The product of the digits of a positive two-digit integer, q, is a positive multiple of 7. How many distinct possible values are there for q?

There are 9 distinct possible values for q.

Step-by-step explanation:

Let ab be a positive two-digit integer.

a*b=q=7k from some positive integer k. either a or b is 7, since 7 is a prime number and k can be maximum 9. assume a=7, then b can be 1,2,3,4,5,6,7,8,9 b cannot be 0 because a*b=q has to be positive if b=7, then a can be 1,2,3,4,5,6,7,8,9 in both cases there are 9 distinct values for q, which are 7,14,21,28,35,42,49,56,63