mathcounts 2001 national competition countdown round
TRANSCRIPT
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
? Express your
answer as a common fraction.
( )( )( )( )23
34
45
56
Answer: 13
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)
The expression
can be written as . What
is the value of ?
125 10 14.
1
2 5m n
m n
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 of does ? x x x x5 4 372
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 such that
.
n
2 3 8! 5 2 n
Answer: 140
At Makettle's, Jim bought30 oranges at a price of threefor 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 35 5 53
Answer: 9
How many isosceles triangles exist which have a perimeter of 10 and integer side lengths?
Answer: 2 (triangles)
The prime factorization
of 2160 is . How
many of its positive integer
factors are perfect squares?
2 3 5 4 3
Answer: 6 (factors)
If f (x) = x 4 + x 2 + 5x, evaluate f (5) - f (-5).
Answer: 50
A piece of lumber feet long
is cut into 9 pieces. If the waste
per cut is inch, how many
inches of lumber are wasted?
51
4
1
8
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.
Answer:2
5
What is the sum of all possible values of for which is the square of a binomial?
kx k x x2 12 16
Answer: 24
What is the maximum number of square centimeters in the area of a triangle whose perimeteris 30 cm? Express your answer in simplest radical form.
Answer: 25 (square centimeters)
3
How many digits are in the decimal representation of the product of and ?2 12 5 7
Answer: 9
Two different integers from1 through 20 inclusive are chosen at random. What is the probability that both numbers are prime? Express your answer as a common fraction.
Answer: 14
95
What is the remainder when
is divided by 8?5137
Answer: 5
Find the distance between the points (1, 1) and (4, 7) . Express your answer in simplest radical form.
Answer: 3 (units)5