BTGmoderatorDC wrote:What is the median of the data set S that consists of the integers 17, 29, 10, 26, 15, and x ?

(1) The average (arithmetic mean) of S is 17.
(2) The range of S is 24.

Target question: What is the median of the data set S

Statement 1: The average (arithmetic mean) of S is 17.
In other words, (17 + 29 + 10 + 26 + 15 + x)/6 = 17
At this point, we should recognize that we COULD solve this equation for x, which means we COULD answer the target question with certainty.
Statement 1 is SUFFICIENT

Statement 2: The range of S is 24.
When we arrange the five known numbers in ASCENDING ORDER, we get: 10, 15, 17, 26, 29
29 - 10 = 19, so the five KNOWN numbers have a range of 19.
To get a range of 24, x can be less than 10 (the smallest of the five known numbers), OR x can be greater than 29 (the biggest of the five known numbers),
That is, there are two possible values of x that will give us a range of 24:
Case a: x = 5. In this case, the set becomes {5, 10, 15, 17, 26, 29}, which has a range of 24. Here, the answer to the target question is the median = (15 + 17)/2 = 16
Case b: x = 34. In this case, the set becomes {10, 15, 17, 26, 29, 34}, which has a range of 24. Here, the answer to the target question is the median = (17 + 26)/2 = 21.5
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent