Please make sure your clocks have been adjusted.
That reminds me of a Jeopardy question a few years ago. This was in the days when Daylight time ended in late October rather than early November as it does now.
The clue was “This month is the longest month of the year in most states.” The correct response was October, which was an hour longer than any of the other 31-day months, and hence longer than any other month.
Bill Smythe
Another great trivia question ruined by Congress.
Now I just ask people which month has the longest day of the year in (pick a DST state).
Strangely enough, the most common answer is June.
Perhaps you need to re-word your question, then. “Day” could reasonably be interpreted to mean “daylight hours”, which would make June the correct answer.
Bill Smythe
June is the correct answer to the (daylight/daytime) question I did not ask, but using day to refer to daylight/daytime is not the first listed definition of the word.
Can I help it if people misinterpret the question 
A little guided trickery can be amusing in inconsequential matters, albeit infuriating in serious matters. Just make sure you stay on the amusing side.
These are what are sometimes called ‘bar bet’ questions. One of the most famous is to claim that Delilah didn’t cut Sampson’s hair.
If you define a “day” as solar noon to solar noon, the longest day would be around Jan 4 when the earth is closest to the sun (perihelion).