6

Explanation

Suppose the first set of numbers is {2, 3, 4}. For the second set to both have greater numbers than the first set and for the two sets to have exactly one integer in common the second set must be {4, 5, 6}.

Excluding the integer the sets have in common, each of the remaining 2 numbers in set two is the corresponding number in set one plus 3. So, the sum of the numbers in set two is \(2 \times 3 = 6\) more than the sum of the numbers in set one.

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