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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] New post 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] New post 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 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.
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S is a set containing 9 different numbers. [#permalink] New post 22 Jan 2013, 00:59
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!
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Re: S is a set containing 9 different numbers. [#permalink] New post 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: S is a set containing 9 different numbers. [#permalink] New post 22 Jan 2013, 04:19
[youtube][/youtube]
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!


Merging similar topics. Please refer to the solutions above.
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Re: cannot be true . mean median range [#permalink] New post 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] New post 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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PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!!

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!


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Re: cannot be true . mean median range   [#permalink] 22 Jan 2013, 06:22
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