San Diego Junior High Math Field Day 2011

Mad Hatter Marathon – 7

  1. Write 2011 using Roman numerals.

2. How much money would you make in 4 days if you made 4 dollars every time the hands of a clock formed a 90 degree angle?

3. What is the probability of drawing two hearts in a row from a normal deck of 52 playing cards? Express your answer as a common fraction.

4. The Mad Hatter needs 80 croissants for his tea party. He wants to get the croissants from the Binary Bakery, where all orders are taken using base 2. Help the Mad Hatter by converting 80, base 10, into base 2.

5. In a right triangle, if the hypotenuse measures 104 cm and one leg measures 40 cm, what is the length of the other leg?

6. What fraction of 3 meters is 95 centimeters?

7. How many seconds are in 3% of a week?

8. The March Hare has six bins containing jellybeans. These bins contain 10, 13, 19, 8, 13, and 9 blue jellybeans. What is the mean number of blue jellybeans per bin?

9. Alice is 5 feet tall. She eats a cake that makes her 1/4 as tall, and then she nibbles a mushroom that makes her shrink to 2/5 as tall as her new height. How many inches tall is she at the end of this eating adventure?

10. What was the mode in question 8?

11. The average of five numbers is 7. If one of the five numbers is removed, the average of the four remaining numbers is 6. What is the value of the number that was removed?

12. Three crumpets and a jar of jam cost $1.24. Five crumpets and a jar of jam cost $1.82. No prices include tax. In cents, what is the cost of a crumpet?

13. What is the reciprocal of 17?

14. What fraction of the one-digit positive integers is prime? Express your answer as a common fraction.

15. Alice was making a trip through Wonderland with a basket of flowers. On her way, she came across the Duchess and gave her half the flowers plus half a flower. Then she ran across the Mad Hatter, to whom she gave half of her remaining flowers plus half a flower. Then she came upon the White Rabbit, who also wanted half her flowers plus half a flower. Unfortunately, this meant that, when Alice met the Queen of Hearts, she no longer had any flowers left. How many flowers did Alice have at the beginning of her journey?

16. Twelve caterpillars have yellow spots and blue spots, with each caterpillar having at least one color of spots. Only six caterpillars have yellow spots and exactly ten caterpillars have blue spots. How many caterpillars have both yellow and blue spots?

17. What is the sum of the reciprocals of the first three positive even integers? Express your answer as a common fraction.

18. The Cheshire Cat vanished at 11:23 AM and reappeared at 1:38 PM the same day. For what fraction of the day had he vanished?

19. If the Mad Hatter’s 3-inch tall hat box has a volume of 75π, how many inches long is the diameter of its base?

20. I am thinking of a special four-digit number that has the following traits:

  • All the digits are different.
  • The digit in the thousands place is 3 times the digit in the tens place.
  • The number is odd.
  • The sum of the digits is 27.

21. How many ounces are there in 3-and-a-half quarts?

22. If 3 hens lay 4 eggs in 5 days, how many days will it take a dozen hens to lay 8 dozen eggs?

23. How many distinct isosceles triangles exist with a perimeter of 99 inches and side lengths that are positive whole number inches?

24. The Mad Hatter is 5 feet 3 inches tall, and the March Hare is 4 feet 10 inches tall. How many inches taller is the Mad Hatter than the March Hare?

25. Find the value of four cubed, to the one half power.

26. Light travels 186,000 miles per second. How many minutes does it take the Sun’s light to reach Earth, which is about 93,000,000 miles away?

27. Twelve of the members of Wonderland are going to form a Chess Club. How many ways can they choose a president, vice president, secretary, and treasurer for their club?

28. The sum of four consecutive integers is 118. What is the greatest of the four integers?

29. How many sixty-fourths, when added together, equal eleven sixteenths?

30. What fraction of 2 cubic yards is 9 cubic feet?

31. A right triangle has one of its sides be 15. If all of its side lengths are whole numbers, then what is the least possible value of its perimeter, in feet?

32. At the Mad Hatter’s tea party, the ratio of tea cakes to crumpets to scones is 2:3:7, and the total number of tea cakes, crumpets, and scones is five dozen. How many crumpets are there?

33. What is the least positive multiple of 12 for which the sum of its digits is also a positive multiple of 12?

34. The caterpillar walked a mile in two hours. The Cheshire Cat ran four miles in forty minutes. What is the ratio of speeds of the Cheshire Cat to the Caterpillar?

35. What is the smallest positive integer that is divisible by the first five natural numbers?

36. 37.5% of the Mad Hatter’s teacups are green. If the Mad Hatter has 96 teacups, how many are green?

37. What is the greatest common factor of 154 and 252?

38. The caterpillar planted tomatoes on one-half of his garden. Then, he planted broccoli on one-fourth of the remaining garden. Then, he planted lettuce in one-half of the remaining garden. The rest of the garden was planted with carrots. What percent of the garden is planted in carrots?

39. What is the smallest positive two-digit integer that has exactly three distinct, positive factors?

40. The probability that the Cheshire Cat will appear is 4/7. What is the probability that he will not appear?

41. The four interior angles of the quadrilateral croquet field at the Palace of Hearts are in the ratio 2:4:4:5. In degrees, what is the measure of the smallest interior angle of the quadrilateral?

42. In Wonderland, they have only two denominations of money, $5 and $8 bills. Also, everyone always pays exactly the amount that something is priced. What is the largest integer dollar amount that an item CANNOT be priced in Wonderland?

43. Alice bought a package of chess pieces on sale. The package was originally $36. Including the 5% sales tax, she paid $32.13. What percent discount did Alice receive on the package of chess pieces?

44. How many different ways can the letters in HATTER be arranged?

45. The four horsemen of the Apocalypse are trying to unlock the end of the world by determining the prime factorization of 5212011. Each horseman represents one of the prime factors. You can prevent the end of the world by finding the sum of the prime factors of 5212011. What is the sum of the prime factors? (HINT: There are two single-digit and two three-digit numbers in the prime factorization of 5212011).

NAME SCHOOL

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KEY

  1. MMXI
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  1. 112 (ounces)
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  1. 48 (degrees)

  1. $704
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  1. 30 (days)
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  1. 27 (dollars)

  1. 3/51
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  1. 25 (triangles)
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  1. 15 (%)

  1. 1010000
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  1. 5 (inches)
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  1. 360 (ways)

  1. 96 (cm)
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  1. 8
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  1. 1170

  1. 19/60
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  1. 8 (minutes)

  1. 18,144 (secs)
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  1. 11880 (ways)

  1. 12
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  1. 31

  1. 6 (in)
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  1. 44

  1. 13
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  1. 1/6

  1. 11
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  1. 36 (feet)

  1. 29 (cents)
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  1. 15 (crumpets)

  1. 5/88
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  1. 48

  1. 4/9
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  1. 12:1

  1. 7 (flowers)
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  1. 60

  1. 4 (caterpillars)
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  1. 36 (cups)

  1. 11/12
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  1. 14

  1. 3/32
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  1. 18 or 18.75 (%)

  1. 10 (inches)
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  1. 25

  1. 9837
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  1. 3/7