2017 AMC 10B Problem 17

The strictly increasing positive integers correspond to the nonempty subsets of $\{1,2,3,4,5,6,7,8,9\}$, written in increasing order. There are $2^9-1=511$ of these. The strictly decreasing positive integers correspond to subsets of $\{0,1,2,3,4,5,6,7,8,9\}$, written in decreasing order, except for the empty set and $\{0\}$. There are $2^{10}-2=1022$ of these. The one-digit numbers $1$ through $9$ were counted in both groups, so the total is $511+1022-9=1524$. Thus, B is the correct answer.