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HMMT 十一月 2008 · 冲刺赛 · 第 5 题

HMMT November 2008 — Guts Round — Problem 5

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 6 ] What is the sum of all integers x such that | x + 2 | ≤ 10?
解析
  1. [ 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. So x must be in the range − 12 ≤ x ≤ 8. If we add up the integers in this range, each positive integer cancels with its additive inverse, so the sum is equal to − 12 − 11 − 10 − 9 = − 42.