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# Is the average of a set of 5 distinct positive integers {a, b, 4, 6, 2

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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?

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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?

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]
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.

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