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# In a set of positive integers {j, k, l, m, n, o}, in which j

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In a set of positive integers {j, k, l, m, n, o}, in which j [#permalink]  01 May 2012, 09:20
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27% (02:49) correct 72% (01:49) wrong based on 62 sessions
In a set of positive integers {j, k, l, m, n, o}, in which j < k < l < m < n < o, is the mean larger than the median?

(1) The sum of n and o is more than twice the sum of j and k.

(2) The sum of k and o is the sum of l and m.
[Reveal] Spoiler: OA
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Re: In a set of positive integers {j, k, l, m, n, o}, in which j [#permalink]  01 May 2012, 23:59
j,k,l,m,n,o
mean = (j+k+l+m+n+o)/6
median = (l+m)/2
we need to compare these two quantities.
statement (1)
The sum of n and o is more than twice the sum of j and k.
n+o > 2(j+k)
If we consider l+m = X and j+k = Y,
then, mean > (Y+X+2Y)/6 => mean > (X+3Y)/6
median = X/2
This alone won't help to find whether mean is larger than median.

statement (2)
The sum of k and o is the sum of l and m.
k+o = l+m
This alone won't help as 'j' and 'n' may take myriad number of values (as we don't have any clues on them) such that affecting the relation between mean and median in either ways.

statements (1) and (2) together are also not sufficient as (2) is not adding any value to (1) towards finding a final conclusion.
[Reveal] Spoiler:
Hence the answer option is "E"

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Ravi Sankar Vemuri

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Re: In a set of positive integers {j, k, l, m, n, o}, in which j [#permalink]  08 Apr 2013, 16:25
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JubtaGubar wrote:
In a set of positive integers {j, k, l, m, n, o}, in which j < k < l < m < n < o, is the mean larger than the median?

(1) The sum of n and o is more than twice the sum of j and k.

(2) The sum of k and o is the sum of l and m.

Stmt (1) - Not sufficient. [Proved above]

Stmt (2) -

mean > median

=> \frac{(j+k+l+m+n+o)}{6} > \frac{(l+m)}{2}

Using stmt (2) [ k+o = l+m ]:

=> \frac{(j+2k+n+2o)}{6} > \frac{(k+o)}{2}

=> (j+2k+n+2o) > 3(k+o)

=> j+n > k+o

But, j < k & n < o

=> j+n < k+o

=> mean < median

Sufficient

Hence, B.
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Re: In a set of positive integers {j, k, l, m, n, o}, in which j [#permalink]  11 Apr 2013, 16:50
I also got B, I approached it from a conceptual manner:

if k+o = l+m, then the median will always equal \frac{(k+o)}{2} meaning the question is asking "is the mean larger than halfway between k+o?"

Because J must be less than k, it will always pull the mean below \frac{(k+o)}{2}

l,m and n are insignificant with this realization because they are always between k and o. So if the numbers were j, k, and o (with the same restriction of j<k<o) the mean could never be more than half way bewtween k and o.
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Intern
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Re: In a set of positive integers {j, k, l, m, n, o}, in which j [#permalink]  11 Apr 2013, 17:13
vsrsankar wrote:
This alone won't help as 'j' and 'n' may take myriad number of values (as we don't have any clues on them) such that affecting the relation between mean and median in either ways.

If we are trying to get the mean as large as possible (in order to make the mean larger than the median) than we need only examine J and N at one value each. Namely, J = (k-1) and N= (o-1). Even when this is the case, it will not pull the mean higher than than halfway between L and M
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Re: In a set of positive integers {j, k, l, m, n, o}, in which j [#permalink]  21 May 2013, 15:32
The question is transcribed incorrectly . Below is the correct version .

In a set of positive integers {j,k,l,m,n,o} in which j<k<l<m<n<o, is the mean larger than the median?

1. The sum of n and o is more than twice the sum of j and k.
2. The sum of k and o is 4/3 the sum of l and m

As per this , statement 2 yields - 2J + 2n > k+o ? . Hence insufficient.
Combining both 1 and 2 , is insufficient.
Hence E

-Jyothi
Re: In a set of positive integers {j, k, l, m, n, o}, in which j   [#permalink] 21 May 2013, 15:32
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# In a set of positive integers {j, k, l, m, n, o}, in which j

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