HMMT 十一月 2008 · 冲刺赛 · 第 5 题

英文解析

5. [ 6 ] What is the sum of all integers x such that | x + 2 | ≤ 10?
   Answer: − 42 The inequality | x + 2 | ≤ 10 holds if and only if x + 2 ≤ 10 and x + 2 ≥ − 10. Sox must be in the range − 12 ≤ x ≤ 8. If we add up the integers in this range, each positive integercancels with its additive inverse, so the sum is equal to − 12 − 11 − 10 − 9 = − 42.