I would think answering two of the longest unanswered (well, one is kind of solved post his death) questions in mathematics would be a very good "test" of advanced intelligence. And if one accepts that our immediate solar system could not have produced these aliens, and considering the vast distance to even the closest star to ours (and with recent "evidence" of which local stars have or do not seem to have planets around them, it's potentially several times farther than the closest star to ours), it would be logical to me that these beings would have to be quite advanced (intellectually) to us to figure out how to get here alive and would probably have quite advanced mathematical knowledge to ours. (I must add that there are a few communities not too far from me that I suspect harbor genetic traits that are not of this earth, sans the advanced intelligence aspect!).
Considering that "good" or "moral judgments" have such a wide array of meanings and values among Earths' various cultures, I would assume it would have an even more different meaning to an extraterrestrial (my assumption, of curse) that it would be the more difficult question to answer than a mathematical one. Therefore being a rather poor "test" for verifying advanced intelligence.
Your first answer did ring well with me, however. I attended a talk a few months back by three philosophy professors from my school. It was about the conflict and competition of teaching evolution and/or creationism in US history with an emphasis on Arkansas. They mentioned that a few decades back when teaching evolution was illegal in Arkansas, there was a growing voice to allow it by some newspapers and citizens, and of course resistance by others. They had numerous public debates and for one of them, Carl Sagan came to Little Rock to "debate" several church leaders. It was held at a large Baptist Church (to which Sagan protested as he was assured it would be at a public auditorium) and many of the more conservative churches in the region organized bus loads of their congregation to attend. It was, to say the least, a highly hostile crowd for an East Coast, big city, pointy-headed intellectual, non-Christian (Jewish), astrophysics professor, outsider to walk into.
The presenter gave several accounts from both news paper reporters and politicians attending and some (those that disagreed with his perspective) referred to Sagan as "arrogant" and accused him of having a condescending attitude. Crowds with signs protested outside, and many were inside as well, often interrupting him with shouts, hymns, and name calling. He was rather hurriedly rushed back to airport and hustled out of town (local sheriff said it was for his own protection), but a few years later they revoked the law and today each school district has the choice to teach one, or the other, or both, or none at all.
I apologize for drifting a bit off topic, but it did remind me of how Sagan was received by my state.
Natch