Another way of thinking about this:
Given any set, the standard deviation will (more or less) go down if we add an EXPECTED number and go up if we add an UNEXPECTED number. For instance, if we take the set {1, 2, 3, 4} and put 2.5 in the set, we're adding an expected number: a number that's hardly unusual given the set we already had. But if we put 7 in the set, we're adding an unexpected number, something outside of the current range, so our standard deviation will go up.
S1:: Our set is something like {1, 2, 3, 4, 5}. So Set B consists of four of these. If B is {2, 3, 4, 5} it will have a SMALLER standard deviation, since A also includes an unexpected number (1). If B is {1, 2, 4, 5} it will have a LARGER standard deviation, since A also includes a very expected number (3). So this is NOT SUFFICIENT.
S2:: Suppose set A is {a, b, c, d, e}, not necessarily in increasing order (i.e. we could have a > c and c > b, or whatever). Suppose set B is {a, b, c, d}. Since the sets have the same mean, e must equal the average of set B. Hence set A is adding a very expected number (its own mean), causing its standard deviation to be less than B's; SUFFICIENT.
