Problem: When a positive integer x is divided by a positive integer y, the quotient is u and the remainder is v,u and v integers. What is the remainder when x+2uy is divided by y?
Answer Choices:
A. 0
B. 2u
C. 3u
D. v
E. 2v
Solution:
yx+2uy=yx+2u. Since yx=u+yv⋅yx+2uy=3u+yv, so that the remainder is v.