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16 Sep 2014, 00:12
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E
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Difficulty:
15%
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Question Stats:
83% (01:10) correct
17%
(01:36)
wrong
based on 274
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If list \(T\) contains more than one element, is the median of list \(T\) greater than its average (arithmetic mean) ?
(1) The range of list \(T\) is positive.
(2) List \(T\) does not consist of consecutive integers.
(1) The range of list \(T\) is positive.
(2) List \(T\) does not consist of consecutive integers.
16 Sep 2014, 00:12
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Official Solution:
If list \(T\) contains more than one element, is the median of list \(T\) greater than its average (arithmetic mean)?
(1) The range of list \(T\) is positive.
The range of a list is the difference between the largest and smallest elements of the list. The range is 0 when all elements of the list are equal, and positive in other cases. If list \(T\) has a positive range, it means that not all elements of the list are equal. However, this information alone is insufficient to compare the median and the mean. Not sufficient.
(2) List \(T\) does not consist of consecutive integers.
If T = {1, 3}, the median and the mean are equal, resulting in a NO answer. However, if T = {0, 3, 3}, the median (3) is greater than the mean (2). This information is also not sufficient to compare the median and the mean. Not sufficient.
(1)+(2) All we know is that not all elements of the list are equal and that the list does not consist of consecutive integers, which is clearly not sufficient to compare the median and the mean. For instance, we can consider similar examples as for (2): if T = {1, 3}, then the median and the mean are equal, resulting in a NO answer. However, if T = {0, 3, 3}, then the median (3) is greater than the mean (2). Not sufficient.
Answer: E
If list \(T\) contains more than one element, is the median of list \(T\) greater than its average (arithmetic mean)?
(1) The range of list \(T\) is positive.
The range of a list is the difference between the largest and smallest elements of the list. The range is 0 when all elements of the list are equal, and positive in other cases. If list \(T\) has a positive range, it means that not all elements of the list are equal. However, this information alone is insufficient to compare the median and the mean. Not sufficient.
(2) List \(T\) does not consist of consecutive integers.
If T = {1, 3}, the median and the mean are equal, resulting in a NO answer. However, if T = {0, 3, 3}, the median (3) is greater than the mean (2). This information is also not sufficient to compare the median and the mean. Not sufficient.
(1)+(2) All we know is that not all elements of the list are equal and that the list does not consist of consecutive integers, which is clearly not sufficient to compare the median and the mean. For instance, we can consider similar examples as for (2): if T = {1, 3}, then the median and the mean are equal, resulting in a NO answer. However, if T = {0, 3, 3}, then the median (3) is greater than the mean (2). Not sufficient.
Answer: E
