1. 1 Northern Arizona University Department of Mathematics and Statistics 2010 Math High School Day College Bowl Competition Students, start your brain cells!

2. 22 Evaluate: [2]

3. 33 If one box of Froot Nootles will feed three adults, or two teenagers, or five children, how many boxes would be needed to feed a crowd of 30 adults, 30 children and 30 teenagers? [31]

4. 44 What number is three more than half of itself? [6]

5. 55 If x$y stands for (x-1)y, what is (5$3)$2? [22]

6. 66 Sam is two years older than his brother Jim. The sum of their ages is 30. When will the sum of their ages be 40? [2015]

7. 77 What number is three less than half of itself? [-6]

8. 88 How many ways are there to travel from S to F along roads, never visiting the same town twice? [4]

9. 99 Simplify: [30/13]

10. 10 How many distinct arrangements of the letters MATH are there? [24]

11. 11 What is 20% of 20 plus 30% of 30? [13]

12. 12 How many ways are there to travel from S to F along roads, never visiting the same town twice? [9]

13. 13 If a is 2 and b is 3, what is a b – b a ? [-1]

14. 14 Evaluate: [4]

15. 15 Compare the two numbers using.  -1.35 [ < ]

16. 16 Solve: [x = 24]

17. 17 If half of it is 5 more than a third of it, how much is all of it? [30]

18. 18 What number is 12 more than its square root? [16]

19. 19 How many distinct arrangements of the letters MATT are there? [12]

20. 20 What number is 12 more than twice itself? [-12]

21. 21 Two numbers differ by 3 and their squares differ by 45. What is their sum? [15]

22. 22 Calculate: [3]

23. 23 The small circle has radius 1 and passes through the center of the big circle. What is the area of the shaded region? [3π]

24. 24 [3]

25. 25 [14]

26. 26 If x@y is, what is (3@4) – (4@3)? [-1]

27. 27 [2]

28. 28 How long is side h of this right triangle? [√24 or 2√6]

29. 29 If I drive at 30 mph for 20 minutes, then 60 mph for 10 minutes, what is my average speed? [40 mph]

30. 30 Which of these consists of a figure 4 and a reflection of it? [D]

31. 31 In a class of 30 students, 8 are blonds, 10 have red hair, and 12 have black hair. If one student is chosen at random, what is the probability that his/her hair is black? [2/5]

32. 32 What is the next number in the sequence below? 192, 96, 48, 24, 12,... [6]

33. 33 Ya wanna sandwich? What kinda bread: white, wheat, rye, or pumpernickel? Meat? We got ham, roast beef and chicken. Cheese? Yeah, Swiss, American, or Muenster. How many different sandwiches can you order? [36]

34. 34 What is the area of a circle with radius π? [π 3 ]

35. 35 10 is 20% of what number? [50]

36. 36 Simplify: 2

37. 37 The square is 8 inches on a side, the diagonals meet the sides at midpoints. What is the area of the white band? [32 in 2 ]

38. 38 Two numbers differ by 9 and their sum is 7. What are they? [8 and -1]

39. 39 The equation below has exactly two solutions. Both of them can be found without any solving. What are they? (x-1)(x-2)(x-3)(x-4) = 24 [0,5]

40. 40 If x is the first number and y is the second, how do you write the statement “the first number is 5 more than twice the second”? [x = 2y+5]

41. 41 [ecd]

42. 42 The radius OD is 5, the segment OC has length 3 and is perpendicular to the chord AB. How long is AB? [8]

43. 43 The sum of a number and its reciprocal is smaller than the number. How can that be? [The number must be negative]

44. 44 George tells you that the average of 4 consecutive numbers (i.e. positive integers) is 120. What do you deduce? [That George is a liar]