# 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 \(n + x\)?