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2016 AMC 10A Problem 4

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2016 AMC 10A Problem 4AMC 10 Step by Step
Name:                             Date: September 13, 2026
Number Properties · difficulty 1 of 5 · about 2 min · position P1-10

The remainder can be defined for all real numbers xx and yy with y≠0y \neq 0 by rem(x,y)=x−y⌊xy⌋\text{rem} (x ,y)=x-y\left \lfloor \frac{x}{y} \right \rfloor where ⌊xy⌋\left \lfloor \dfrac{x}{y} \right \rfloor denotes the greatest integer less than or equal to xy\dfrac{x}{y} . What is the value of rem(38,−25)\text{rem}\left(\dfrac{3}{8}, -\dfrac{2}{5}\right) ?

  1. A)

    −38-\frac{3}{8}

  2. B)

    −140-\frac{1}{40}

  3. C)

    00

  4. D)

    38\frac{3}{8}

  5. E)

    3140\frac{31}{40}

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