MATHCOUNTS 2001 National Competition Countdown Round The NASA
- Slides: 51
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 250 g control module?
Answer: 5500 (dollars)
What is the value of ? Express your 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 . ´ 10 The expression 125 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 + 5 x, 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)