Practice GMAT Problem Solving Question

Return to the list of practice GMAT problem solving questions.

rss
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
  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.

Return to the list of practice GMAT problem solving questions.