201617 mathcounts handbook answer keys - ANSWERS In addition to the answer we have provided a difficulty rating for each problem Our scale is 1-7 with 7

201617 mathcounts handbook answer keys - ANSWERS In...

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MATHCOUNTS 2016-2017 51 56. (3) 57. (4) 58. (2) 59. (4) 60. (3) 51. (4) 52. (3) 53. (4) 54. (2) 55. (3) In addition to the answer, we have provided a difficulty rating for each problem. Our scale is 1-7, with 7 being the most difficult. These are only approximations, and how difficult a problem is for a particular student will vary. Below is a gen- eral guide to the ratings: Difficulty 1/2/3 - One concept; one- to two-step solution; appropriate for students just starting the middle school curriculum. 4/5 - One or two concepts; multistep solution; knowledge of some middle school topics is necessary. 6/7 - Multiple and/or advanced concepts; multistep solution; knowledge of advanced middle school topics and/or problem-solving strategies is necessary. * The plural form of the units is always provided in the answer blank, even if the answer appears to require the singular form of the units. ANSWERS Warm-Up 1 1. (1) 2. (2) 3. (2) 4. (2) 5. (2) 6. (4) 7. (4) 8. (2) 9. (3) 10. (2) Answer Difficulty 77 3 1 5 11 1 1/6 30 9/16 1.7 × 10 5 0 170 or 170.00 Warm-Up 2 Answer Difficulty 11. (2) 12. (3) 13. (3) 14. (3) 15. (4) 16. (3) 17. (5) 18. (4) 19. (3) 20. (4) 16 5 12 5 3.16 × 10 −14 720 36 7/12 12 2 17 88 86 38 12 1/64 380 15/64 −3 2/5 8 21. (2) 22. (2) 23. (2) 24. (1) 25. (4) 26. (4) 27. (4) 28. (4) 29. (4) 30. (2) Warm-Up 3 Answer Difficulty Warm-Up 4 Answer Difficulty 22 3 8 621 9 25/81 18/25 8 6 1 Workout 1 Answer Difficulty 31. (3) 32. (4) 33. (4) 34. (4) 35. (4) 36. (4) 37. (3) 38. (2) 39. (3) 40. (4) 1.30 721 1100 12 14.6 7 Q 16 6 36 Workout 2 Answer Difficulty 41. (3) 42. (3) 43. (3) 44. (1) 45. (4) 46. (4) 47. (4) 48. (4) 49. (4) 50. (4) 1* 90 1.65 41 120 4 1/4 36 7 21.3
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MATHCOUNTS 2016-2017 52 Warm-Up 6 Answer Difficulty 71. (2) 72. (3) 73. (3) 74. (4) 75. (4) 76. (4) 77. (5) 78. (3) 79. (4) 80. (4) 24 or 24.00 17 175 33 867 34 2 π 7 −5 17 Warm-Up 7 Answer Difficulty 101. (2) 102. (3) 103. (5) 104. (2) 105. (4) 106. (4) 107. (4) 108. (4) 109. (5) 110. (4) 0 2 74 8.10 1/16 48 3 500 14 3 678 Workout 3 81. (3) 82. (3) 83. (4) 84. (2) 85. (2) 86. (4) 87. (4) 88. (4) 89. (4) 90. (4) Answer Difficulty −4 18 19 2 2 8 2018 29 2.45 750 4 192 π Workout 4 91. (3) 92. (3) 93. (4) 94. (2) 95. (5) 96. (4) 97. (4) 98. (4) 99. (4) 100. (3) Answer Difficulty 60 776 10.5 3 35 36 4094 870 100 922 Warm-Up 8 111. (2) 112. (4) 113. (4) 114. (4) 115. (5) 116. (5) 117. (4) 118. (4) 119. (5) 120. (4) Answer Difficulty 6 1/32 37 π 9 18 1/39 9 42 72 π 12022 61. (2) 62. (4) 63. (4) 64. (3) 65. (4) 66. (5) 67. (3) 68. (3) 69. (5) 70. (4) Warm-Up 5 Answer Difficulty 216 38 11 6 275,000 or 275,000.00 4851 30 720 160 −3
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MATHCOUNTS 2016-2017 53 Warm-Up 10 Answer Difficulty 151. (4) 152. (4) 153. (4) 154. (5) 155. (5) 156. (3) 157. (6) 158. (4) 159. (4) 160. (4) 38 78230 14 30 1760 18/55 40 2031 31 32 Warm-Up 11 161. (4) 162. (3) 163. (5) 164. (3) 165. (4) 166. (4) 167. (3) 168. (4) 169. (5) 170. (5) Answer Difficulty 7/64 18 27 62 30 8008 6 9.2 9 2 Warm-Up 9 141. (2) 142. (4) 143. (3) 144. (3) 145. (4) 146. (6) 147. (3) 148. (5) 149. (3) 150. (3) Answer Difficulty 5 3/2 40 15 981 32 132 28 3 512 Workout 5 121. (4) 122. (4) 123. (5) 124. (4) 125. (5) 126. (3) 127. (3) 128. (5) 129. (6) 130. (3) Answer Difficulty 29 7.2 10/3 3 9.4 45 1/8 0.5 1.14 90 Workout 6 Answer Difficulty 131. (3) 132. (5) 133. (4) 134. (5) 135. (3) 136. (4) 137. (5) 138. (4) 139. (3) 140. (3) 61,900 20 24 346 3/7 42 8 3/65 22 or 22.00 272 171. (4) 172. (5) 173. (3) 174. (5) 175. (4) Workout 7 Answer Difficulty 176. (3) 177. (5) 178. (4) 179. (5) 180. (4) 3/20 60 1.11 9/5 2.6 40.5 24 1.7 27 0.94
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MATHCOUNTS 2016-2017 54 201. (5) 202. (5) 203. (4) 204. (5) 205. (5) 206. (5) 207. (5) 208. (6) 209. (4) 210. (6) Warm-Up 13 Answer Difficulty 279 121 7 15/2 5/3 6777 1/9 6 7 48/5 216. (5) 217. (5) 218. (5) 219. (5) 220. (5) Warm-Up 14 211. (3) 212. (5) 213. (4) 214. (7) 215. (5) Answer Difficulty 28 7/15 16 124/133 12 5 21/8 47 169 or 40+ 2 3 Workout 8 181. (2) 182. (2) 183. (5) 184. (5) 185. (5) 186. (4) 187. (4) 188. (6) 189. (6) 190. (4) Answer Difficulty 2 1/210 4 29 6 13 10 16/5 6 5/18 73 806 241. (2) 242. (2) 243. (2) 244. (3) 245. (3) 246. (3) 247. (4) 248. (5) 249. (5) 250. (6) Answer Difficulty Bases Stretch 33 2A7B 2355 7 19 22 20 18 26 30 Warm-Up 12 191. (3) 192. (4) 193. (5) 194. (4) 195. (4) 196. (5) 197. (7) 198. (3) 199. (4) 200. (5)
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