Title: 1. What is the greatest prime factor of 99?
1MATHCOUNTS?
2004 Chapter Competition Countdown Round
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31. What is the greatest prime factor of 99?
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5Answer 11
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72. 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?
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9Answer 40 (square units)
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113. 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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13Answer
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154. How many zeros are at the end of the product
25 240?
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17Answer 3 (zeros)
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195. Following the directions of the arrows, how
many different paths are there from A to C?
B
C
A
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21Answer 5 (paths)
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236. 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?
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25Answer 430 (p.m.)
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277. If 3x 8 5x - 6, what is the value of the
product 10x ?
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29Answer 70
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318. How many prime numbers are between 30 and 40?
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33Answer 2 (numbers)
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359. 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?
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37Answer 80 (degrees)
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3910. 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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41Answer 24 (inches)
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4311. Simplify .
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45Answer 3
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4712. 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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49Answer 24 (orders)
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5113. How many integers n satisfy
?
52(No Transcript)
53Answer 5 (integers)
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5514. In a 30-year period, what is the maximum
possible number of leap years?
56(No Transcript)
57Answer 8 (leap years)
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5915. 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?
60(No Transcript)
61Answer Silver
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6316. What is the least prime factor of 74 - 73 ?
64(No Transcript)
65Answer 2
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6717. If x 3y2, what is the value of 4x in terms
of y?
68(No Transcript)
69Answer 12y2
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7118. What is the 2004th positive odd integer?
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73Answer 4007
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7519. Solve for x 5 - x 8.
76(No Transcript)
77Answer -3
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7920. What is the greatest two-digit whole number,
the product of whose digits is 8?
80(No Transcript)
81Answer 81
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8321. 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?
84(No Transcript)
85Answer 85 (units)
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8722. 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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89Answer -1.4 (degrees)
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9123. Compute . Express your
answer as a common fraction.
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93Answer
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9524. 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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97Answer 3 (gallons)
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9925. What is the units digit of the product of all
of the odd integers between 0 and 12?
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101Answer 5
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10326. 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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105Answer 5
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10727. 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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109Answer 36 (handshakes)
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11128. 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?
112(No Transcript)
113Answer 12
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11529. 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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117Answer
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11930. What is the value of the 25th term of the
arithmetic sequence 2, 5, 8, ... ?
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121Answer 74
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12331. 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?
124(No Transcript)
125Answer 192 (cents)
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12732. 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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129Answer 7 (centimeters)
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13133. Solve for x 2(3x) 162.
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133Answer 4
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13534. The sum of two numbers is 12 and their
product is 35. What is the positive difference
between the numbers?
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137Answer 2
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13935. 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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141Answer 15 (degrees)
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14336. 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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145Answer 4074 (dollars)
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14737. Five toppings for a pizza are available at
Polinas Pizza. How many combinations of two
different toppings are possible?
148(No Transcript)
149Answer 10 (combinations)
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15138. 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?
152(No Transcript)
153Answer Tony
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15539. How many positive integers can be represented
as the difference of two distinct members of the
set 1, 3, 5, 7, 9, 11, 13?
156(No Transcript)
157Answer 6 (integers)
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15940. Define a b as 2a - b2. If a 5 9, what
is the value of a?
160(No Transcript)
161Answer 17
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16341. Compute 15 82 - 3.
164(No Transcript)
165Answer 76
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16742. In a rectangular coordinate system, what is
the number of units in the distance from the
origin to the point (-15, 8)?
168(No Transcript)
169Answer 17 (units)
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17143. Simplify if x ¹ 0.
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173Answer 3
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17544. How many three-digit positive integers are
multiples of 4?
176(No Transcript)
177Answer 225 (integers)
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17945. 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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181Answer
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18346. In square centimeters, what is the area of
triangle ABC?
A
10 cm
B
8 cm
C
184(No Transcript)
185Answer 40 (square centimeters)
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18747. 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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189Answer
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19148. Given . If y 18, what is
the value of x?
192(No Transcript)
193Answer 45
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19549. What is the number of square units in the
area of a triangle whose sides measure 5, 5 and
6 units?
196(No Transcript)
197Answer 12 (square units)
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19950. 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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201Answer 5937 (pounds)
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20351. What is the smallest positive perfect cube
that can be written as the sum of three
consecutive integers?
204(No Transcript)
205Answer 27
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20752. The perimeter of a square is 44 meters. How
many square meters are in the area of the square?
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209Answer 121 (square meters)
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21153. For how many positive integers x is x2 6x
9 between 20 and 40?
212(No Transcript)
213Answer 2 (integers)
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21554. 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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217Answer 64
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21955. At an average speed of 60 miles per hour,
how many miles does a car travel in six hours and
30 minutes?
220(No Transcript)
221Answer 390 (miles)
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22356. 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?
224(No Transcript)
225Answer 7
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22757. 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.
228(No Transcript)
229Answer 2.8 (degrees)
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23158. 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?
232(No Transcript)
233Answer 17
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23559. The sequence 2, 7, 12, a, b, 27 is
arithmetic. What is the value of a b?
236(No Transcript)
237Answer 39
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23960. Express the value of as a
decimal to the nearest tenth.
240(No Transcript)
241Answer 1.5
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24361. There are two pints in one quart and four
quarts in one gallon. How many pints are there
in gallons of milk?
244(No Transcript)
245Answer 20 (pints)
246(No Transcript)
24762. Simplify .
Express your answer
in simplest radical form.
248(No Transcript)
249Answer
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25163. How many positive integers are less than
100p?
252(No Transcript)
253Answer 314 (integers)
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25564. A prism has 15 edges. How many faces does
the prism have?
256(No Transcript)
257Answer 7 (faces)
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25965. What is the remainder of 2004 divided by 12?
260(No Transcript)
261Answer 0
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26366. 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?
264(No Transcript)
265Answer 4
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26767. What is the 100th digit to the right of the
decimal point in the decimal representation of
?
268(No Transcript)
269Answer 4
270(No Transcript)
27168. 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?
272(No Transcript)
273Answer 21 (dogs)
274(No Transcript)
27569. What is the least positive integer with
exactly five distinct positive factors?
276(No Transcript)
277Answer 16
278(No Transcript)
27970. Engineers use the formula
to find the crushing load for square pillars.
If T 4 and H 8, what is the value of L ?
280(No Transcript)
281Answer 100
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28371. What is the least positive integer divisible
by each of the first eight positive integers?
284(No Transcript)
285Answer 840
286(No Transcript)
28772. How many integers fall between
on a number line?
288(No Transcript)
289Answer 5 (integers)
290(No Transcript)
29173. At lunch, 60 of the students selected soda
while 20 selected milk. If 72 students selected
soda, how many students selected milk?
292(No Transcript)
293Answer 24 (students)
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29574. The sum of the first n positive integers is
6. What is the sum of the first n 1 positive
integers?
296(No Transcript)
297Answer 10
298(No Transcript)
29975. Angelique averaged 14.4 points per game for
15 games. What is the total number of points
that she scored during those 15 games?
300(No Transcript)
301Answer 216 (points)
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30376. What is the smallest prime number that is the
sum of two other distinct prime numbers?
304(No Transcript)
305Answer 5
306(No Transcript)
30777. 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.
308(No Transcript)
309Answer 28 (people)
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31178. 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?
312(No Transcript)
313Answer 2019
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31579. 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.
316(No Transcript)
317Answer 4.5 (miles)
318(No Transcript)
31980. How many distinct positive factors does 32
have?
320(No Transcript)
321Answer 6 (factors)
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