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Spot The Median

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Tanweer
 Post subject: Spot The Median
 Post Posted: Thu Jun 12, 2008 11:04 am 
Given distinct positive integers 1, 11, 3, x, 2, 15, and 9, which of the following could be the median?
3
5
11
14
It cannot be determined from the given information.


The question came in my CAT 1. the answer says its " 5"

Can anyone explain How as i feel it cant be determined?

[/b]
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imran.lakhani
 Post subject:
 Post Posted: Thu Jun 12, 2008 9:37 pm 
Given the set and arranging it in increasing order we get Set{1, 2, 3, 9, 11, 15, x}, where x can be any number. Since the problem says "distinct positive interger" it is fair to assume that x>3. When x=4,5,6,7,8, x is the median, because it is in the middle of the set. When x>10, x cannot equal 9, because the values must be distinct, the median becomes 9, since 9 is the middle term. Therefore, scanning the answer choices only 5 is represented as what the median could be and since we said x would be the median when it equaled 4,5,6,7 or 8, that would be our answer.

Hope that helps.
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Guest
 Post subject:
 Post Posted: Sat Jun 14, 2008 3:19 pm 
Dear Imraan

Thanks for the nice explanation.

tan
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RonPurewal
 Post subject:
 Post Posted: Sun Jun 15, 2008 10:49 pm 
Offline
ManhattanGMAT Staff


Posts: 7146
imran.lakhani wrote:
Given the set and arranging it in increasing order we get Set{1, 2, 3, 9, 11, 15, x}, where x can be any number. Since the problem says "distinct positive interger" it is fair to assume that x>3. When x=4,5,6,7,8, x is the median, because it is in the middle of the set. When x>10, x cannot equal 9, because the values must be distinct, the median becomes 9, since 9 is the middle term. Therefore, scanning the answer choices only 5 is represented as what the median could be and since we said x would be the median when it equaled 4,5,6,7 or 8, that would be our answer.

Hope that helps.


nicely done.
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