Math Field Day 2011

Tri-Team Attack Part II

1. Professor Vector wants to give each student in her Arithmancy class some stones for an activity. She wants everyone to get an equal number of stones. If she splits the class into groups of 2, 3, or 4, she will have one counter left after passing them all out. If she uses groups of 5, she will have no counters left. What is the least number of counters that Professor Vector can have?

2. You have exactly $4.40 in the U.S. currency of quarters, dimes, and nickels. How many of each coin do you have if you have the same number of each type of coin?

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

4. Donald buys a new MP3 player for $150 on the Internet, sells it on the Internet for $175, buys it back for $195, and sells it again for $230. After all these transactions, how many dollars in profit has he made?

5. If one erg equals 3 regs, 6 figs equal 3 ergs, and 3 hamadas equal 9 figs, then how many regs will 10 hamadas equal?

6. Solve for x:

7. You have a standard six-sided number cube with the numbers 1 to 6 on respective sides. If you roll the cube six consecutive times, what is the probability that you will not roll any 6s? Express your number as a percent rounded to the nearest tenth.

8. Find the positive solution to the equation: 7x2 – 9x = 13. Round your answer to the nearest tenth.

9. Simplify the expression: .

10. Two different rectangles each have an area of 360 square centimeters. The length of the second rectangle is 12 centimeters greater than the first, whereas its width is 5 centimeters less than the first rectangle. Find the difference of the perimeters of the two rectangles.

11. You are given two sets of numbers:

A = {6, 9, 11, 13} B = {2, 3, 5, 7}

You randomly select two different numbers from set A and add them. You randomly select two different numbers from set B and multiply them. What is the probability that the sum of the two numbers from set A is greater than the product of the two numbers in set B? Express your answer as a common fraction.

12. Your savings account earns 1.8% interest, compounded annually. Another bank in town is offering 2.3% interest, compounded annually. The balance in your account is $777. How much additional interest, in dollars, could you earn in 5 years by moving your account to the bank with the higher interest rate?

13. Corinne took a 20-question exam in which 10 points were awarded for each correct answer and 5 points were deducted for each incorrect answer. She answered all 20 questions and received a score of 125 points. How many questions did Corinne answer correctly?

14. A right triangle has one leg that is 84 inches longer than the other leg. The hypotenuse is 156 inches. Find the length of the longer leg, in inches.

15. How many distinct 3-letter license plates are possible, using only the letters A through Z, if A must always be followed immediately by Z?

16. Point A on a coordinate plane is located at (-3, 2). The distance between point A and point B is 5 units. Find the smaller possible x-coordinate of point B if the y-coordinate is -1.

17. You are standing 19 feet from the base of the world’s largest catsup bottle located in Collinsville, Illinois. You estimate that the angle between your eye and the line from your eye to the top of the bottle is 55º. If you are 4’9” tall, about how many feet higher is the top of the bottle than your eyes? Round to the nearest foot.

18. Simplify the following expression: .
State your answer as a common fraction.

19. The vertices of a parallelogram are located at (–1, 4), (3, 7), (3, 3), and (–1, 0). What is the exact perimeter of the parallelogram?

20. 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?

THE END
Math Field Day

Tri-Team Attack Part II

Answer Key

21. 25 (counters)

22. 11

23. 25 (triangles)

24. 60 (dollars)

25. 45 (regs)

26. 3

27. 33.5 (%)

28. 2.1

29. 2560x4 y

30. 14 (cm)

31. 25/36

32. ($) 19.43

33. 15 (questions)

34. 144 (inches)

35. 15,675

36. -7

37. 32

38.

39. 18

40. 1170