We have this equation:

Sum = Number of terms * Average.

The number of terms is fixed if you multiply all the integers by a constant, and the average does not budge as defined in problem. So, that means the sum can not change either, when multiplied by any constant.

This tells me that the set has positive and negative numbers, because the net result is fixed. However, what if all the integers were zero? Statement 3 doesn't always have to be true.

So what about S1 and S2? What if you had 3, -1, -1, and -1? If you took them all times 5, you'd get:

15, -5, -5, and -5.

Clearly, the smallest and largest doesn't add up to zero.

However, the constant in both of these examples has been the mean has been zero. So the answer is A.

Side note: I rushed through this problem and jumped to the conclusion they were all true. I need to go to bed now, and then have a notepad out so I can work through the problem on paper anytime I do these problems on here. Good practice, but I need to take it more seriously...after all, you play like you practice . Wanted to share so you guys don't make same mistake!

Thanks for the explanation.