2025 AMC 8 Problems/Problem 20

Sarika, Dev, and Rajiv are sharing a large block of cheese. They take turns cutting off half of what remains and eating it: first Sarika eats half of the cheese, then Dev eats half of the remaining half, then Rajiv eats half of what remains, then back to Sarika, and so on. They stop when the cheese is too small to see. About what fraction of the original block of cheese does Sarika eat in total?

$\hspace*{5mm}\text{(A) } \frac{4}{7} \quad \text{(B) } \frac{3}{5} \quad \text{(C) } \frac{2}{3} \quad \text{(D) } \frac{3}{4} \quad \text{(E) } \frac{7}{8}$

Video Solution

Key Idea: Let $x$ be the fraction eaten by Sarika. Then Dev eats $\frac{x}{2}$ and Rajiv eats $\frac{x}{4}$ . Hence $x + \frac{x}{2} + \frac{x}{4} = 1$ so solving for $x$ we get $x = \frac{4}{7}$ , $\boxed{\textbf{(A)}}$ .

Video Link: https://www.youtube.com/watch?v=VUR5VYabbrc

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2025 AMC 8 Problems/Problem 20

Video Solution