Problem: For the natural numbers, when P is divided by D, the quotient is Q and the remainder is R. When Q is divided by D′, the quotient is Q′ and the remainder is R′. Then, when P is divided by D′, the remainder is:
Answer Choices:
A. R+R′D
B. R′+RD
C. RR′
D. R
E. R′
Solution:
P=QD+R and Q=Q′D′+R′∴P=Q′DD′+R′D+R, which means that when P is divided by D′ the quotient is Q′ and the remainder is R+R′D.