Problem:
The remainder function can be defined for all real numbers x and y with y=0 by
rem(x,y)=x−y⌊yx⌋
where ⌊yx⌋ denotes the greatest integer less than or equal to yx. What is the value of rem(83,−52)?
Answer Choices:
A. −83
B. −401
C. 0
D. 83
E. 4031
Solution:
83−(−52)⎣⎢⎢⎢⎢⎢−5283⎦⎥⎥⎥⎥⎥=83+52⌊−1615⌋=83+52(−1)=−401
The problems on this page are the property of the MAA's American Mathematics Competitions