For the most part, I concur with the previous answers.

I do want to clarify: There is no Google penalty for duplicate content. A Google penalty is a specific kind of action. Duplicate content, generally speaking, can certainly hurt your sites performance, but there's no penalty.

So much depends on the specifics of your situation. If this other site is the primary source of your revenue (or leads), then you probably want to do what will add gas to that fire.

Again, it depends on your business objectives. Providing them with content, traffic, links, whatever, doesn't provide you any long term "seo equity," but that may be ok.

Couple of additional ideas to consider, if appropriate:

1) Index the pages on your site, but add an rel=canonical tag that points Google to the source of the content (i.e. the huge organic traffic site). You might get a little more traffic. You won't hurt the other site.

2) Come up with a creative way to promote those Q&A's with original content on your site.