For a,q,d are the positive integers, and d|a means that “a is divisible by d”, if d|aq, which of the following must be true?
Choose the correct choice from the following choices:
A) d|a
B) d|q
C) d|2aq
D) d|(a+q)
E) d|(a-q)
d/a means a is divisible by d   d/aq means ab divisible by d.   all are integers so ,   if ab is divisible by d,   1 a can be divisible by d   or   2 q 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 2aq divisible by d. if ab is divisible by d then 2aq is divisible by d.   option d and e we can't predict.   so option d|2aq is correct.
<result>C</result>
For a,q,d are the positive integers, and d|a means that “a is divisible by d”, if d|aq, which of the following must be true?