Transcript { 1. The NASA Space Shuttle transports material to the

MATHCOUNTS

2001 National Competition
Countdown Round
The NASA Space Shuttle
transports material to the
International Space Station at a
cost of $22,000 per kilogram.
What is the number of dollars in
the cost of transporting a 250g
control module?
Answer: 5500 (dollars)
What is the value of
2
3
3
4
4
5
5
?
Express
your
6
( )( )( )( )
answer as a common fraction.
Answer:
1
3
Two rectangles have integer
dimensions, and both have a
perimeter of 144 cm. What is the
greatest possible difference
between the areas of two such
rectangles?
Answer: 1225 (square
centimeters)
-14
The expression 125
. 10
can be written as
the value of
1
m
n

2 5
m+ n ?
. What is
Answer: 29
How many ways can change for
$16.00 be made using quarters
and dimes if at least one of each
type of coin must be used?
Answer: 31 (ways)
For how many different values
5
4
3
of x does x = x + 72 x ?
Answer: 3 (values)
What is the sum of the odd
integers between 46 and 64?
Answer: 495
It takes 64 identical wooden
cubes to fill a cubical box. How
many of these cubes does it take
to make the bottom layer of the
box?
Answer: 16 (cubes)
Find n such that
2  3  n = 8! .
5
2
Answer: 140
At Makettle's, Jim bought
30 oranges at a price of three
for 59¢. At Paduka's, he then
bought 20 oranges at a price of
two for 41¢. What was the
number of cents in the average
price of an orange?
Answer: 20 (cents)
If each edge of a cube is
increased by 50% , what is the
percent increase in the surface
area of the cube?
Answer: 125 (percent)
What is the value of
3
3 +3 +3 ?
5
5
5
Answer: 9
How many isosceles triangles
exist which have a perimeter
of 10 and integer side lengths?
Answer: 2 (triangles)
The prime factorization
4
3
of 2160 is 2  3  5 . How
many of its positive integer
factors are perfect squares?
Answer: 6 (factors)
If f (x) = x 4 + x 2 + 5x,
evaluate f (5) - f (-5).
Answer: 50
1
A piece of lumber 5 feet long
4
is cut into 9 pieces. If the waste
1
per cut is inch, how many
8
inches of lumber are wasted?
Answer: 1 (inch)
The product of three consecutive
multiples of 5 is 26,250. What is
the largest of these three factors?
Answer: 35
What is the value of the
arithmetic series
28 + 30 + 32 + ... + 86 ?
Answer: 1710
What is the probability that a
two-digit number selected at
random has a tens digit less than
its units digit? Express your
answer as a common fraction.
2
Answer:
5
What is the sum of all possible
values of k for which
2
x + k x - 12 x + 16 is the
square of a binomial?
Answer: 24
What is the maximum number of
square centimeters in the area of
a triangle whose perimeter
is 30 cm? Express your answer
in simplest radical form.
Answer: 25 3 (square
centimeters)
How many digits are in the
decimal representation of the
7
12
product of 2 and 5 ?
Answer: 9
Two different integers from
1 through 20 inclusive are chosen
at random. What is the
probability that both numbers are
prime? Express your answer as a
common fraction.
14
Answer:
95
What is the remainder when
5
137
is divided by 8?
Answer: 5
Find the distance between the
points (1, 1) and (4, 7) . Express
your answer in simplest radical
form.
Answer: 3 5 (units)