I think that there's some grey area here when it comes to "induce" vs. "inducing" -- and of course, all of the usual cautions apply about non-official questions.
Let's strip down (D) and (E) a little bit, so we can focus on the difference between "induce" and "inducing":
(D) Mysterious flashing lights in the night sky distract pilots and induce them to veer from their flight path.
(E) Mysterious flashing lights in the night sky distract pilots, inducing them to veer from their flight paths.
In (D), the two verbs are parallel, and that suggests that the flashing lights perform two actions: they distract pilots, and they induce them to veer from their flight path. But in some sense, the two actions are separate -- these are two different things that the flashing lights do, but the two actions may or may not be related or simultaneous.
In (E), "inducing" isn't a verb -- it's a modifier (a participle, if you want to get technical). It's modifying the previous action in this case: "inducing them to veer from their flight path" is telling us more information about what happens when lights distract pilots.
The meaning is different between the two, but I'm not sure that one is inherently right and the other is inherently wrong -- it just depends on what you think the question is trying to say. And as is often the case with non-official questions, we could probably argue about this a little.
That said: yes, Teerex is right about the singular vs. plural issue. It's just that the verb vs. modifier difference isn't 100% clear here.