Could be false. The stimulus does nothing to rule out this possibility—maybe the residents that will put more recyclables in with their regular garbage will stop recycling altogether, and maybe these residents make up the majority!

Could be false. It’s quite possible that some residents might continue to recycle but ignore the sorting mandate.

Could be false. (C) has three problems. First, we only know two consequences of implementing the sorting requirement, and neither of them involve the sanitation budget. Second, (C) isn’t even about the sanitation budget; it’s about the city’s costs. Third, (C) makes an unhelpful comparison because it compares landfill costs to current sorting costs. But don’t know if, or how, implementing the sorting requirement might change those sorting costs. Maybe implementing the sorting requirement would lower sorting costs. So (C) could be false; it’s possible that implementing the sorting requirement would cause landfill costs to increase slightly and exceed current sorting costs... while also causing sorting costs to drop considerably below their current value.

Must be true. By chaining the conditionals, we see that “more recyclables in landfill” is a necessary condition of the sanitation department staying within its budget.

Could be false. (E) flips the sufficient and necessary conditions. “Require sorting” is a necessary condition of “stay within budget”—it’s not a sufficient condition. So implementing the sorting requirement doesn’t guarantee that the sanitation department will stay within its budget.