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Question Stats:
44% (02:24) correct
56%
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wrong
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There are 5 integers such that the difference of the biggest number and the median is 4. Is the average (arithmetic mean) of them less than the median of them?
(1) The sum of biggest numbers and the median is 34.
(2) The difference of median and the smallest number is 10
(1) The sum of biggest numbers and the median is 34.
(2) The difference of median and the smallest number is 10
We have 5 integers such that:
\(n_1 , n_2 , n_3 , n_4 , n_5\)
where \(n_3\) is the median.
We know that \(n_5 - n_3 = 4\).
\(1. n_5 + n_3 = 34\). We could find \(n_5\) and \(n_3\) but are useless: we can infer nothing about the average.
\(2. n_3 - n_1 = 10\). Take \(n_3\) as reference point. On the left, difference is 10. On the right, 4. So, \(10 + 4 = 14\). It is the range from \(n_1\) to \(n_5\). Since \(14 : 2 = 7\) and \(n_3 = n + 10\), we conclude that the average is less than the median.
Correct answer is B.
\(n_1 , n_2 , n_3 , n_4 , n_5\)
where \(n_3\) is the median.
We know that \(n_5 - n_3 = 4\).
\(1. n_5 + n_3 = 34\). We could find \(n_5\) and \(n_3\) but are useless: we can infer nothing about the average.
\(2. n_3 - n_1 = 10\). Take \(n_3\) as reference point. On the left, difference is 10. On the right, 4. So, \(10 + 4 = 14\). It is the range from \(n_1\) to \(n_5\). Since \(14 : 2 = 7\) and \(n_3 = n + 10\), we conclude that the average is less than the median.
Correct answer is B.
05 Mar 2019, 21:24
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