# Practice GMAT Problem Solving Question

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?
 A) 1 B) 9 C) 14 D) 17 E) It Cannot Be Determined
1. 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
2. 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.
3. 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.
4. It is important to reiterate that set S consists of "unique integers." Consequently, n cannot equal any of the existing values of S.
5. By logically examining set S, there are three options for the median:
6. Option 1: n > 3 and Median = 2.5
1. 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
7. Option 2: n < -3 and Median = 0
1. 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
8. Option 3: Median Is (n+2)/2
1. 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).
2. 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
3. Since 1 is the only possible median that is included as an answer choice, it is the correct answer.