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16 Sep 2014, 01:22
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
43% (01:28) correct
57%
(01:49)
wrong
based on 103
sessions
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If lists \(S\) and \(T\) are combined into a single list, will the mean of this combined list be smaller than the sum of the means of lists \(S\) and \(T\)?
(1) Lists \(S\) and \(T\) each contain only one element.
(2) Neither list \(S\) nor list \(T\) contains negative numbers
(1) Lists \(S\) and \(T\) each contain only one element.
(2) Neither list \(S\) nor list \(T\) contains negative numbers
16 Sep 2014, 01:22
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Official Solution:
If lists \(S\) and \(T\) are combined into a single list, will the mean of this combined list be smaller than the sum of the means of lists \(S\) and \(T\)?
(1) Lists \(S\) and \(T\) each contain only one element.
The mean of a one-element set is that element itself. Now, if \(S=\{0\}\) and \(T=\{0\}\), then the mean of the combined set (0) will be equal to the sum of the means of lists \(S\) and \(T\) (0), giving a NO answer to the question. However, if \(S=\{0\}\) and \(T=\{1\}\), then the mean of the combined set (0.5) will be less than the sum of the means of lists \(S\) and \(T\) (1), giving a YES answer to the question. Not sufficient.
(2) Neither list \(S\) nor list \(T\) contains negative numbers.
We can consider the same examples as in (1). Not sufficient.
(1)+(2) As examples, we came up in (1) .. complete
(1)+(2) The examples we came up with in (1) show that even when both conditions are taken into account, we can still have both YES and NO answers to the question. Therefore, the information provided is not sufficient to answer the question.
Answer: E
If lists \(S\) and \(T\) are combined into a single list, will the mean of this combined list be smaller than the sum of the means of lists \(S\) and \(T\)?
(1) Lists \(S\) and \(T\) each contain only one element.
The mean of a one-element set is that element itself. Now, if \(S=\{0\}\) and \(T=\{0\}\), then the mean of the combined set (0) will be equal to the sum of the means of lists \(S\) and \(T\) (0), giving a NO answer to the question. However, if \(S=\{0\}\) and \(T=\{1\}\), then the mean of the combined set (0.5) will be less than the sum of the means of lists \(S\) and \(T\) (1), giving a YES answer to the question. Not sufficient.
(2) Neither list \(S\) nor list \(T\) contains negative numbers.
We can consider the same examples as in (1). Not sufficient.
(1)+(2) As examples, we came up in (1) .. complete
(1)+(2) The examples we came up with in (1) show that even when both conditions are taken into account, we can still have both YES and NO answers to the question. Therefore, the information provided is not sufficient to answer the question.
Answer: E
09 May 2023, 09:12
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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.
