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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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12 Aug 2008, 11:07
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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

OPEN DISCUSSION OF THIS QUESTION IS HERE: s-is-a-set-containing-9-different-numbers-t-is-a-set-contai-101912.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 18 Jan 2014, 03:46, edited 1 time in total.
Renamed the topic, edited the question and added the OA.

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12 Aug 2008, 11:30
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E. Assuming a set cannot contain anything but integers.

vksunder 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
Take {1,2,3,4,5,6,7,8,9} for Set S => Mean is 5 so for Set t, remove number 5 and you have the same mean.
Take {1,2,3,4,6,7,8,9} for set T

b) The median of S is equal to the median of T
Again, remove number 5 and you have 4 and 6, which you need the averge of the 4th and 5th numbers, (4 and 6 respectively) for the median of set T, again median is 5 too.
c) The range of S is equal to the range of T
Again, if you remove any of the numbers EXCEPT for 1 and 9 to get Set T, you still have 1 and 9 ans your ends so the range is 8 on both.
d) The mean of S is greater than the mean of T
mean of S with 1 through 9 is 5 (9 numbers with total of 45). If you remove number 9 to make Set T, you have 8 numbers with total of 36, or an average of less than 5 (average of 5 across 8 numbers would be a total of 40, so less than that would be less than 5 average)
e) The range of S is less than the range of T
1 through 9 would be a range of 8. It would be impossible to have Set T to be within Set S and set S have a smaller range than set T because that would mean Set T included numbers not in set S.

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12 Aug 2008, 11:38
vksunder 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
possible :
e.g S={3,5,4} T={3,5}
b) The median of S is equal to the median of T
possible
S={2,4,6} T={2,6}
c) The range of S is equal to the range of T
POSSIBLE
S={ 1,2,3,4} T ={1,2,4 }
d) The mean of S is greater than the mean of T
POSSIBLE
e) The range of S is less than the range of T

Not possible
E.

IF T is subset of S.. then Always range of S must be equal or greather than T

e.g S={ 1,2,3,4} range 3
T={1,2,3 } range 2
T ={1,2,4 } range 3
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Re: S is a set containing 9 different numbers. T is a set [#permalink]

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17 Jan 2014, 10:35
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Re: S is a set containing 9 different numbers. T is a set contai [#permalink]

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18 Jan 2014, 03:47
Expert's post
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vksunder 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

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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: s-is-a-set-containing-9-different-numbers-t-is-a-set-contai-101912.html
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Re: S is a set containing 9 different numbers. T is a set contai   [#permalink] 18 Jan 2014, 03:47
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