A-12 ANSWERS 67. a) 1 ,3 2 ,3 103 11 ,3 12 ,3 20 ,3 21 ,3 22 ,3 100 ,3 101 ,3 102 ,3 110 ,3 111 ,3 112 ,3 120 ,3 121 ,3 122 ,3 200 ,3 201 ,3 2023 71. b) 4 SECTION 4.4, PAGE 201 55. 5 56. 5 57. 5 58. 5 59. 4 60. 4 61. 4 62. 4 63. 4 64. 4 65. 4 66. 4 71. 5 0, 5 1, 5 2, 5 3 SECTION 4.5, PAGE 206 33. REVIEW EXERCISES, PAGE 209 5. 6. 7. 8. 21. 22. 23. 24. 37. 38. 39. 40. 45. 46. 47. 48. CHAPTER TEST, PAGE 211 7. 8. o βυ ι f 9. 10. Chapter 5 SECTION 5.1, PAGE 220 11. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97. 12. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, and 149. 57. 2 60, 3 40, 4 30, 5 24, 6 20, 8 15, 10 12, 12 10, 15 8, 20 6, 24 5, 30 4, 40 3, 60 2 × × × × × × × × × × × × × × 66. No. Any other two consecutive natural numbers will include one number that is divisible by 2 and is therefore composite. 70. 4 22,6 33,8 35,10 37, 12 5 7,14=7 7,16 3 13,18 5 13, 20 3 17 = + = + = + = + = + + = + = + = + 86. No, not every number divisible by both 2 and 4 is divisible by 8, for example, 20. If two prime numbers divide a number, then their product will divide the number. 87. For any three consecutive natural numbers, one of the numbers is divisible by 2 and another number is divisible by 3. Therefore, the product of the three numbers would be divisible by 6. 91. 8 233,9 333,10 235, = + + = + + = + + 11 227,12 255,13 337, 14 257,15 357,16 277, 17 5 5 7,18 2 5 11,19 3 5 11, 20 2 7 11 = + + = + + = + + = + + = + + = + + = + + = + + = + + = + + SECTION 5.2, PAGE 232 Answer to Recreational Math box on page 234 = + − − 0 4 4 4 4 = + + 1 4 4 4 4 = ⋅ + 2 4 4 4 4 = + + 3 4 4 4 4 = − + 4 4 4 4 4 = ⋅ + 5 4 4 4 4 = + + 6 4 4 4 4 = + − 7 4 4 4 4 = + + − 8 4 4 4 4 = + + 9 4 4 4 4 Other answers are possible. 80. b) From the diagram, notice that the third pentagonal number is + + = 3 2 1 12; 2 the fourth pentagonal number is + + + = 4 3 2 1 22. 2 The next five pentagonal numbers then are 5 4 3 2 1 35, 6 5 4 3 2 1 51, 7 65432170, 8 765432192,and 9 87654321117. 2 2 2 2 2 + + + + = + + + + + = + + + + + + = + + + + + + + = + + + + + + + + =
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