2012 AMC 10A Problem 8

Let the three numbers be $a, b, c$ where $a \lt b \lt c.$ None of them are equal, since all three sums are different. Then $$a + b = 12, a + c = 17,$$ and $$b + c = 19.$$ Adding all three equations together gives us $$2(a + b + c) = 48.$$ Then $$a + b + c = 24,$$ from which we can subtract $$a + c = 17,$$ to get $b = 7.$ Thus, D is the correct answer.