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16 Sep 2014, 01:16
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\(\{2, 3, 5, 7\}\)
Upon adding \(x\) as a fifth term to the list above, the median of the list increases by 25%. Which of the following cannot be the value of \(x\)?
A. 4.8
B. 5.0
C. \(\sqrt{29}\)
D. 7.7
E. \(\frac{49}{4}\)
Upon adding \(x\) as a fifth term to the list above, the median of the list increases by 25%. Which of the following cannot be the value of \(x\)?
A. 4.8
B. 5.0
C. \(\sqrt{29}\)
D. 7.7
E. \(\frac{49}{4}\)
16 Sep 2014, 01:16
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Official Solution:
\(\{2, 3, 5, 7\}\)
Upon adding \(x\) as a fifth term to the list above, the median of the list increases by 25%. Which of the following cannot be the value of \(x\)?
A. 4.8
B. 5.0
C. \(\sqrt{29}\)
D. 7.7
E. \(\frac{49}{4}\)
The original list was \(\{2, 3, 5, 7\}\). Its median was \(\frac{3 + 5}{2} = 4\). With the addition of a term, the new median becomes \(4*1.25 = 5\). Since the median of a list with an odd number of terms (5 in this instance) is the middle term when sorted in ascending or descending order, the new list can be:
\(\{2, \ 3, \ 5, \ x, \ 7\}\) or \(\{2, \ 3, \ 5, \ 7, \ x\}\)
Thus, \(x\), the number added, cannot be less than 5. If \(x\) were less than 5, the median (the middle term) would no longer be 5.
The only option that is less than 5 is A (4.8).
Answer: A
\(\{2, 3, 5, 7\}\)
Upon adding \(x\) as a fifth term to the list above, the median of the list increases by 25%. Which of the following cannot be the value of \(x\)?
A. 4.8
B. 5.0
C. \(\sqrt{29}\)
D. 7.7
E. \(\frac{49}{4}\)
The original list was \(\{2, 3, 5, 7\}\). Its median was \(\frac{3 + 5}{2} = 4\). With the addition of a term, the new median becomes \(4*1.25 = 5\). Since the median of a list with an odd number of terms (5 in this instance) is the middle term when sorted in ascending or descending order, the new list can be:
\(\{2, \ 3, \ 5, \ x, \ 7\}\) or \(\{2, \ 3, \ 5, \ 7, \ x\}\)
Thus, \(x\), the number added, cannot be less than 5. If \(x\) were less than 5, the median (the middle term) would no longer be 5.
The only option that is less than 5 is A (4.8).
Answer: A
15 Nov 2017, 22:54
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since the new median is 5, all options except B are wrong....????
in other words, if the question mentioned that the median grew by atleast 35%, A would be the answer.
in other words, if the question mentioned that the median grew by atleast 35%, A would be the answer.
