For a,r,d are the positive integers, and d|a means that “a is divisible by d”, if d|ar, which of the following must be true?  Answers.
A) d|a
B) d|r
C) d|2ar
D) d|(a+r)
E) d|(a-r)
d/a means a is divisible by d   d/ar means ab divisible by d.   all are integers so ,   if ar is divisible by d,   1 a can be divisible by d   or   2 r can be divisble by d.   so the question stem asks must true.   so option a and b are could but not must.   option c is 2ar divisible by d. if ab is divisible by d then 2ar is divisible by d.   option d and e we can't predict.   so option d|2ar is correct.
<result>C</result>
For a,r,d are the positive integers, and d|a means that “a is divisible by d”, if d|ar, which of the following must be true?