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Re: Is the average of a set of 5 distinct positive integers {a, b, 4, 6, 2 [#permalink]
Thanks Guys, i know what i was missing ...
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Re: Is the average of a set of 5 distinct positive integers {a, b, 4, 6, 2 [#permalink]
I have a question w.r.t Statement 2. Can we get a 'Yes' case. The cases that I can see in the official solution and the ones that are posted here produce a 'No' in case of Statement 2 (precisely Mean is not greater than Median, and Mean=Median) I cannot locate a case where Mean > Median and I believe that probably can make Statement 2 sufficient.

Bunuel - I would like to understand where am I going wrong or may be there is an altered version of this question that's present in the database?

Thank You in advance
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Re: Is the average of a set of 5 distinct positive integers {a, b, 4, 6, 2 [#permalink]
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Keats wrote:
I have a question w.r.t Statement 2. Can we get a 'Yes' case. The cases that I can see in the official solution and the ones that are posted here produce a 'No' in case of Statement 2 (precisely Mean is not greater than Median, and Mean=Median) I cannot locate a case where Mean > Median and I believe that probably can make Statement 2 sufficient.

Bunuel - I would like to understand where am I going wrong or may be there is an altered version of this question that's present in the database?

Thank You in advance


The average of {2, 4, 6, 100, 200}, which is ~62, is greater than the median of {2, 4, 6, 100, 200}, which is 6.
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Re: Is the average of a set of 5 distinct positive integers {a, b, 4, 6, 2 [#permalink]
Thanks Bunuel
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Re: Is the average of a set of 5 distinct positive integers {a, b, 4, 6, 2 [#permalink]
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shrive555 wrote:
Is the average of a set of 5 distinct positive integers {a, b, 4, 6, 2} greater than the median?

(1) The highest number in the set is 6

(2) The lowest number in the set is 2

is my understanding correct ? 1) possibilities of sets with 6 highest number are [1,2,3,4,6], [1,2,4,5,6], [2,3,4,5,6] ... Thus sufficient.... 2) 2 being the lowest element in set, the possibility of the sets are numerous but Avg will be always greater than Mean. e.g [2,3,4,6,100] or [2,4,5,6,1000] in all cases Avg will greater than Mean, thus sufficient. So answer is D.....


M05-37


Is the average of a set of 5 distinct positive integers {\(a\), \(b\), 4, 6, 2} greater than the median?

First of all, we must remember that the set contains distinct positive integers.

(1) The largest number in the set is 6.

Since 6 is the largest number in the set, both \(a\) and \(b\) must be less than 6. Therefore, \(a\) and \(b\) can be any two from 1, 3, and 5. If \(a = 1\) and \(b = 3\), the median is 3 and the average is 3.2. However, if \(a = 3\) and \(b = 5\), the average and the median are equal, at 4. Not sufficient.

(2) The smallest number in the set is 2.

Since 2 is the smallest number in the set, both \(a\) and \(b\) must be greater than 2. If \(a\) and \(b\) are very large numbers, say 10 and 20, the average will be greater than the median, which will be 6. However, if \(a = 3\) and \(b = 5\), the average and the median are equal, at 4. Not sufficient.

(1)+(2) From the information given, we know that both \(a\) and \(b\) must be greater than 2, and less than 6. Thus, \(a=3\) and \(b=5\), or vice-versa. In either case, the average and the median are equal, at 4. Sufficient.


Answer: C
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Re: Is the average of a set of 5 distinct positive integers {a, b, 4, 6, 2 [#permalink]
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