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# S is a set containing 9 different numbers. T is a set contai

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S is a set containing 9 different numbers. T is a set contai [#permalink]

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29 Sep 2010, 06:25
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S is a set containing 9 different numbers. T is a set containing 8 different numbers, all of which are members of S. which of the following statements cannot be true?

A. The mean of S is equal to the mean of T
B. The median of S is equal to the median of T
C. The range of S is equal to the range of T
D. The mean of S is greater than the mean of T
E. The range of S is less than the range of T

my question : what if the extra number is zero ?? ???
[Reveal] Spoiler: OA
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S is a set containing 9 different numbers. T is a set contai [#permalink]

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29 Sep 2010, 06:47
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S is a set containing 9 different numbers. T is a set containing 8 different numbers, all of which are members of S. which of the following statements cannot be true?

The range of a set is the difference between the largest and smallest elements of a set.

Consider the set S to be {-4, -3, -2, -1, 0, 1, 2, 3, 4} --> $$mean=median=0$$ and $$range=8$$.

A. Mean of S = mean of T --> remove 0 from set S, then the mean of T still would be 0;
B. Median of S = Median of T --> again remove 0 from set S, then the median of T still would be 0;
C. Range of S = range of T --> again remove 0 from set S, then the range of T still would be 8;
D. Mean of S > mean of T --> remove 4, then the mean of T would be negative -0.5 so less than 0;
E. Range of S < range of T --> the range of a subset cannot be more than the range of a whole set: how can the difference between the largest and smallest elements of a subset be more than the difference between the largest and smallest elements of a whole set.

Hope it helps.
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Re: S is a set containing 9 different numbers. [#permalink]

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22 Jan 2013, 01:20
fozzzy wrote:
S is a set containing 9 different numbers. T is a set containing 8 different numbers, all of which are members of S. which of the following statements cannot be true?

A) The mean of S is equal to the mean of T
B) The median of S is equal to the median of T
C) The range of S is equal to the range of T
D) The mean of S is greater than the mean of T
E) The range of S is less than the range of T

Detailed explanation will be appreciated. Thanks!

Mean of both the sets can be equal. Let us suppose the mean of any 8 number is 10 then the 9th number could also be 10 and mean remains the same.
In the same way median can also be same. In set of 9 numbers median will be the 5th number when arranged in ascending order and in set T it will be the mean of 4th and 5th number.
If we take S = { 1, 2, 3, 4 ,5, 6, 7, 8, 9 } and T as { 1, 2, 3, 4, 6, 7, 8, 9 } then median in both the cases will be 5.
From the above eg range is same in both the cases.
If the number which is not the part of set T is greater than mean of T then the mean of set S will be greater than that of set T
Range of S will always be greater than or equal to range of T because of an additional number. If that number is greater than the greatest number in set T the range will be more, if that number is smaller than the smallest number in set T again the range will be more since now the new number is the smallest number. If that number lies in between then the range will be equal.

If you like my explanation please give a kudo.
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Re: cannot be true . mean median range [#permalink]

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22 Jan 2013, 05:40
Bunuel wrote:
The range of a set is the difference between the largest and smallest elements of a set.

Consider the set S to be {-4, -3, -2, -1, 0, 1, 2, 3, 4} --> $$mean=median=0$$ and $$range=8$$.

A. Mean of S = mean of T --> remove 0 from set S, then the mean of T still would be 0;
B. Median of S = Median of T --> again remove 0 from set S, then the median of T still would be 0;
C. Range of S = range of T --> again remove 0 from set S, then the range of T still would be 8;
D. Mean of S > mean of T --> remove 4, then the mean of T would be negative -0.5 so less than 0;
E. Range of S < range of T --> the range of a subset can not be more than the range of a whole set: how can the difference between the largest and smallest elements of a subset be more than the difference between the largest and smallest elements of a whole set.

Hope it helps.

So this is a property of sets?
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Re: cannot be true . mean median range [#permalink]

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22 Jan 2013, 06:22
fozzzy wrote:
Bunuel wrote:
The range of a set is the difference between the largest and smallest elements of a set.

Consider the set S to be {-4, -3, -2, -1, 0, 1, 2, 3, 4} --> $$mean=median=0$$ and $$range=8$$.

A. Mean of S = mean of T --> remove 0 from set S, then the mean of T still would be 0;
B. Median of S = Median of T --> again remove 0 from set S, then the median of T still would be 0;
C. Range of S = range of T --> again remove 0 from set S, then the range of T still would be 8;
D. Mean of S > mean of T --> remove 4, then the mean of T would be negative -0.5 so less than 0;
E. Range of S < range of T --> the range of a subset can not be more than the range of a whole set: how can the difference between the largest and smallest elements of a subset be more than the difference between the largest and smallest elements of a whole set.

Hope it helps.

So this is a property of sets?

Sure. The range of a subset cannot be greater than the range of the whole set.
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Re: S is a set containing 9 different numbers. T is a set contai [#permalink]

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03 Jun 2013, 03:09
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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Re: S is a set containing 9 different numbers. T is a set contai [#permalink]

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03 Jun 2013, 11:51
@Bunuel:

I agree with you that the range of subsequent set is less than the whole set, but it can also be the same ? For exmaple:

100 14 13 2 whole set.
100 14 2 subsequent set.

All mebers of the subsequent set are also members of the whole set. But the range are in both cases the same. So it must be as follows: The range of the subsequent set can be equal or less than that of the whole set ?
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Re: S is a set containing 9 different numbers. T is a set contai [#permalink]

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04 Jun 2013, 03:53
Alexmsi wrote:
@Bunuel:

I agree with you that the range of subsequent set is less than the whole set, but it can also be the same ? For exmaple:

100 14 13 2 whole set.
100 14 2 subsequent set.

All mebers of the subsequent set are also members of the whole set. But the range are in both cases the same. So it must be as follows: The range of the subsequent set can be equal or less than that of the whole set ?

The way it's written in my post is the same: the range of a subset cannot be greater than the range of a whole set. This means that the range of a subset is always less than or equal to the range of the whole set.
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Re: S is a set containing 9 different numbers. T is a set contai [#permalink]

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20 Nov 2013, 09:12
Solve for an "easier" problem and make up an example to see what's going on in the problem.

Set S = {1,2,3}
Set T = {2,3}

Okay so if we can get an answer that is true, we can eliminate that answer choice.

a) hmm, how to get the mean equal each other? Oh, just remove the 2 instead of 1.
b) same
c) same
d) remove 3 instead of 1

At this point we can choose e) and move on, but to be sure just test some numbers again.

e)
range set S = 3-1 = 2
range set T = 3-2 = 1
range set T = 3-1 = 1

So, this can never be true. --> Bingo

This is basically the same method as Bunuel posted above, but for me it sometimes works better if I have a simpler set to work with.
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Re: S is a set containing 9 different numbers. T is a set contai [#permalink]

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30 Nov 2014, 19:45
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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S is a set containing 9 different numbers. T is a set contai [#permalink]

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12 Nov 2015, 00:40
[quote="Bunuel"]The range of a set is the difference between the largest and smallest elements of a set.

Consider the set S to be {-4, -3, -2, -1, 0, 1, 2, 3, 4} --> $$mean=median=0$$ and $$range=8$$.

A. Mean of S = mean of T --> remove 0 from set S, then the mean of T still would be 0;
B. Median of S = Median of T --> again remove 0 from set S, then the median of T still would be 0;
C. Range of S = range of T --> again remove 0 from set S, then the range of T still would be 8;
D. Mean of S > mean of T --> remove 4, then the mean of T would be negative -0.5 so less than 0;
E. Range of S < range of T --> the range of a subset cannot be more than the range of a whole set: how can the difference between the largest and smallest elements of a subset be more than the difference between the largest and smallest elements of a whole set.

Hope it helps.[/quote

If the numbers are all different and positive in the question and S has 8 numbers and T has 7 numbers, then will mean of Set S be ever equal to mean of set T as in option [A]
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Re: S is a set containing 9 different numbers. T is a set contai [#permalink]

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20 Nov 2016, 09:31
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: S is a set containing 9 different numbers. T is a set contai [#permalink]

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17 Apr 2017, 22:32
Bunuel wrote:
The range of a set is the difference between the largest and smallest elements of a set.

Consider the set S to be {-4, -3, -2, -1, 0, 1, 2, 3, 4} --> $$mean=median=0$$ and $$range=8$$.

A. Mean of S = mean of T --> remove 0 from set S, then the mean of T still would be 0;
B. Median of S = Median of T --> again remove 0 from set S, then the median of T still would be 0;
C. Range of S = range of T --> again remove 0 from set S, then the range of T still would be 8;
D. Mean of S > mean of T --> remove 4, then the mean of T would be negative -0.5 so less than 0;
E. Range of S < range of T --> the range of a subset cannot be more than the range of a whole set: how can the difference between the largest and smallest elements of a subset be more than the difference between the largest and smallest elements of a whole set.

Hope it helps.[/quote

If the numbers are all different and positive in the question and S has 8 numbers and T has 7 numbers, then will mean of Set S be ever equal to mean of set T as in option [A]

Yes, it is still possible.

Consider following examples:

T = {2, 4, 6, 8, 10, 12, 21} Mean of T = 63/7 = 9

S = {2, 4, 6, 8, 9, 10, 12, 21} Mean of S = 9

Key idea is that create a set with 7 elements such that the mean is not a member of the set.

For larger set (i.e. set S) you can always add mean as an additional element and mean of the larger set will still be same as smaller set (set T).

Hope it helps.
Re: S is a set containing 9 different numbers. T is a set contai   [#permalink] 17 Apr 2017, 22:32
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