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]

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 ?? ???

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Re: cannot be true . mean median range [#permalink]

29 Sep 2010, 06:47

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.

Answer: E.

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

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.

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Re: cannot be true . mean median range [#permalink]

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.

Answer: E.

Hope it helps.

So this is a property of sets?

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Re: cannot be true . mean median range [#permalink]

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.

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

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]

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]

04 Jun 2013, 03:53

Alexmsi wrote:

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] 04 Jun 2013, 03:53

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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

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