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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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24 Aug 2017, 11:25



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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 \(S\)". Your example does not work. Thanks Bunuel ,understood ! Posted from my mobile device



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25 Aug 2017, 01:47
Just need to confirm one thing.S={1,2,3} then can the subset be like A={1,1,}



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25 Aug 2017, 04:50
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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29 Aug 2017, 05:04
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 reread 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 Here Set S has different values. Please advise. Thanks, Arpit



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29 Aug 2017, 05:07
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 reread 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 Here Set S has different values. Please advise. Thanks, Arpit I'd advice to reread the stem and the solution carefully and go through the discussion once more.
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29 Aug 2017, 05:56
[quote="Bunuel"
I'd advice to reread 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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18 Sep 2017, 23:48
What is S= 1,2,3,4,5 Mean=3 Median=3 Subset(4,5); Mean =4.5>3 So, Statment 3: False



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18 Sep 2017, 23:50



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22 Dec 2017, 14:18
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 ?



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23 Dec 2017, 00:14



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20 Jun 2018, 23:03
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.



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20 Jun 2018, 23:16
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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10 Aug 2018, 02:47
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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10 Aug 2018, 02:59



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21 Sep 2018, 00:47
As the question stem says "what must be true"?
let's consider S=(1,2,3,4,5) Subset of S say S'=(3,4,5)
If the mean of set S does not exceed mean of any subset of set S(Given) Mean of the Set= 3 Mean of the subset= 4 Does not exceed means, either the mean of the set is smaller than that of its subset or the mean of the set is equal to that of its subset. 3<4 so the consideration of the numbers is correct.
Here, option 3 is valid, but Could you guys please tell me why the second option is correct as the question specifically given "must be true"????
Thanks,



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11 Oct 2018, 00:26
Hi Bunel I am bit confused between statement 1 and 2 statement 1 cannot always be true because stmt 2 is a possibility we can say the same to stmt 2 also right it cannot always be true stmt 1 is also a possibility and what if there was an option that says both statment 1& 3 thanks a lot in advance Bunuel wrote: Official Solution:
If the mean of set \(S\) does not exceed mean of any subset of set \(S\), which of the following must be true about set \(S\)? I. Set \(S\) contains only one element II. All elements in set \(S\) are equal III. The median of set \(S\) equals the mean of set \(S\)
A. none of the three qualities is necessary B. II only C. III only D. II and III only E. I, II, and III
"The mean of set \(S\) does not exceed mean of ANY subset of set \(S\)" implies that set \(S\) could be: A. \(S=\{x\}\)  \(S\) contains only one element (e.g. {7 }); B. \(S=\{x, x, ...\}\)  \(S\) contains more than one element and all elements are equal (e.g. {7,7,7,7 }). Why is that? Because if set \(S\) contains two (or more) different elements, then we can always consider the subset with smallest number and the mean of this subset (mean of subset=smallest number) will be less than mean of entire set (mean of full set\(\gt\)smallest number). Example: if \(S=\{3, 5\}\), then mean of \(S=4\). Pick subset with the smallest number: \(s'=\{3\}\), mean of \(s'=3\). As we see \(3 \lt 4\). Now let's consider the statements: I. Set \(S\) contains only one element  not always true, we can have scenario \(B\) too (\(S=\{x, x, ...\}\)); II. All elements in set \(S\) are equal  true for both \(A\) and \(B\) scenarios, hence always true; III. The median of set \(S\) equals the mean of set \(S\)   true for both \(A\) and \(B\) scenarios, hence always true. So statements II and III are always true.
Answer: D







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