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2025 AMC 10A Problem 13

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2025 AMC 10A Problem 13AMC 10 Step by Step
Name:                             Date: September 13, 2026
Sequences & Series · difficulty 3 of 5 · about 4 min · position P11-15

In the figure below, the outside square contains infinitely many squares, each of them with the same center and sides parallel to the outside square. The ratio of the side length of a square to the side length of the next inner square is kk , where 0<k<1.0 < k < 1. The spaces between squares are alternately shaded as shown in the figure (which is not necessarily drawn to scale).

The area of the shaded portion of the figure is 64%64\% of the area of the original square. What is kk ?

figure

  1. A)

    35\frac{3}{5}

  2. B)

    1625\frac{16}{25}

  3. C)

    23\frac{2}{3}

  4. D)

    34\frac{3}{4}

  5. E)

    45\frac{4}{5}

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