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MATHCOUNTS

MATHCOUNTS. 1990-1991 State Countdown Round. How many of the even counting numbers less than 100 are prime?. 1. The probability of rain on any given day in Atlanta is 20%. After how many days would you expect it to have rained on 30 days?. 150 (days).

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MATHCOUNTS

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  1. MATHCOUNTS 1990-1991 State Countdown Round

  2. How many of the even counting numbers less than 100 are prime?

  3. 1

  4. The probability of rain on any given day in Atlanta is 20%. After how many days would you expect it to have rained on 30 days?

  5. 150 (days)

  6. Two fair tetrahedral (four-sided) dice are thrown. If the faces of each are numbered 3, 5, 7, and 9, what is the probability that the sum of the numbers on the bottom faces is a prime?

  7. 0

  8. What is the shortest distance that can be traveled if you start at any point, A, B, C, or D and visit the other three points once? A65 D3B645 C

  9. 13

  10. How many positive integer pairs (x, y) satisfy A = x + y, 3when A = 2?

  11. 5 (pairs)

  12. If the digit 7 is placed to the right of a three-digit number, forming a four-digit number, the value of the original number increases by 7,000. What was the original number?

  13. 777

  14. Fifty cards numbered 1 to 50 are placed in a box. If a card is selected at random, what is the probability that the card is a prime number and a multiple of seven? Express your answer as a common fraction.

  15. 1 50

  16. What is the last digit in the product of all natural numbers between 1 and 100?

  17. 0

  18. If 5! is expressed as the product of its prime factors in exponential form, what is the sum of its exponents?

  19. 5

  20. This table shows the distribution of scores of Mr. Sampson’s 10-point quiz. What is the median score?

  21. 7

  22. A certain type of 8 ½“ by 11” paper has a thickness of 0.02 cm. If 15,000 sheets of paper are stacked on top of each other, what is the height, in meters, of the stack?

  23. 3 (meters)

  24. Points A, B, C, and D are located on AB such that AB = 3AD = 6BC. If a point is selected at random, what is the probability that it is between C and D? Express your answer as a common fraction.A D C B

  25. 1 2

  26. Three identical squares are placed side by side to form a rectangle with a perimeter of 104 inches. What is the area, in square inches, of each square?

  27. 169 (sq. in.)

  28. Brad is less than 30 years old. His age is a multiple of 5. Next year his age will be a multiple of 7. How old is Brad now?

  29. 20 (years old)

  30. How many different triangles are in the figure?

  31. 13 (triangles)

  32. How many even numbers are between 202 and 405?

  33. 101

  34. What is the positive square root of 16x16?

  35. 4x8

  36. When n is divided by 5, the remainder is 1. What is the remainder when 3n is divided by 5?

  37. 3

  38. Express 10% of 30% of 50 as a decimal.

  39. 1.5

  40. A = { 1, 2, 3, 4, 5, 6, 7, 8, 9, …}. What fractional part of the numbers in set A are not divisible by 3?

  41. 2 3

  42. Six softball teams are to play each other once. How many games are needed?

  43. 15 (games)

  44. Two ropes, 18 meters in length and 24 meters in length, need to be cut into pieces which are all the same length. What is the greatest possible length of each piece?

  45. 6 (meters)

  46. What value of n makes this sentence true? n = n + 1 6 9

  47. 2

  48. If f(x) = 3x + 2 and g(x) = (x – 1)2, what is f(g(-2))?

  49. 29

  50. If March 1 is a Monday, what day of the week will it be 270 days later?

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