Two sets of 3 consecutive positive integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?

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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