BukrsGmat wrote:
Set S consists of positive numbers. If -1 is added as an element to set S, which of the following is impossible?
A. The mean will decrease but median will not change.
B. The median will decrease but mean will not change.
C. The range will increase but median will not change.
D. The range will increase but mean will decrease.
E. The standard deviation will increase but mean will decrease.
The question becomes a simple one because of one word : Positive.
So, in case the set consists of only positive number, the mean will be positive.
Now, when we add a negative number, the mean HAS to go down.
Any option that tells you ' mean does not change' or 'mean will increase' are impossible.
Only B stands.
But let us work on each of the cases.
Mean: Will decrease always.Median: Will decrease or remain the same. It will NEVER increase.{2,2,2,3} and {-1,2,2,2,3}....Median is 2 in each case
{1,2,3} and {-1,1,2,3}....Median is 2 and 1.5 respectively
Range: Will increase always.(by at least 1){2,2,2,3} and {-1,2,2,2,3}....Range is 1 and 4 respectively
SD: Should increase almost always as the spread increases.A. The mean will decrease but median will not change.
Possible
B. The median will decrease but mean will not change.
Impossible
C. The range will increase but median will not change.
Possible
D. The range will increase but mean will decrease.
Possible
E. The standard deviation will increase but mean will decrease.
Possible
B