Set A, Set B & Set C each contain only positive integers. If Set A is composed entirely of all the members of Set B plus all the members of Set C, is the median of Set C greater than the median of Set A?
1) The mean of Set A is greater than the median of Set B.
2) The median of Set A is greater than the median of Set C.
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Median Problem 4
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aditiniyer
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Jay@ManhattanReview
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Hi aditiniyer,aditiniyer wrote:Set A, Set B & Set C each contain only positive integers. If Set A is composed entirely of all the members of Set B plus all the members of Set C, is the median of Set C greater than the median of Set A?
1) The mean of Set A is greater than the median of Set B.
2) The median of Set A is greater than the median of Set C.
I think there is a typo/incorrect information in this question.
The question is: Median of Set C > Median of Set A?
Statement 2 clearly states Median of Set A > Median of Set C. The answer is No. Sufficient.
As far as statement 1 is concerned, it is not sufficient.
Say Set B: {1, 2, 3, 4}; median of Set B = 2.5 and Set C: {5}; median of Set C = 5
Thus,
We have A: {1, 2, 3, 4, 5}; mean/median of Set A = 3. Mean of Set A (3) > median of Set B (2.5).
We see that 'median of Set C (5) > median of Set A (3).' The answer is Yes.
However, if
Say Set B: {1, 4}; median of Set B = 2.5 and Set C: {2, 3, 5}; median of Set C = 3
Thus,
We have A: {1, 2, 3, 4, 5}; mean/median of Set A = 3. Mean of Set A (3) > median of Set B (2.5).
We see that 'median of Set C (3) = median of Set A (3).' The answer is No. Insufficient.
The correct answer: B
Hope this helps!
Relevant book: Manhattan Review GMAT Data Sufficiency Guide
-Jay
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Hi aditiniyer,
I think that there is a typo in your question. It should probably read:
Set A, Set B, and Set C each contain only positive integers. If Set A is composed entirely of all the members of Set B plus all the members of Set C, is the median of Set B greater than the median of Set A?
1) The mean of Set A is greater than the median of Set B.
2) The median of Set A is greater than the median of Set C.
An old discussion of this question can be found here:
https://www.beatthegmat.com/mean-median-t40936.html
GMAT assassins aren't born, they're made,
Rich
I think that there is a typo in your question. It should probably read:
Set A, Set B, and Set C each contain only positive integers. If Set A is composed entirely of all the members of Set B plus all the members of Set C, is the median of Set B greater than the median of Set A?
1) The mean of Set A is greater than the median of Set B.
2) The median of Set A is greater than the median of Set C.
An old discussion of this question can be found here:
https://www.beatthegmat.com/mean-median-t40936.html
GMAT assassins aren't born, they're made,
Rich
