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2011 AMC 10B Problem 24

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2011 AMC 10B Problem 24AMC 10 Step by Step
Name:                             Date: September 13, 2026
Coordinate Geometry · difficulty 4 of 5 · about 6 min · position P21-25

A lattice point in an xyxy -coordinate system is any point (x,y)(x, y) where both xx and yy are integers. The graph of y=mx+2y = mx +2 passes through no lattice point with 0<x≤1000 < x \le 100 for all mm such that 1/2<m<a1/2 < m < a . What is the maximum possible value of aa ?

  1. A)

    51101\frac{51}{101}

  2. B)

    5099\frac{50}{99}

  3. C)

    51100\frac{51}{100}

  4. D)

    52101\frac{52}{101}

  5. E)

    1325\frac{13}{25}

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