Whis is 'van' used here? I thought this was the kind of third-person construction that omitted 'van'.
Although this is a lesson on adjectives, "zárva' isn't - it's an adverb - so you need "van".
It's omitted when you state something like the apple is red (az alma piros) You can read http://www.hungarianreference.com/Van-is-exists-omitting.aspx for more information
Right. It is omitted when you state something like "the apple is red". But:
1. the apple is red
2. the bank is closed
The above two sentences look exactly parallel to me. So why does the sentence in this exercise include "van"? Is it because Hungarian considers "zarva" an adverb rather than an adjective?
Yes, I've just discovered that it's because "zarva" is treated as an adverb. See http://www.hungarianreference.com/Participles/Verbal-participle-verbal-adverb-va.aspx?From=AdverbsSitemap
Uh.. honestly I have no idea about that; I'm going to guess that's the case?.. maybe a native can confirm it.