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enigma123
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R is a set containing 8 different numbers. S is a set containing 7 Updated on: 27 Jul 2025, 23:58
Originally posted by enigma123 on 25 Feb 2012, 05:06.
Last edited by Bunuel on 27 Jul 2025, 23:58, edited 1 time in total.
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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.

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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?
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A
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Bunuel
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R is a set containing 8 different numbers. S is a set containing 7 25 Feb 2012, 05:39
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enigma123
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?
Show more

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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R is a set containing 8 different numbers. S is a set containing 7 07 May 2014, 04:59
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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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R is a set containing 8 different numbers. S is a set containing 7 07 May 2014, 05:34
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virinchiwiwo
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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Yes, the ranges are equal but what's your question?
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R is a set containing 8 different numbers. S is a set containing 7 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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R is a set containing 8 different numbers. S is a set containing 7 16 Oct 2017, 16:53
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enigma123
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.
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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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R is a set containing 8 different numbers. S is a set containing 7 27 Jul 2025, 23:08
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Hi Bunuel could you give an explanation for option E? Between the two sets its just one number (which according to the question should be different than the rest) that creates the dfference in mean. So that number in set R, if one were to visualize on the number line, can either be more or less than the either of the rest and that would shift the mean such that it is either greater or less than mean of S but never equal.... So option E could also never be true? Pls correct me if im wrong
Bunuel
enigma123
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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R is a set containing 8 different numbers. S is a set containing 7 28 Jul 2025, 00:05
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xcvb
Hi Bunuel could you give an explanation for option E? Between the two sets its just one number (which according to the question should be different than the rest) that creates the dfference in mean. So that number in set R, if one were to visualize on the number line, can either be more or less than the either of the rest and that would shift the mean such that it is either greater or less than mean of S but never equal.... So option E could also never be true? Pls correct me if im wrong
Bunuel
enigma123
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.
Show more


To get a case where the mean of a set and its subset are equal, we just need to construct a set where the mean equals one of its elements. Then, if we remove that element, the mean stays the same.

For example, let R = {0, 1, 2, 3, 4, 5, 6, 11}. The mean of R is 4. If we remove the number 4, we get S = {0, 1, 2, 3, 5, 6, 11}, and its mean is also 4. So option E can be true.
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