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2026 AMC 10A Problem 15

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2026 AMC 10A Problem 15AMC 10 Step by Step

Name: Date: November 10, 2026

Games & Processes · difficulty 3 of 5 · about 4 min · position P11-15

The tree diagram below has nodes labeled with rational numbers. The top node, at level 0, is $\frac{1}{2}$ . Each node $\frac{a}{b}$ sprouts two nodes in the level below it, $\frac{a}{a+b}$ and $\frac{b}{a+b}$ . For example, level $1$ has nodes $\frac{1}{1+2} = \frac{1}{3}$ and $\frac{2}{1+2} = \frac{2}{3}$ .

At what level does the node $\frac{20}{27}$ appear in the diagram?

A) $5$
B) $8$
C) $12$
D) $26$
E) $\text{The node } \dfrac{20}{27} \text{ does not appear in the diagram.}$

2026 AMC 10A Problem 15

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