Work through 2026 AMC 8 Problem 8 on fractions and divisibility with a written solution, hints, and a visual explanation.
Number TheoryLevel 2 · Core skill
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?
A. 10
B. 20
C. 25
D. 50
E. 100
Hints
Write 74% as a fraction and reduce it to lowest terms.
Once reduced, the denominator tells you the smallest group size for which 74% can be a whole number of people.
Check whether the reduced numerator is prime — if so, the fraction can't be simplified further, and the denominator alone gives the answer.
Read the step-by-step solution
Answer: D · 50
Set up the fraction
74% = 74/100 = 37/50. We need the number of people n such that 74% of n is a whole number.
74/100 = 37/50
Find minimum n
37/50 is in lowest terms (37 is prime). So n must be a multiple of 50. The smallest is 50.