Problem 8 · 2026 AMC 8
Medium
Fractions, Decimals & Percents
reduce-fraction
A poll asked some people whether they liked solving mathematics problems, and exactly 74% answered "yes." What is the fewest possible number of people who could have been asked?
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Answer: D — 50 people.
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Hint 1 of 2
You can't have a fraction of a person, so 74% of the group has to land on a whole number. What does that force about the group size?
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Hint 2 of 2
Reduce 74/100 to lowest terms. The denominator of the reduced fraction is the smallest group size that makes the count whole.
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Approach: the reduced denominator is the smallest workable group
- ‘74% said yes’ means (yes count) = 74100 × (group), and that has to be a whole number of people.
- Reduce: 74100 = 3750. Since 37 and 50 share no factors, the group must be a multiple of 50 for 37/50 of it to be whole — so the fewest is 50 people (with 37 yeses).
- Why this transfers: ‘exactly p% must be a whole count’ problems always come down to reducing p/100 — the smallest group is the reduced denominator, because that's the first size that clears the fraction.
Mark:
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