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16 Sep 2014, 01:03
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If the data set \(S =\{2, 5, 1, x, 7\}\), what is the value of \(x\)?
(1) The range of the data set \(S\) is 8
(2) The median of the data set \(S\) is 2
(1) The range of the data set \(S\) is 8
(2) The median of the data set \(S\) is 2
16 Sep 2014, 01:03
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Official Solution:
If the data set \(S =\{2, 5, 1, x, 7\}\), what is the value of \(x\)?
(1) The range of the data set \(S\) is 8.
When considering the range of \(\{2, 5, 1, x, 7\}\) without \(x\), the difference between the largest and smallest elements is 7 - 1 = 6. Given that the range of \(S\) is 8, \(x\) must be either the largest or the smallest element. If \(x\) is the largest element, then \(x - 1 = 8\), implying that \(x = 9\). If \(x\) is the smallest element, then \(7 - x = 8\), implying that \(x = -1\). Not sufficient.
(2) The median of data set \(S\) is 2.
The median of a set with an odd number of elements is the middle term when the set is arranged in ascending or descending order. Since 2 is the median, it occupies the middle position: {\(x\), 1, 2, 5, 7}. This indicates that \(x\) must be less than or equal to 2. Not sufficient.
(1)+(2) (1)+(2) From (1) \(x = 9\) or \(x = -1\), and from (2) \(x \leq 2\), hence \(x = -1\). Sufficient.
Answer: C
If the data set \(S =\{2, 5, 1, x, 7\}\), what is the value of \(x\)?
(1) The range of the data set \(S\) is 8.
When considering the range of \(\{2, 5, 1, x, 7\}\) without \(x\), the difference between the largest and smallest elements is 7 - 1 = 6. Given that the range of \(S\) is 8, \(x\) must be either the largest or the smallest element. If \(x\) is the largest element, then \(x - 1 = 8\), implying that \(x = 9\). If \(x\) is the smallest element, then \(7 - x = 8\), implying that \(x = -1\). Not sufficient.
(2) The median of data set \(S\) is 2.
The median of a set with an odd number of elements is the middle term when the set is arranged in ascending or descending order. Since 2 is the median, it occupies the middle position: {\(x\), 1, 2, 5, 7}. This indicates that \(x\) must be less than or equal to 2. Not sufficient.
(1)+(2) (1)+(2) From (1) \(x = 9\) or \(x = -1\), and from (2) \(x \leq 2\), hence \(x = -1\). Sufficient.
Answer: C
20 Oct 2023, 10:50
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
