1. NRP MATH CHALLENGE CLUB TEAM CHALLENGE MAY 4 TH, 2016

2. ROUND ONE Individual Round 1 minute time limit

3. One angle in an isosceles triangle is one- hundred degrees. What is the degree measure of one of the other two angles? Question 1

4. One angle in an isosceles triangle is one- hundred degrees. What is the degree measure of one of the other two angles? Answer : 40 degrees Question 1

5. If Andrew has six times as many marbles as Rachel, Rachel has thirteen more marbles than Nathan, and Nathan has twelve marbles, how many marbles does Andrew have? Question 2

6. If Andrew has six times as many marbles as Rachel, Rachel has thirteen more marbles than Nathan, and Nathan has twelve marbles, how many marbles does Andrew have? Answer : 150 marbles Question 2

7. The first term of a sequence is sixty-two. Each term after the first term is five less than the previous term of the sequence. What is the sixth term of this sequence? Question 3

8. The first term of a sequence is sixty-two. Each term after the first term is five less than the previous term of the sequence. What is the sixth term of this sequence? Answer : 37 Question 3

9. Andy begins reading his math book at 4:38pm and finish reading his math book at 6:12pm, for how many minutes was Andy reading? Question 4

10. Andy begins reading his math book at 4:38pm and finish reading his math book at 6:12pm, for how many minutes was Andy reading? Answer : 94 minutes Question 4

11. If a square with a perimeter of twenty is split into two congruent rectangles, what is the sum of the two rectangles’ perimeters? Question 5

12. If a square with a perimeter of twenty is split into two congruent rectangles, what is the sum of the two rectangles’ perimeters? Answer : 30 Question 5

13. How many multiples of six are there between twenty-five and ninety-five? Question 6

14. How many multiples of six are there between twenty-five and ninety-five? Answer : 11 Question 6

15. If two-fifths of a number is sixteen, what is twice that number? Question 7

16. If two-fifths of a number is sixteen, what is twice that number? Answer : 80 Question 7

17. If each child in a family has at least 3 brothers and 2 sisters, what is the fewest number of children that could be in the family? Question 8

18. If each child in a family has at least 3 brothers and 2 sisters, what is the fewest number of children that could be in the family? Answer : 7 children Question 8

19. What is the sum of the positive factors of twenty? Question 9

20. What is the sum of the positive factors of twenty? Answer : 42 Question 9

21. If Jennifer has twenty-five cents, Daniel has twice as much as Jennifer, and Michael has three times as much as Daniel, how much money, in cents, do they have altogether? Question 10

22. If Jennifer has twenty-five cents, Daniel has twice as much as Jennifer, and Michael has three times as much as Daniel, how much money, in cents, do they have altogether? Answer : 225 cents Question 10

23. If there are seven people in a room, and each person shakes hands with every other person in the room exactly once, how many handshakes will occur? Question 11

24. If there are seven people in a room, and each person shakes hands with every other person in the room exactly once, how many handshakes will occur? Answer : 21 handshakes Question 11

25. What is the product of the reciprocals of one half, two, and four, expressed as a reduced fraction? Question 12

27. How many positive integers less than 1000 are divisible by 4 and 6 but not 8? Question 13

28. How many positive integers less than 1000 are divisible by 4 and 6 but not 8? Answer : 42 integers Question 13

29. Arta walked sixty-four pi meters around a circular track. If he walked four full laps, what is the radius of the track in meters? Question 14

30. Arta walked sixty-four pi meters around a circular track. If he walked four full laps, what is the radius of the track in meters? Answer : 8 meters Question 14

31. What is the probability of drawing either a five or a heart from a standard deck of fifty- two cards? Express your answer as a reduced fraction. Question 15

33. How many positive two-digit integers have an odd number of positive factors? Question 16

34. How many positive two-digit integers have an odd number of positive factors? Answer : 6 integers Question 16

35. If you were to walk twelve yards north, thirteen yards east, six yards south, then five yards west, how many yards will you be from your original position? Question 17

36. If you were to walk twelve yards north, thirteen yards east, six yards south, then five yards west, how many yards will you be from your original position? Answer : 10 yards Question 17

37. If you roll two fair standard six-sided dice, what is the probability that the sum of the numbers rolled is six? Express your answer as a reduced fraction. Question 18

39. What is the probability of not selecting a blue marble from a bag of six red marbles, two blue marbles, and twelve yellow marbles? Express your answer as a percent. Question 19

40. What is the probability of not selecting a blue marble from a bag of six red marbles, two blue marbles, and twelve yellow marbles? Express your answer as a percent. Answer : 90% Question 19

41. If you randomly select two numbers, with replacement, from the numbers one to five, what is the probability that both numbers will be even? Express your answer as a percent. Question 20

42. If you randomly select two numbers, with replacement, from the numbers one to five, what is the probability that both numbers will be even? Express your answer as a percent. Answer : 16% Question 20

43. ROUND TWO Team Round 3 minutes time limit

44. Cindy was given an envelope filled with cash as a graduation present. She immediately put 70% of that money into a savings account. She then used 25% of the remaining money to buy herself new clothes. Finally, she used the remaining $270 to buy herself the supplies she needed for college. How much money, in dollars, did she put in her savings account? Question 1

45. Cindy was given an envelope filled with cash as a graduation present. She immediately put 70% of that money into a savings account. She then used 25% of the remaining money to buy herself new clothes. Finally, she used the remaining $270 to buy herself the supplies she needed for college. How much money, in dollars, did she put in her savings account? Answer : $840 Question 1

46. How many unordered pairs of integers have a product of 400? Question 2

47. How many unordered pairs of integers have a product of 400? Answer : 16 pairs Question 2

48. Question 3

50. A 4-unit by 4-unit square is broken into sixteen 1-unit by 1-unit squares. If each of the unit squares can only share a side with a maximum of one other shaded square, what is the greatest number of unit squares that could be shaded? Question 4

51. A 4-unit by 4-unit square is broken into sixteen 1-unit by 1-unit squares. If each of the unit squares can only share a side with a maximum of one other shaded square, what is the greatest number of unit squares that could be shaded? Answer : 6 unit squares Question 4

52. A palindrome is defined as a number whose digits are the same when read both from left to right and right to left. For example, 434 is a palindrome. How many three-digit numbers are palindromes? Question 5

53. A palindrome is defined as a number whose digits are the same when read both from left to right and right to left. For example, 434 is a palindrome. How many three-digit numbers are palindromes? Answer : 90 numbers Question 5

54. If you begin writing down the counting numbers in increasing order, beginning with 1, what three- digit number will you be in the process of writing when writing your 403rd digit? Question 6

55. If you begin writing down the counting numbers in increasing order, beginning with 1, what three- digit number will you be in the process of writing when writing your 403rd digit? Answer : 171 Question 6

56. How many positive three-digit numbers contain at least one of the following digits: 1, 2, 4, 5, 6, 7, 8, 9? Question 7

57. How many positive three-digit numbers contain at least one of the following digits: 1, 2, 4, 5, 6, 7, 8, 9? Answer : 896 numbers Question 7

58. What is the smallest three-digit positive integer that, when halved four consecutive times, will be greater than 10? Question 8

59. What is the smallest three-digit positive integer that, when halved four consecutive times, will be greater than 10? Answer : 161 Question 8

60. How many positive three-digit integers contain exactly two identical digits? Question 9

61. How many positive three-digit integers contain exactly two identical digits? Answer : 243 integers Question 9

62. During a campaign for Math Team President, three candidates – Justin, Jonathan, and Henry – decided to advertise themselves using the following strategies in a hall of 200 lockers: Justin went to every 2nd locker and put up his campaign poster. Jonathan went to every 3rd locker and put up her campaign poster. Henry went to every 6th locker and put up her campaign poster. Michelle then went through and counted how many of the lockers had at least one campaign poster on it. How many lockers did Michelle count? Question 10

63. During a campaign for Math Team President, three candidates – Justin, Jonathan, and Henry – decided to advertise themselves using the following strategies in a hall of 200 lockers: Justin went to every 2nd locker and put up his campaign poster. Jonathan went to every 3rd locker and put up his campaign poster. Henry went to every 6th locker and put up his campaign poster. Michelle then went through and counted how many of the lockers had at least one campaign poster on it. How many lockers did Michelle count? Answer : 133 lockers Question 10

64. How many integers satisfy all of the following requirements? It must be a positive four-digit integer. It is not divisible by five. The sum of its digits is twelve. The number is a palindrome. Question 11

65. How many integers satisfy all of the following requirements? It must be a positive four-digit integer. It is not divisible by five. The sum of its digits is twelve. The number is a palindrome. Answer : 5 integers Question 11

66. Question 12

68. Suppose that the five-digit number 89xyz is divisible by 2, 4, 5, and 9. If x, y, and z are unique digits, what is the sum of the three missing digits? Question 13

69. Suppose that the five-digit number 89xyz is divisible by 2, 4, 5, and 9. If x, y, and z are unique digits, what is the sum of the three missing digits? Answer : 10 Question 13

70. Two students took an identical 8-question true-or- false test. Using “T” for “true” and “F” for “false”, student 1 answered “TTFFFFTF” and student 2 answered “TFTFTTTF”. Both students got 6 out of their 8 questions correct. What is the greatest number of questions that could have had the correct answer of “true”? Question 14

71. Two students took an identical 8-question true-or-false test. Using “T” for “true” and “F” for “false”, student 1 answered “TTFFFFTF” and student 2 answered “TFTFTTTF”. Both students got 6 out of their 8 questions correct. What is the greatest number of questions that could have had the correct answer of “true”? Answer : 5 questions Question 14

72. Question 15

74. NOW LET’S SEE WHICH TEAM IS THE WINNER!