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

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R is a set containing 8 different numbers. S is a set [#permalink] New post 25 Feb 2012, 04:06
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

50% (02:05) correct 50% (01:04) wrong based on 129 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.

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

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E.

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Re: CANNOT be true [#permalink] New post 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.

Hope it's clear.
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Re: R is a set containing 8 different numbers. S is a set [#permalink] New post 07 May 2014, 03:59
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 [#permalink] New post 07 May 2014, 04:34
Expert's post
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?
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. Tricky questions from previous years.

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. ,11 Mixed Questions, 12 Fresh Meat

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., 11 New DS set.


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Re: CANNOT be true [#permalink] New post 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 ! :)
Re: CANNOT be true   [#permalink] 09 May 2014, 00:15
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