Yuri A. answered • 08/05/19
Chicago Booth MBA (GMAT 760)
This is a very typical data sufficiency question, where one is tempted to find every single unknown given in the question (x and y), while in fact it's enough to use the value of an expression. Also it is helpful to know the definition of the median.
First, let's see if we can algebraically express what is being asked. In this set, 3x + y (larger than either x or y) is the largest term and x-y is the smallest term (less than zero). Hence range of set is (3x+y) - (x-y) = 2x +2y = 2(x+y)
Looking at statement 1, as we just established the largest and smallest values in the set, then those could be dropped from calculation of the median. There are an even number of terms in the remaining set, therefore the median is simply average of 2 middle terms from a set of 3 xs and 3 ys--it must be equal to (x+y) / 2 . From above, the range is equal to 2(x+y): therefore the range is easily expressed in term of median * 4 , which is equal to 40. Statement (1) is sufficient -- and we do NOT need to know what x or y are.
The average (adding up everything and dividing by # of terms looks to me equal to (7x+3y)/8, which does not get us close to the range. Statement (2) by itself is not sufficient.
