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# m08#23

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Joined: 28 Dec 2004
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02 Nov 2008, 15:43
Is the mean of a non-empty set S bigger than its median?

1. All members of S are consecutive multiples of 3
2. The sum of all members of S equals 75

[Reveal] Spoiler: OA
A

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however i think it should be E..

how do we know all the elements in S are positive? what if we have -3, -6, -9, 0, 3, etc?
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04 Nov 2008, 23:20
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fresinha12 wrote:
Is the mean of a non-empty set S bigger than its median?

1. All members of S are consecutive multiples of 3
2. The sum of all members of S equals 75

OA is A..

however i think it should be E..

how do we know all the elements in S are positive? what if we have -3, -6, -9, 0, 3, etc?

Stmt1 simply says that the members of S are in arithmatic series and hence mean and median will be the same.
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29 Aug 2011, 05:51
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Median will equal mean in consecutive integers
Not B because it does give any information about the numbers in question.
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29 Aug 2012, 08:01
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Expert's post
FN wrote:
Is the mean of a non-empty set S bigger than its median?

1. All members of S are consecutive multiples of 3
2. The sum of all members of S equals 75

[Reveal] Spoiler: OA
A

Source: GMAT Club Tests - hardest GMAT questions

however i think it should be E..

how do we know all the elements in S are positive? what if we have -3, -6, -9, 0, 3, etc?

REVISED VERSION OF THIS QUESTION IS BELOW:

Is the mean of set S greater than its median?

(1) Set S consist of consecutive multiples of 3 --> set S is evenly spaced. One of the most important properties of evenly spaced set (aka arithmetic progression) is: in any evenly spaced set the arithmetic mean (average) is equal to the median. So, the mean of S = the median of S. Sufficient.

(2) The sum of all terms of set S is 75 --> if S={75} then mean=median but if S={0, 0, 75} then (mean=25)>(0=median). Not sufficient.

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02 Nov 2008, 16:43
fresinha12 wrote:
Is the mean of a non-empty set S bigger than its median?

1. All members of S are consecutive multiples of 3
2. The sum of all members of S equals 75

OA is A..

however i think it should be E..

how do we know all the elements in S are positive? what if we have -3, -6, -9, 0, 3, etc?

I think OA is ok.

-9, -6, -3, 0, 3,
sum = -15
mean = -15/5 = -3
median = -3
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24 Aug 2010, 07:27
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Statement 1 : Evenly spaced sets means MEDIAN = MEAN, so ---> sufficient

Statement 2: You are only given the sum of numbers in set, they could be (1, 75) or (1, 5, 70) so, ---> not sufficient.

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24 Aug 2010, 23:57
what if there is an even number of elements in the Set S,For example 27,30,33,36
Mean=31.5
Median=30 or 33
then?
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Joined: 02 Oct 2007
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25 Aug 2010, 01:04
The median will equal the mean then.

Here's a quote from Wikipedia
Quote:
If there is an even number of observations, then there is no single middle value; the median is then usually defined to be the mean of the two middle values

mundasingh123 wrote:
what if there is an even number of elements in the Set S,For example 27,30,33,36
Mean=31.5
Median=30 or 33
then?

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Joined: 11 Nov 2009
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29 Aug 2011, 07:02
A looks good....bu can any one give example of B where Mean is bigger than Median....
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29 Aug 2011, 07:53
gsd85 wrote:
A looks good....bu can any one give example of B where Mean is bigger than Median....

15+2+1/3 = 18/3 = 6

Mean of 6 > Median of 2
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29 Aug 2011, 08:21
for consecutive integers: mean = median
Also, equals (max + min)/2
example: 7, 8, 9, 10, and 11
mean = (7+11)/2 = 9
median = 9

By the same token, for 12, 14, 16, and 18
mean = (12 + 18)/2 = 15
median also = average of 14 and 16 = 15

Hope this helps.
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Joined: 11 Nov 2009
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29 Aug 2011, 09:35
I want to know for no's whose sum =75 is there any combination where mean > median........

for e.g 25+25+25 ..........mean= median

for 25 +25+16+9 ............mean < median...

so i want to know a combination where mean > median........i could not figure out ....so just need help
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Joined: 14 Mar 2011
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29 Aug 2011, 09:54
Lets take some examples

1. Let set is two number (3,6) mean=4.5, median=4.5 now let take 3 nos. (15, 18, 21) mean=18, Median=18 now lets take a bigger set (-12, -9,-6,-3,0,3,6,9) Median = -1.5, Mean = -12/8= -3/2 = -1.5

Regards
Jagdeep
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29 Aug 2011, 11:21
Senior Manager
Joined: 19 Oct 2010
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Location: India
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03 Sep 2011, 09:27
celluloidandroid wrote:

Median will equal mean in consecutive integers
Not B because it does give any information about the numbers in question.

Good information. Thank you.
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29 Aug 2012, 07:15
Remember that evenly spaced sets, the mean = median. Regardless of # of items.

A) Sufficient
b) Insufficient
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29 Aug 2012, 11:21
True, as Bunuel said,
Mean=Median or evenly spaced sets, so (i) sufficient
in (ii) the sets have a sum of 75 ; we can have many combinations to do so (0,0,75),(25,25,25), etc..-insufficient
(A)wins
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Re: m08#23   [#permalink] 29 Aug 2012, 11:21
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# m08#23

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