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# M16-23

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Intern
Joined: 06 Apr 2016
Posts: 22
GMAT 1: 540 Q42 V23

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24 Aug 2017, 12:14
Hello Bunuel,

What if : set S = {1,2,3,4} ; Mean=2.5
subset of S ={1,2} ; Mean =1.5

Then option 2 " All elements in set S are equal" does not fit in.
Please let me where am i going wrong.

Thanks,
Saba
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Joined: 02 Sep 2009
Posts: 58396

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24 Aug 2017, 12:25
1
saba@4010 wrote:
Hello Bunuel,

What if : set S = {1,2,3,4} ; Mean=2.5
subset of S ={1,2} ; Mean =1.5

Then option 2 " All elements in set S are equal" does not fit in.
Please let me where am i going wrong.

Thanks,
Saba

"The mean of set $$S$$ does not exceed mean of ANY subset of set $$S$$".

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Intern
Joined: 06 Apr 2016
Posts: 22
GMAT 1: 540 Q42 V23

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24 Aug 2017, 19:53
Bunuel wrote:
saba@4010 wrote:
Hello Bunuel,

What if : set S = {1,2,3,4} ; Mean=2.5
subset of S ={1,2} ; Mean =1.5

Then option 2 " All elements in set S are equal" does not fit in.
Please let me where am i going wrong.

Thanks,
Saba

"The mean of set $$S$$ does not exceed mean of ANY subset of set $$S$$".

Thanks Bunuel ,understood !

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Joined: 12 Feb 2015
Posts: 54
Location: India
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25 Aug 2017, 02:47
Just need to confirm one thing.S={1,2,3} then can the subset be like A={1,1,}
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Joined: 02 Sep 2009
Posts: 58396

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25 Aug 2017, 05:50
himanshukamra2711 wrote:
Just need to confirm one thing.S={1,2,3} then can the subset be like A={1,1,}

No, you don't have three 1's in S. Subsets of {1, 2, 3} are:
{1, 2, 3}
{1, 2}
{1, 3}
{2, 3}
{1}
{2}
{3}
{} - an empty set.
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Joined: 14 May 2017
Posts: 44

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29 Aug 2017, 06:04
Bunuel wrote:
ManSab wrote:
1. Set S contains only one element.
Does it mean count of element or value of element?
My understanding is that set S has only one element by count not by value... therefore {X,X...} is not possible. Please help understand.

Option 1, Set S contains only one element means that there is only one elements in S: {X}. This option is not necessarily true. Please re-read the solution.

Hi,

I am confused with second option. If i didn't misunderstood the question, it state that mean of Set S should be less than mean of its subset.

Lets Consider:

S =(2,4,6) - mean =4
S'= (4,6) - mean = 5

Thanks,
Arpit
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Joined: 02 Sep 2009
Posts: 58396

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29 Aug 2017, 06:07
NeverGiveUp- Arpit wrote:
Bunuel wrote:
ManSab wrote:
1. Set S contains only one element.
Does it mean count of element or value of element?
My understanding is that set S has only one element by count not by value... therefore {X,X...} is not possible. Please help understand.

Option 1, Set S contains only one element means that there is only one elements in S: {X}. This option is not necessarily true. Please re-read the solution.

Hi,

I am confused with second option. If i didn't misunderstood the question, it state that mean of Set S should be less than mean of its subset.

Lets Consider:

S =(2,4,6) - mean =4
S'= (4,6) - mean = 5

Thanks,
Arpit

I'd advice to re-read the stem and the solution carefully and go through the discussion once more.
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Joined: 14 May 2017
Posts: 44

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29 Aug 2017, 06:56
[quote="Bunuel"

I'd advice to re-read the stem and the solution carefully and go through the discussion once more.[/quote]

Got it. Thanks mate.

I overlooked the word 'Any '.

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Intern
Joined: 07 Oct 2015
Posts: 7

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19 Sep 2017, 00:48
What is S= 1,2,3,4,5
Mean=3
Median=3
Subset(4,5); Mean =4.5>3
So, Statment 3: False
Math Expert
Joined: 02 Sep 2009
Posts: 58396

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19 Sep 2017, 00:50
3ksnikhil wrote:
What is S= 1,2,3,4,5
Mean=3
Median=3
Subset(4,5); Mean =4.5>3
So, Statment 3: False

"The mean of set $$S$$ does not exceed mean of ANY subset of set $$S$$".

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Joined: 19 Jun 2017
Posts: 2

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22 Dec 2017, 15:18
Hello !
For case III, let's take an example where the median of set S equals the mean of set S : set S = {1,2,3}, mean=median=2. In that case, {1} is a subset of set S and 2>1. Conclusion: the mean of set S DOES exceed mean of a subset of set S
How is III still correct ?
Math Expert
Joined: 02 Sep 2009
Posts: 58396

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23 Dec 2017, 01:14
mahagmat wrote:
Hello !
For case III, let's take an example where the median of set S equals the mean of set S : set S = {1,2,3}, mean=median=2. In that case, {1} is a subset of set S and 2>1. Conclusion: the mean of set S DOES exceed mean of a subset of set S
How is III still correct ?

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Joined: 23 Aug 2016
Posts: 10

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21 Jun 2018, 00:03
Hi Bunuel,

"If the mean of set S does not exceed mean of any subset of set S''

Does it have to be true that Mean of S and Mean of any subset of S is equal? What if set S has negative numbers?

For Ex:- S= {3,4,5,6,-7} and subset of S is {3,4,5,6}. Here mean does not exceed but is lower that its subset.

In above example none of the three statement holds true? Could you please advise.

Thank you.
Math Expert
Joined: 02 Sep 2009
Posts: 58396

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21 Jun 2018, 00:16
hrishipatil72 wrote:
Hi Bunuel,

"If the mean of set S does not exceed mean of any subset of set S''

Does it have to be true that Mean of S and Mean of any subset of S is equal? What if set S has negative numbers?

For Ex:- S= {3,4,5,6,-7} and subset of S is {3,4,5,6}. Here mean does not exceed but is lower that its subset.

In above example none of the three statement holds true? Could you please advise.

Thank you.

The mean of {3, 4, 5, 6, -7} is 2.2.
The mean of one of the subset of the above set, {3, -7}, is 2.

So, your example is not valid.

The stem says: "The mean of set $$S$$ does not exceed mean of ANY subset of set $$S$$".
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Joined: 05 Mar 2018
Posts: 29

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10 Aug 2018, 03:47
I don't agree with the explanation. Statement III.
If median of set = mean of set
eg. mean {0,1,2} = median {0,1,2} = 1
here, mean exceeds the subset of set which is {2}.

Only II should be the corret answer?
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Joined: 02 Sep 2009
Posts: 58396

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10 Aug 2018, 03:59
I don't agree with the explanation. Statement III.
If median of set = mean of set
eg. mean {0,1,2} = median {0,1,2} = 1
here, mean exceeds the subset of set which is {2}.

Only II should be the corret answer?

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Joined: 26 Jun 2018
Posts: 1

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16 Aug 2019, 07:42
I think this is a high-quality question and I don't agree with the explanation.

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Joined: 02 Sep 2009
Posts: 58396

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16 Aug 2019, 07:46
Koushini wrote:
I think this is a high-quality question and I don't agree with the explanation.

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The solution is 100% correct. Please read the whole discussion. Hope it helps.
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Re: M16-23   [#permalink] 16 Aug 2019, 07:46

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# M16-23

Moderators: chetan2u, Bunuel