PASCAL 2021 Problem 20

Suppose that R, S and T are digits and that N is the four-digit positive integer 8 R S T. That is, N has thousands digit 8 , hundreds digit R, tens digits S, and ones (units) digit T, which means that N=8000+100 R+10 S+T. Suppose that the following conditions are all true:

  • The two-digit integer 8 R is divisible by 3.
  • The three-digit integer 8 R S is divisible by 4.
  • The four-digit integer 8 R S T is divisible by 5.
  • The digits of N are not necessarily all different.

The number of possible values for the integer N is

Answer Choices
A. 8
B. 16
C. 12
D. 10
E. 14