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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?

User Kurtzmarc
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1 Answer

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Answer:

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

User Fabian Rivera
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