The follwing question seems fairly easy to me, but my answer differs from the OA. I believe the OA is wrong as the authors make an unstated assumption in the detailed solution. I would like to have your opinion.
The crew of the Voelkle Mountain Observatory traks the outdoor temperature for x days. If the temperature increases of exactly 1 degree per day, and the sum of all the temperatures is 0, then which of the following must be true?
I. x represents an even number of days.
II. x represents an odd number of days.
II. the average temperature for the x days is 0
(A) I only
(B) II only
(C) I and III
(D) II and III
(E) None of the above
E. The solution makes the unstated assumption that the temperature on day 1 is an integer value. The only option that is certainly true is III, but this is not one of the answers.