Set S contains more than one element. Is the range of the set S larger than its mean?
1) Set S does not contain positive elements
2) The median of set S is negative
Target question:
Is the range of the set S greater than its mean?
Statement 1:
Set S does not contain positive elements
There are several sets of numbers that meet this condition. Here are two:
Case a: Set S = {-1, -2}, in which case
the range (1) is greater than the mean (-1.5)
Case b: Set S = {0, 0}, in which case
the range (0) is not greater than the mean (0)
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2:
The median of set S is negative
If the median is negative, then there are two possible scenarios, both of which lead us to the same conclusion.
Scenario 1: all of the values are negative. In this scenario, the mean must be negative. Since the range is always greater than or equal to zero, we can be certain that
the range is greater than the mean.
Scenario 2: some values are negative, and some are positive. In this scenario, the mean will be greater then the smallest value and less than the biggest value. Since the range equals the biggest value (a positive value) minus the smallest value (a negative value), the range will greater than the biggest value in the set. So, we can be certain that
the range is greater than the mean.
In both possible scenarios, we come to the same conclusion:
the range is greater than the mean.
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer =
B
Cheers,
Brent
