If sets X and Y have an equal number of elements, does set X have a

Where are these questions from? You've tagged this as a GMATPrep question, but it certainly is not from GMATPrep, since it doesn't make any mathematical sense. The elements in a set are not in any order, so the wording in each of the Statements is nonsensical - a set doesn't have a 'first element', a 'second element', or 'neighboring elements'.

In any case, I think Statement 2 means to say that the two smallest elements in Set Y are twice greater than the two smallest elements in Set X. Then Statement 1 is not sufficient alone - it only tells us the two sets are equally spaced. Whichever set has the greatest distances separating elements will have the greater standard deviation, but we don't know in which set the spacing is larger. Statement 2 alone only discusses two elements in each set, and standard deviation is based on every element in a set, so Statement 2 cannot possibly be sufficient.

Taking the two Statements together, they are almost sufficient, at least if we assume Statement 2 is talking about the two smallest elements in each set. If we assume that the elements in each set are all distinct, then if x and y are the two smallest elements in the first set, then 2x and 2y are the two smallest elements in the second set. Thus the spacing in the second set is 2y - 2x = 2(y -x), so is twice as large as the spacing in the first set. Since the sets have the same number of elements but those elements are further apart in the second set, the second set will have a larger standard deviation.

There is, however, one technicality that prevents the two statements together from being sufficient: it is possible that the standard deviation of each set is 0. That is, it's possible, even using both statements, that all of the elements in each set are identical. I would guess whoever designed the question meant to make clear that the elements were different in each set, because it's not a very interesting question if the elements can all be the same, but it's a very badly worded question to begin with. I don't know what "Ivy 6" means - what is that?