PR1012 - Must Be True - Q12

Let's deal with the easy statement first.

III. the average temperature for the x days is 0.

We are told that the sum of all temperatures for x days is 0. Average=Sum/x=0/x=0. Hence this statement is always true no matter temperatures are integers or not.

Now, if the temperatures per x days have integer values it means that we have consecutive integers and the number of terms is x. In consecutive integers average=median, and we know that the average=0=median, which means that integers are symmetric to 0. Hence x is odd. So II is always true, again if we assume that temperatures have integer values.

But if we are not told that temperatures have integer values, the above won't be always true. We could have the following temperatures:
-1.5, -0.5, 0.5, 1.5.

The sum is 0, but x=4, so II must not be always true.

I would say that if stem doesn't specify that temperatures have integer values answer should be E. As only III is always true and we don't have this option.