"The Hungarian boss is not waiting."
Translation:A magyar főnök nem vár.
"Egy" translates to "a/an" (lit. "one") in English, so whenever you would use those two you should write egy! Egy does not change with respect to whether the word has a vowel or consonant after it.
E.g. an apple = egy alma ; a banana = egy banán
Make sure you don't confuse the Hungarian "a/az" with these as they both mean "the" in English! They change according to whether the word after them begins with a vowel or consonant.
E.g. the apple = az alma ; the banana = a banán
I hope this helped! I know it's a bit late to answer this.
If it really gave you "nincs vár" or similar as a correct answer, that needs to be reported. It should be "nem vár" for verbs. I think for most (or all?) cases you can think of "nincs" as the contraction of "nem van", as in smthing doesnt exist. "Nincs kanál." -> "There is no spoon." For other verbs "nem" is the proper word for negation.