Data Sufficiency

A series of 5 numbers is 3, 4, 5, 5, x, is the range greater than 2?
1. the median of the numbers is greater than the mean
2. the median is 4

nahid078 wrote:A series of 5 numbers is 3, 4, 5, 5, x, is the range greater than 2?
1. the median of the numbers is greater than the mean
2. the median is 4

Sum of the 5 numbers = x+3+4+5+5 = x+17.
In each case, test whether it's possible for the range of the 5 numbers to be EQUAL TO 2.

Statement 1: the median of the numbers is greater than the mean
Case 1: median = 4
If x=3, then the range is equal to 2 and the set looks as follows: x=3, 3, 4, 5, 5.
Average = (3+17)/5 = 4.
Not viable: the average must be LESS than the median.
To decrease the average, x must be LESS than 3.
Thus, the set must look as follows:
x<3, 3, 4, 5, 5.
Since the smallest value is less than 3 and the greatest value is 5, the range of the 5 numbers is GREATER THAN 2.

Case 2: median = 5
If x=5, then the range is equal to 2 and the set looks as follows: 3, 4, 5, 5, x=5.
Average = (5+17)/5 = 22/5 = 4.4.
This works, since the average is less than the median.
Since the smallest value is 3 and the greatest value is 5, the range of the 5 numbers is EQUAL TO 2.

Since the range is greater than 2 in Case 1 but equal to 2 in Case 2, INSUFFICIENT.

Statement 2: the median is 4
Case 1 also satisfies statement 2.
In Case 1, the range > 2.

Case 3:
If x=5, then the range is EQUAL TO 2 and the set looks as follows: x=3, 3, 4, 5, 5.

Since the range is greater than 2 in Case 1 but equal to 2 in Case 3, INSUFFICIENT.

Statements combined:
Both statements are satisfied only by Case 1.
Thus, the range > 2.
SUFFICIENT.

The correct answer is C.