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

[BTGModeratorVI]

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.

Answer: A
Source: Official guide

[Jay@ManhattanReview]

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.

Answer: A
Source: Official guide

Let's take each statement one by one.

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

=> 17 = (17 + 29 +10 + 26 + 15 + x )/6
=> x = a unique value. We can calculate the value of median. Sufficient.

(2) The range of S is 24.

Case 1: Say x > 10. Thus, the smallest value = 10; thus, the largest value = 10 + 24 = 34. Since there no value as 34 in the set, x = 34.

So, the median = (17 + 26)/2 = 43/2

Case 2: Say the latest value = 29, thus, the smallest value = 29 – 24 = 5. Since there no value as 5 in the set, x = 5.

So, the median = (15 + 17)/2 = 16

No unique answer. Insufficient.

The correct answer: A

Hope this helps!

-Jay
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[Brent@GMATPrepNow]

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.

Answer: A
Source: Official guide

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