If a b and c are integers greater than 1 and if ab=21 and bc=39 which of the following must be true?

A * b = 21 and b * c = 39. then b is the common factor of the two numbers.

We need to factor these two numbers to know their equivalent values.

21 factors are 1, 3, 7, 21
39 factors are 1, 3, 13, 39

if b = 3, then a = 7 and c = 13.  

To check:
a * b = 21 where 7 * 3 = 21              and          b * c = 39 where  3 * 13 = 39
 
We can then conclude the following:

3 is lesser than 7 which is lesser than 13. where b < a < c

OR 13 is greater than 7 which is greater than 3. where c > a > b

not sure if these answers are included in your choices but i hope this helps.