Practice GMAT Problem Solving Question
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Set S consists of the following unique integers: 2, 17, 3, n, 2, 15, 3, and 27; which of the following could be the median of set S?
Correct Answer: A
 Order the members of set S in ascending order. Leave out n since you do not yet know where it will fall.
27, 3, 2, 2, 3, 15, 17  At this point, you do not know where n will be. However, it is not essential to know the exact placement of n in order to find which answer choice could be the median of set S.
 When n is included in set S, set S has an even number of terms. Consequently, the median will be the average of the middle two terms of set S.
 It is important to reiterate that set S consists of "unique integers." Consequently, n cannot equal any of the existing values of S.
 By logically examining set S, there are three options for the median:

Option 1: n > 3 and Median = 2.5
 If n > 3, the median will be 2.5
27, 3, 2, 2, 3, n, 15, 17
27, 3, 2, 2, 3, 15, n, 17
27, 3, 2, 2, 3, 15, 17, n
In each case, the median will be between 2 and 3 > Median will be 2.5
 If n > 3, the median will be 2.5

Option 2: n < 3 and Median = 0
 If n < 3, the median will be 0
27, n, 3, 2, 2, 3,15, 17
n, 27, 3, 2, 2, 3,15, 17
In each case, the median will be between 2 and 2 > Median will be 0
 If n < 3, the median will be 0

Option 3: Median Is (n+2)/2
 If 2 < n < 2, n could be 1, 0, 1 (remember n must be a unique integer, so it cannot be 2 or 2 since these numbers are already used).
 The series is now ordered: 27, 3, 2, n, 2, 3, 15, 17
Since the median will be the average of the middle two terms, we can simplify the series to:
2, n, 2, 3, which will simplify to:
n, 2
The median of the series will be the average of n and 2.
Remember that n can equal 1, 0, or 1.
If n = 1 > Median will be 0.5
If n = 0 > Median will be 1
If n = 1 > Median will be 1.5  Since 1 is the only possible median that is included as an answer choice, it is the correct answer.
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