimeter is 17 cm.
In centimeters, what is the length of the base?
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129
Answer 7 (centimeters)
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131
33. Solve for x 2(3x) 162.
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Answer 4
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135
34. The sum of two numbers is 12 and their
product is 35. What is the positive difference
between the numbers?
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Answer 2
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139
35. Equilateral triangle ABC and square BCDE are
coplanar, as shown. What is the number of
degrees in the measure of angle CAD?
A
C
B
E
D
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Answer 15 (degrees)
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143
36. At the Marian County Antique Show, 202
tickets were sold on Friday, 357 were sold on
Saturday, and 408 were sold Sunday. How many
dollars were collected if the Friday tickets cost
3 each, the Saturday tickets cost 4 each, and
the Sunday tickets cost 5 each?
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145
Answer 4074 (dollars)
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147
37. Five toppings for a pizza are available at
Polinas Pizza. How many combinations of two
different toppings are possible?
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Answer 10 (combinations)
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151
38. Five friends raced each other. Bill finished
next to last. John finished behind Bill. Al
finished after Clark and before Tony. Which
friend finished third?
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Answer Tony
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155
39. How many positive integers can be represented
as the difference of two distinct members of the
set 1, 3, 5, 7, 9, 11, 13?
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Answer 6 (integers)
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159
40. Define a b as 2a - b2. If a 5 9, what
is the value of a?
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Answer 17
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41. Compute 15 82 - 3.
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Answer 76
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42. In a rectangular coordinate system, what is
the number of units in the distance from the
origin to the point (-15, 8)?
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Answer 17 (units)
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171
43. Simplify if x ¹ 0.
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Answer 3
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175
44. How many three-digit positive integers are
multiples of 4?
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177
Answer 225 (integers)
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179
45. The fair spinner shown is spun once. What is
the probability of spinning an odd number?
Express your answer as a common fraction.
23
15
14
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Answer
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183
46. In square centimeters, what is the area of
triangle ABC?
A
10 cm
B
8 cm
C
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Answer 40 (square centimeters)
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187
47. The sum of two numbers is 13, while their
product is 36. What is the sum of their
reciprocals? Express your answer as a common
fraction.
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Answer
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48. Given . If y 18, what is
the value of x?
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Answer 45
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49. What is the number of square units in the
area of a triangle whose sides measure 5, 5 and
6 units?
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Answer 12 (square units)
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50. For a world record, George Adrian picked
15,832 pounds of apples in 8 hours. Assuming he
maintained a constant rate of picking, how many
pounds of apples did he pick in 3 hours?
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Answer 5937 (pounds)
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51. What is the smallest positive perfect cube
that can be written as the sum of three
consecutive integers?
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Answer 27
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52. The perimeter of a square is 44 meters. How
many square meters are in the area of the square?
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Answer 121 (square meters)
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53. For how many positive integers x is x2 6x
9 between 20 and 40?
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Answer 2 (integers)
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54. What is the least positive integer such that
it is a multiple of 16 and the product of its
digits is a multiple of 12?
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Answer 64
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55. At an average speed of 60 miles per hour,
how many miles does a car travel in six hours and
30 minutes?
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Answer 390 (miles)
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56. The area of rectangle ABCD with vertices A(0,
0), B(0, 4), C(x, 4) and D(x, 0) is 28 square
units. If x gt 0, what is the value of x?
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Answer 7
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57. Sean had a temperature of 99.6F at 3 p.m.
Five hours later his temperature was 102.4F. By
how many degrees Fahrenheit did his temperature
rise during those five hours? Express your
answer as a decimal to the nearest tenth.
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Answer 2.8 (degrees)
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58. The coordinates of a parallelogram are (5,
3), (6, 8), (7, 4) and (x, y) and x gt 7. What is
the value of x y?
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Answer 17
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59. The sequence 2, 7, 12, a, b, 27 is
arithmetic. What is the value of a b?
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Answer 39
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239
60. Express the value of as a
decimal to the nearest tenth.
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Answer 1.5
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243
61. There are two pints in one quart and four
quarts in one gallon. How many pints are there
in gallons of milk?
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Answer 20 (pints)
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62. Simplify .
Express your answer
in simplest radical form.
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Answer
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251
63. How many positive integers are less than
100p?
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Answer 314 (integers)
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255
64. A prism has 15 edges. How many faces does
the prism have?
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Answer 7 (faces)
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65. What is the remainder of 2004 divided by 12?
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Answer 0
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66. In a rectangular coordinate system, the line
3y x intersects the line 2x 5y 11 at point
A. What is the sum of the coordinates of point
A?
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Answer 4
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67. What is the 100th digit to the right of the
decimal point in the decimal representation of
?
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Answer 4
270
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68. The ratio of cats to dogs at the pet store is
23. There are 14 cats. How many dogs are
there at the pet store?
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Answer 21 (dogs)
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275
69. What is the least positive integer with
exactly five distinct positive factors?
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Answer 16
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279
70. Engineers use the formula
to find the crushing load for square pillars.
If T 4 and H 8, what is the value of L ?
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Answer 100
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283
71. What is the least positive integer divisible
by each of the first eight positive integers?
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Answer 840
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287
72. How many integers fall between
on a number line?
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Answer 5 (integers)
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291
73. At lunch, 60 of the students selected soda
while 20 selected milk. If 72 students selected
soda, how many students selected milk?
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Answer 24 (students)
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74. The sum of the first n positive integers is
6. What is the sum of the first n 1 positive
integers?
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Answer 10
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299
75. Angelique averaged 14.4 points per game for
15 games. What is the total number of points
that she scored during those 15 games?
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Answer 216 (points)
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303
76. What is the smallest prime number that is the
sum of two other distinct prime numbers?
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305
Answer 5
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307
77. In the next three days, 2000 people will
move to Florida. How many people, on average,
will move to Florida each hour? Express your
answer to the nearest whole number.
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Answer 28 (people)
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78. The sum of the digits of the year 2004 is 6.
What is the first year after 2000 for which the
sum of the digits is 12?
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Answer 2019
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315
79. Shari walks at a constant rate of 3 miles per
hour. After 1.5 hours, how many miles did she
walk? Express your answer as a decimal to the
nearest tenth.
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Answer 4.5 (miles)
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80. How many distinct positive factors does 32
have?
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Answer 6 (factors)
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