A prep DS

Using statement 2, the median of each set certainly could be zero. We only need to know if it must be zero.

In sets of consecutive integers, as in any 'evenly spaced' set, the average is always equal to the median. Since:

avg = sum/n

we have

sum = n*avg

Now, if a is the median (and thus the average) of our set of 5 consecutive integers, and b is the median (and thus the average) of our set of 7 consecutive integers, we know the sum of the first set is 5a and the sum of our second set is 7b. So we just want to know whether it's possible to find numbers a and b so that

5a = 7b

and certainly we could use a = 7, and b = 5, among many other possibilities. That is, the following two sets will have the same sum:

5, 6, 7, 8, 9

2, 3, 4, 5, 6, 7, 8

but have different medians, and Statement 2 is not sufficient alone.