Question

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?

Answer 1

There are 9 distinct possible values for q.

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