Uva@90 wrote:The table below represents three sets of numbers with their respective medians, means and standard deviations. The third set, Set [A+B], denotes the set that is formed by combining Set A and Set B.
-----:Median,Mean,StandardDeviation
Set A: X, Y, Z.
Set B: L, M, N.
Set[A + B]: Q, R, S.
If X – Y > 0 and L – M = 0, then which of the following must be true?
I. Z > N
II. R > M
III. Q > R
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) None
OA E
I don't this could ever be a true GMAT, since it's a total time killer (unless I'm missing a very easy approach)
We're asked to determine which MUST be true. So, if we can find a counter-example to a statement, then we can eliminate that statement.
First of all, we need to find two sets (sets A and B) that meet the criteria that X - Y > 0 and L - M = 0. This alone took some time to wrap my head around and find two sets that meet these conditions.
FULL DISCLOSURE: Once I found 2 sets that worked for the above conditions, it turned out they they proved to be counter-examples for all three statements. So, I think I got lucky.
Here are my sets:
Set A: {1, 5, 6}
[notice that median - mean > 0]
Set B: {1, 100}
[notice that median - mean = 0]
So, the combined set is {1, 1, 5, 6, 100}
I. Z > N
This suggests that the standard deviation (SD) of set A is greater than the standard deviation of set B
We can see that this is not true.
The SD of {1, 5, 6} is NOT greater than the SD of {1, 100}
So, statement I NEED NOT BE TRUE
II. R > M
This suggests that the mean of the combined set is greater than the mean of set B
We can see that this is not true.
The mean of {1, 1, 5, 6, 100} is NOT greater than the mean of {1, 100}
So, statement II NEED NOT BE TRUE
III. Q > R
This suggests that the median of the combined set is greater than the mean of the combined set.
We can see that this is not true.
The median of {1, 1, 5, 6, 100} is NOT greater than the mean of {1, 1, 5, 6, 100}
So, statement III NEED NOT BE TRUE
Aside: I'll leave it to you to make the necessary calculations to verify my conclusions
Since none of the statements must be true, the correct answer is
E
Cheers,
Brent
