MATHCOUNTS  2001 National Competition Countdown Round

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Transcript of MATHCOUNTS  2001 National Competition Countdown Round

  • MATHCOUNTS2001 National CompetitionCountdown 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.

  • 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 ? 12 5m 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

  • 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

  • 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 ?

  • 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?

  • 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?

  • 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:

  • What is the sum of all possible values of for which is the square of a binomial?k

  • 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 ?

  • 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:

  • What is the remainder when 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 (units)