• date post

19-Jan-2016
• Category

## Documents

• view

275

18

TAGS:

Embed Size (px)

### 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?

• What is the value of ? Express your answer as a common fraction.

• 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?

• The expression can be written as . What is the value of ? 12 5m n

• 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?

• For how many different values of does ? x

• What is the sum of the odd integers between 46 and 64?

• 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?

• Find such that

. n

• 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?

• If each edge of a cube is increased by 50% , what is the percent increase in the surface area of the cube?

• What is the value of ?

• How many isosceles triangles exist which have a perimeter of 10 and integer side lengths?

• The prime factorization of 2160 is . How many of its positive integer factors are perfect squares?

• If f (x) = x 4 + x 2 + 5x, evaluate f (5) - f (-5).

• 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?

• The product of three consecutive multiples of 5 is 26,250. What is the largest of these three factors?

• What is the value of the arithmetic series 28 + 30 + 32 + ... + 86 ?

• 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.

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

• 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.

• How many digits are in the decimal representation of the product of and ?