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S is a set containing 9 different numbers. T is a set contai [#permalink]
29 Sep 2010, 05:25

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Difficulty:

55% (hard)

Question Stats:

52% (01:58) correct
48% (01:21) wrong based on 328 sessions

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 ?? ???

Re: cannot be true . mean median range [#permalink]
29 Sep 2010, 05:47

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Expert's post

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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.

Re: S is a set containing 9 different numbers. [#permalink]
22 Jan 2013, 00:20

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.

Re: cannot be true . mean median range [#permalink]
22 Jan 2013, 04:40

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.

Re: cannot be true . mean median range [#permalink]
22 Jan 2013, 05:22

Expert's post

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.

Answer: E.

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. _________________

Re: S is a set containing 9 different numbers. T is a set contai [#permalink]
03 Jun 2013, 10:51

@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 ?

Re: S is a set containing 9 different numbers. T is a set contai [#permalink]
04 Jun 2013, 02:53

Expert's post

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. _________________

Re: S is a set containing 9 different numbers. T is a set contai [#permalink]
30 Nov 2014, 18:45

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