GMAT question 19, 20

The mean of four integers will not change if all the integers are multiplied by any constant. What is always true about this set of numbers? 
I. The mean of the set is 0
 II. The sum of the largest member and the smallest member of the set is 0
 III. The set contains both positive and negative integers

 I only 
II only 
III only
 I and II only 
I, II, and III

Solution:
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 cannot 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.

A jewelry store sells customized rings in which 3 gems selected by the customer are set in a straight row along the band of the ring. If exactly 5 different gems are available and if at least 2 gems in any given ring must be different, how many different rings are possible?  20  60  90  120  210

Solution:
So you have unlimited jewels essentially, so there's 5 possibilities for the first slot, 5 for the second, and 5 for the third slot.  5 x 5 x 5 = 125 = Number of possibilities.
  However, at least two gems must be different. So we subtract out the possibilities where all the gems are the same. There are five types of gems, so there are five possibilities where all the gems would be the same.  125 - 5 = 120. 
The answer is D.