Cool question: It's difficult to really get what's going on until you reach the second statement.
Stat. (1): since the two sets have different numbers of consecutive integers, how could their sum be the same? One way is hinted in stat. (2): if the sets are both symmetrical around the median of zero, with each positive term canceled out by the equivalent negative term, their sum will be zero. In this case, set X is -3, -2, -1, 0, 1, 2, 3
And
set Y is -4, -3, -2, -1, 0, 1, 2, 3, 4.
The sums are zero, and the medians are equal, and the answer seems to be yes.
But can we find another example, where the two sets have equal sums but different medians?
Let x be the median of set X, and y be the median of set Y. It is now possible to model the terms of the sets as a relationship to the medians:
set X is {x-3, x-2, x-1, x, x+1, x+2, x+3}
set Y is {y-4, y-3, y-2, y-1, y, y+1, y+2, y+3, y+4}
the sums of the terms in set X will be 7x , and 9y for set Y - the numbers in each set cancel each other out.
According to stat. (1), the sums are equal, so we get that 7x=9y. This happens when x and y are both zero (previous scenario), but also when x=9 and y=7, since 7*9 is equal to 9*7 = 63.
Thus, we have two cases, one where the medians are equal (and equal to zero), the other when they're not equal. Stat. (1) is insufficient.
Stat. (2): alone this tells us nothing about set X, so Xs median can be greater, lower or equal to Ys median. Insufficient
Combined: stat. (1) says 7x=9y.
Stat. (2) says y=0. It follows that 7x=9*0, so x must equal zero as well, and the medians are equal. Sufficient. Answer is C.
