AMC8 2026

AMC8 2026 · Q8

AMC8 2026 · Q8. It mainly tests Percent, Divisibility & factors.

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?

一项调查问了若干人他们是否喜欢解数学题。恰好有 $74\%$ 的人回答“喜欢”。被问的最少人数可能是多少？

(A) 10 10

(B) 20 20

(D) 50 50

(E) 100 100

Answer

Correct choice: (D)

正确答案：（D）

Solution

We can see that $74 \% = \frac{74}{100}$ by definition. This fraction can be simplified to $\frac{37}{50}$, meaning $37$ out of $50$ people said "Yes". Since $\gcd(37,50) = 1$, if this fraction was divided any further, we would have fractional numerator and denominator, which is clearly impossible. Therefore, the minimum number of people surveyed was $\boxed{ \textbf{(D) } 50}$.

我们可以看到 $74\% = \frac{74}{100}$，这是定义。该分数可约分为 $\frac{37}{50}$，意味着 $50$ 人中有 $37$ 人回答“喜欢”。由于 $\gcd(37,50) = 1$，如果进一步约分，分子分母就会变成分数，显然不可能。因此，最少被调查的人数是 $\boxed{ \textbf{(D) } 50}$。

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