2022 AMC 10A Problem 8

The average of the $6$ numbers is $$\dfrac{1 + 7 + \cdots + X}{6} = \dfrac{20 + X}{6}.$$ This value can equal any of the terms in the set, so we can case on what it equals. $$\dfrac{20 + X}{6} = 1 \iff X = -14$$ $$\dfrac{20 + X}{6} = 7 \iff X = 22$$ $$\dfrac{20 + X}{6} = 5 \iff X = 10$$ $$\dfrac{20 + X}{6} = 2 \iff X = -8$$ $$\dfrac{20 + X}{6} = X \iff X = 4$$ Adding up all the positive values for $X,$ we get $36.$ Thus, D is the correct answer.