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2016 AMC 10B Problem 25

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2016 AMC 10B Problem 25AMC 10 Step by Step
Name:                             Date: September 13, 2026
Number Properties · difficulty 5 of 5 · about 10 min · position P21-25

Let f(x)=∑k=210(⌊kx⌋−k⌊x⌋)f(x)=\sum_{k=2}^{10}(\lfloor kx \rfloor -k \lfloor x \rfloor) , where ⌊r⌋\lfloor r \rfloor denotes the greatest integer less than or equal to rr . How many distinct values does f(x)f(x) assume for x≥0x \ge 0 ?

  1. A)

    3232

  2. B)

    3636

  3. C)

    4545

  4. D)

    4646

  5. E)

    infinitely many\text{infinitely many}

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