A rectangular field is half as wide as it is long, and it is completely enclosed by 54 meters of fencing. What is the number of square meters in the area of the field?

1
MATHCOUNTS?
2004 National Competition Countdown Round
2
The time right now is 9 oclock. On a 12-hour
clock, what time will it be 2004 hours from now?
3
Answer 9 (oclock)
4
The first spinner is divided into 4 equal
sections, and the second is divided into 3 equal
sections. When these 2 fair spinners are each
spun once, what is the probability that the
product of the 2 numbers to which the arrows
point is odd? Express your answer as a common
fraction.
1
6
4
8
7
5
3
5
Answer
6
How many liters of water must be added to 40
liters of a 40 salt solution in order to produce
a 25 salt solution?
7
Answer 24 (liters)
8
Matt has exactly 1.60 in his pocket. He only
has nickels and dimes. There are twice as many
nickels as dimes. What is the number of coins in
Matts pocket?
9
Answer 24 (coins)
10
What is the largest prime factor of 999?
11
Answer 37
12
What is the units digit of 32004?
13
Answer 1
14
At the recent cat show, Moon scored 40 points
lower than Foof in the judging. Foofs score was
double Kooks score. How many points did Kook
score if Moons score was 32 points?
15
Answer 36 (points)
16
When this net is folded to form a cube, which
face (A, B, C, D or E) will be opposite the face
labeled S?
A
S
B
C
D
E
17
Answer (face) C
18
If 5x 100, what is the value of 5x2?
19
Answer 2500
20
Twenty percent of the 20 boys in Ms. Schmidts
class live on a farm. Thirty percent of the 30
girls in her class also live on a farm. What
percent of the students in the class live on a
farm?
21
Answer 26 (percent)
22
If and x lt 0, what is the
value of x?
23
Answer -3
24
The height of a right cylinder is 2.5 times its
radius. If the surface area of the cylinder is
112p cm2, what is the radius of the cylinder in
centimeters?
25
Answer 4 (centimeters)
26
A strip of paper is available for each whole
number length from 1 inch to 15 inches. What is
the probability that if a strip is randomly
selected, it can be used as the third side of a
triangle with two sides of 5 inches and 7 inches?
Express your answer as a common fraction.
27
Answer
28
Solve for N 82,400 4780 500
82,300 4760 N.
29
Answer 620
30
A square is divided into five congruent
rectangles, as shown. If the perimeter of each
of these five rectangles is 36 inches, what is
the perimeter of the square, in inches?
31
Answer 60 (inches)
32
The ratio of irises to roses in Nikkis garden is
25. She currently has 25 roses. She is
planning to add 20 more roses and enough irises
to keep the same ratio. How many irises will she
have in total after this addition?
33
Answer 18 (irises)
34
What is the number of square units in the area of
trapezoid ABCD with vertices A(0, 0), B(0, -2),
C(4, 0) and D(4, 6)?
35
Answer 16 (square units)
36
The four-digit number 25AB is divisible by
nine, with A the tens digit and B the units
digit. How many different such four-digit
numbers could 25AB represent?
37
Answer 11 (numbers)
38
At what point does the line 3y - 4x 12
intersect the x-axis? Express your answer as an
ordered pair.
39
Answer (-3, 0)
40
How many even perfect square factors does 24 79
have?
41
Answer 10 (factors)
42
The number of cubic inches in the volume of a
6-inch high cylindrical can equals the number of
square inches in the area of the label that
covers the lateral surface of the can. In
inches, what is the radius of the can?
43
Answer 2 (inches)
44
Evaluate . Express your
answer as a common fraction.
45
Answer
46
What is the ratio of the number of 2?2 squares to
the number of 3?3 squares in the 5?5 square
diagram shown (using only the existing horizontal
and vertical segments)? Express your answer as
a common fraction.
47
Answer
48
Evaluate x2 - x3 if x -0.5. Express your
answer as a common fraction.
49
Answer
50
Angle EAB is a right angle, and BE 9 units.
What is the number of square units in the sum
of the areas of the two squares ABCD and AEFG?
F
G
E
A
9
B
D
C
51
Answer 81 (square units)