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Which could be the median?

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by Anurag@Gurome » Tue Jul 17, 2012 10:20 pm
alex.gellatly wrote:150, 200, 250, n
Which of the following could be the median of the 4 integers listed above?
If n ≤ 150,
  • The integers in increasing order : n, 150, 200, 250
    Hence, median = (150 + 200)/2 = 175
If 150 < n < 250,
  • The integers in increasing order : 150, n, 200, 250 or 150, 200, n, 250
    Hence, median = (n + 200)/2 = n/2 + 100
    As 150 < n < 250 ---> (150/2 + 100) < median < (250/2 + 100) ---> 175 < median < 225
If n ≥ 250,
  • The integers in increasing order : 150, 200, 250, n
    Hence, median = (200 + 250)/2 = 225
Hence, only I and II can be the median.

The correct answer is C.
Anurag Mairal, Ph.D., MBA
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