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R is a set containing 8 different numbers. S is a set containing 7

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enigma123
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R is a set containing 8 different numbers. S is a set containing 7 [#permalink] New post   25 Feb 2012, 05:06
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R is a set containing 8 different numbers. S is a set containing 7 different numbers, all of which are members of R. Which of the following statements CANNOT be true?

(A) The range of R is less than the range of S.
(B) The mean of R is greater than the mean of S.
(C) The range of R is equal to the range of S.
(D) The mean of R is less than the mean of S.
(E) The mean of R is equal to the mean of S.

I got he right answer (
Show Spoiler
A
) but had to some guess work on choice D. Any idea how can we prove that choice
Show Spoiler
D
can be true as well?
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A
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Bunuel
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Re: R is a set containing 8 different numbers. S is a set containing 7 [#permalink] New post   25 Feb 2012, 05:39
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enigma123 wrote:
R is a set containing 8 different numbers. S is a set containing 7 different numbers, all of which are members of R. Which of the following statements CANNOT be true?

(A) The range of R is less than the range of S.
(B) The mean of R is greater than the mean of S.
(C) The range of R is equal to the range of S.
(D) The mean of R is less than the mean of S.
(E) The mean of R is equal to the mean of S.

I got he right answer (A) but had to some guess work on choice D. Any idea how can we prove that choice D can be true as well?


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

So, the answer is straight A: 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.

As for D:
Consider set R to be {-3, -2, -1, 0, 1, 2, 3, 4} --> mean=0.5.

(D) The mean of R is less than the mean of S --> remove the smallest term -3, then the mean of S will be 1, so more than 0.5.

Hope it's clear.
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Re: R is a set containing 8 different numbers. S is a set containing 7 [#permalink] New post   07 May 2014, 04:59
HI Bunuel, consider this Set R = { 1,2,3,4,5,6,7,8} and set S = {1,2,3,5,6,7,8}, in this case, the range for both set R and set S is 7.

Kindly let me know if am missing something here ?

Thanks
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Re: R is a set containing 8 different numbers. S is a set containing 7 [#permalink] New post   07 May 2014, 05:34
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virinchiwiwo wrote:
HI Bunuel, consider this Set R = { 1,2,3,4,5,6,7,8} and set S = {1,2,3,5,6,7,8}, in this case, the range for both set R and set S is 7.

Kindly let me know if am missing something here ?

Thanks


Yes, the ranges are equal but what's your question?
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Re: R is a set containing 8 different numbers. S is a set containing 7 [#permalink] New post   11 Oct 2017, 23:30
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construct a set
R=1,2,3,4,5,6,7,8=range=8-1=7 and mean=4
If S=1, 2,3,4,5,6,7=range=7-1=6 and mean is=4
If S=2,3,4,5,6,7,8=range=8-2=6 and mean is=35/7=5
so A is not possible
and E, D,C are possible.

as for B
Let R=0,1,2,3,4,5,6,7,mean=28/8=3.8
Let X=0,1,2,3,4,5,6, mean=21/7=3 hence B is also possible.
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Re: R is a set containing 8 different numbers. S is a set containing 7 [#permalink] New post   16 Oct 2017, 16:53
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enigma123 wrote:
R is a set containing 8 different numbers. S is a set containing 7 different numbers, all of which are members of R. Which of the following statements CANNOT be true?

(A) The range of R is less than the range of S.
(B) The mean of R is greater than the mean of S.
(C) The range of R is equal to the range of S.
(D) The mean of R is less than the mean of S.
(E) The mean of R is equal to the mean of S.


Since every number from set S is in set R, there is no way for the range of set S to be greater than that of set R. Thus, answer A cannot be true.

Answer: A
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Re: R is a set containing 8 different numbers. S is a set containing 7 [#permalink] New post   02 May 2019, 18:28
Bunuel -- I am not very clear in what case option E can be true. Specially since set R has an even number of members. It cannot be a case that the means of both the sets are zero. Please could you shed some light on when option E can be true.

Bunuel wrote:
enigma123 wrote:
R is a set containing 8 different numbers. S is a set containing 7 different numbers, all of which are members of R. Which of the following statements CANNOT be true?

(A) The range of R is less than the range of S.
(B) The mean of R is greater than the mean of S.
(C) The range of R is equal to the range of S.
(D) The mean of R is less than the mean of S.
(E) The mean of R is equal to the mean of S.

I got he right answer (A) but had to some guess work on choice D. Any idea how can we prove that choice D can be true as well?


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

So, the answer is straight A: 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.

As for D:
Consider set R to be {-3, -2, -1, 0, 1, 2, 3, 4} --> mean=0.5.

(D) The mean of R is less than the mean of S --> remove the smallest term -3, then the mean of S will be 1, so more than 0.5.

Hope it's clear.
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Re: R is a set containing 8 different numbers. S is a set containing 7 [#permalink]
02 May 2019, 18:28
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