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R is a set containing 8 different numbers. S is a set [#permalink]
25 Feb 2012, 04:06

00:00

A

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D

E

Difficulty:

45% (medium)

Question Stats:

51% (02:02) correct
49% (01:05) wrong based on 135 sessions

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.

Re: CANNOT be true [#permalink]
25 Feb 2012, 04:39

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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.

Re: CANNOT be true [#permalink]
09 May 2014, 00:15

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.

Hello Bunuel

Sorry ! I am not able to imagine the case where the Mean of the subset will be same as the Mean of its Super Set. i.e. Option E Please provide an example for that

Thanks a lot for your help !

gmatclubot

Re: CANNOT be true
[#permalink]
09 May 2014, 00:15

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