# Pretty Properties

Number Theory Level 5

Let $$A$$ be the set of all two-digit integers for which the product of their digits is exactly twice as much as the sum of their digits.

Let $$B$$ be the set of all two-digit integers which become 75% greater when the digits are flipped.

Let $$n$$ be the number of two-digit integers in the union $$A \cup B$$.

Let $$x$$ be the only two-digit integer that is a member of the intersection $$A \cap B$$.

How much is $$n + x$$?

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