Is it justified to downvote a complete answer to a question which does not show much effort on the asker's part toward solving the question? I believe this is a question applicable to most problem-solving-based communities on SE, but if it's needed, I'm writing with specific reference to questions on Math Stack Exchange.
Notwithstanding that any answer should apply to the question asked, I think questions and answers should be assessed independently.
The guideline, which is available as a tooltip, when downvoting an answer is to do so when:
This answer is not useful
There are myriad reasons why a particular voter may find an answer to be not useful, but if an answers' usefulness is assessed that way by them, then they are free to downvote, and should not be questioned about that because it is their opinion.
If another user thinks the same answer is useful, then they are equally free to express that opinion using an upvote.