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If set \(S\) consists of positive integers, is the median of set \(S\) greater than its range?
(1) Every element of set \(S\) is less than 40.
(2) Every element of set \(S\) is greater than 20.
(1) Every element of set \(S\) is less than 40.
(2) Every element of set \(S\) is greater than 20.
16 Sep 2014, 01:00
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Official Solution:
If set \(S\) consists of positive integers, is the median of set \(S\) greater than its range?
(1) Every element of set \(S\) is less than 40.
The range can be less than the median (for instance \(\{5,6,7\}\)) or greater than the median (for instance, \(\{1, 20, 39\}\)). Not sufficient.
(2) Every element of set \(S\) is greater than 20.
Again, the range can be less than the median (as in sets like \(\{21,22,23\}\)) or greater than the median (as in sets like \(\{21, 60, 100\}\)).
(1)+(2) If all elements fall between 21 and 39, inclusive, the range of the set cannot exceed \(39 - 21 = 18\). The median, however, will fall between 21 and 39. Thus, the median of set \(S\) (which will be between 21 and 39) is larger than its range (which will be at most 18).
Answer: C
If set \(S\) consists of positive integers, is the median of set \(S\) greater than its range?
(1) Every element of set \(S\) is less than 40.
The range can be less than the median (for instance \(\{5,6,7\}\)) or greater than the median (for instance, \(\{1, 20, 39\}\)). Not sufficient.
(2) Every element of set \(S\) is greater than 20.
Again, the range can be less than the median (as in sets like \(\{21,22,23\}\)) or greater than the median (as in sets like \(\{21, 60, 100\}\)).
(1)+(2) If all elements fall between 21 and 39, inclusive, the range of the set cannot exceed \(39 - 21 = 18\). The median, however, will fall between 21 and 39. Thus, the median of set \(S\) (which will be between 21 and 39) is larger than its range (which will be at most 18).
Answer: C
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Schools: Tepper '21 (A) INSEAD Jan '20 Booth '21 (I) Wharton '21 (D) Kellogg MMM '21 (I) Haas '21 (D) Ross '21 (WL)
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03 Sep 2018, 22:25
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I think this is a high-quality question and I agree with explanation.
