Problem:
Find the sum of all prime numbers between and that are simultaneously greater than a multiple of and less than a multiple of .
Answer Choices:
A.
B.
C.
D.
E.
Solution:
A number one less than a multiple of is has a units digit of or . A number whose units digit is cannot be one greater than a multiple of . Thus, it is sufficient to examine the numbers of the form where is one of the ten digits. Of these, only and are one greater than a multiple of . Among these, only and are prime and their sum is .