GMATinsight wrote:Find the Median of the set of integers A?

1) Mean of the set A is 10
2) Range of the set A is 2

Source: www.GMATinsight.com

Answer: option C

Statement 1: Mean of Set A is 10.

Clearly insufficient.

Say, for example, Set A: {10, 10, 10}; Mean = 10 and Median = 10; however, if Set A: {0, 0, 30}; Mean = 10 and Median = 0. No unique value. Insufficient.

Statement 2: Range of Set A is 2.

Clearly insufficient.

Say, for example, Set A: {10, 10, 12}; Median = 10; however, if Set A: {20, 20, 22}; Median = 20. No unique value. Insufficient.

Statement 1 and 2:

Since the mean of the set is 10, the maximum value of an element of the set must be at least 10, thus the minimum value of an element of the set must be at least 10 - 2 = 8.

We cannot have a set such that the minimum value of an element equals 8, and have mean = 10. Thus, the minimum value of an element must be 9; this follows that the maximum value of an element of the set must be 11.

If there are Odd numbers of elements in the set, the middlemost element must 10, or Median = 10; however, if there are Even numbers of elements in the set, there is no middlemost element, thus Median = Average of 9 and 11 = 10. In each case Median = 10. Sufficient.

The correct answer: C

-Jay
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