AMC 8 2026 Problem 8
AMC8 2026 年第 8 题
整除与因数★★☆☆☆
A poll asked a number of people if they liked solving mathematics problems. Exactly 74% answered "yes." What is the fewest possible number of people who could have been asked the question?
一项民意调查询问若干人是否喜欢解数学题。恰好有 74% 的人回答“是”。最少可能有多少人接受了这项调查？
- A.10
- B.20
- C.25
- D.50
- E.100
正确答案 · Correct Answer
D
解析 · Solution
解法1
74% = 。37 和 50 互质，分数已最简。要使 为整数， 必须是 50 的倍数，最小为 50。
逐一验证选项（不推荐，耗时，仅作备选）：总人数 10 → 7.4 人（非整数，排除）；20 → 14.8（排除）；25 → 18.5（排除）；50 → 37 人（整数 ✓）。答案：50。此方法可行但比分数化简法慢得多，考试时不建议优先使用。
Solution 1
74% = . Since 37 and 50 are coprime (gcd=1), this fraction is in simplest form. For of people to be a whole number, must be a multiple of 50. The smallest positive multiple is 50.
Check each answer choice until a whole number appears. 10 people → 10×74% = 7.4 (not integer); 20 → 14.8; 25 → 18.5; 50 → 37 (integer). Answer: 50. Note: this method works but is slower than the fraction approach above; use only if you forget the simplification step.
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