Transcript A rectangular field is half as wide as it is long, and it

MATHCOUNTS

2004 National Competition
Countdown Round
The time right now is
9 o’clock. On a 12-hour
clock, what time will it be 2004
hours from now?
Answer: 9 (o’clock)
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
5
7
4
8
3
1
Answer:
4
How many liters of water must
be added to 40 liters of a 40%
salt solution in order to
produce a 25% salt solution?
Answer: 24 (liters)
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
Matt’s pocket?
Answer: 24 (coins)
What is the largest prime
factor of 999?
Answer: 37
What is the units digit of 32004?
Answer: 1
At the recent cat show, Moon
scored 40 points lower than
Foof in the judging. Foof’s
score was double Kook’s
score. How many points did
Kook score if Moon’s score
was 32 points?
Answer: 36 (points)
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
C
E
D
B
S
Answer: (face) C
x
5
If = 100, what is the value
x+2
of 5 ?
Answer: 2500
Twenty percent of the 20 boys
in Ms. Schmidt’s 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?
Answer: 26 (percent)
If 4x  2  10 and x < 0, what
is the value of x?
Answer: -3
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?
Answer: 4 (centimeters)
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.
3
Answer:
5
Solve for N:
82,400 + 4780 + 500 =
82,300 + 4760 + N.
Answer: 620
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?
Answer: 60 (inches)
The ratio of irises to roses in
Nikki’s garden is 2:5. 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?
Answer: 18 (irises)
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)?
Answer: 16 (square units)
The four-digit number “25AB”
is divisible by nine, with A the
tens digit and B the units digit.
How many different such fourdigit numbers could “25AB”
represent?
Answer: 11 (numbers)
At what point does the line
3y - 4x = 12 intersect the
x-axis? Express your
answer as an ordered pair.
Answer: (-3, 0)
How many even perfect
square factors does 24 · 79
have?
Answer: 10 (factors)
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?
Answer: 2 (inches)
Evaluate
F
I
F
I
G
J
G
J
HK HK.
2 5
5 5

7 9
7 9
Express your answer as a
common fraction.
5
Answer:
9
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.
16
Answer:
9
Evaluate x2 - x3 if x = -0.5.
Express your answer as a
common fraction.
3
Answer:
8
Angle EAB is a right angle,
and BE = 9 units.
F
What is the number
of square units in
G
E
the sum of the
A
areas of the two
9
squares ABCD
D
B
and AEFG?
C
Answer: 81 (square units)