• Board contributors include instructors with "800" GMAT scores.
  • 95% of posts have replies within 24 hours.
  • Join for discounts with 800score, VeritasPrep and ManhattanGMAT


FAQ  - Register  - Search - Login 

All times are UTC - 7 hours




Post new topic Reply to topic  [ 4 posts ] 
Author Message
 Post subject: GMAT Sets
PostPosted: Mon Sep 10, 2012 11:03 am 
Offline
User avatar

Joined: Tue Apr 13, 2010 8:48 am
Posts: 477
A set of integers, S, contains more than one element. Is the range of S greater than its mean?
(1) S does not contain positive integers.
(2) The mean of S is negative.

A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
D. Either statement BY ITSELF is sufficient to answer the question.
E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, meaning that further information would be needed to answer the question.

(B) If S does not contain positive integers, as statement (1) defines, then S contains negative integers and/or zeroes.

If S consists of zeroes only, S = {0, 0, …, 0}, then its range is 0, because all the elements are the same. Besides, its mean is 0 as well, because the sum of the elements is 0. So in this case the mean and the range are equal.

If there is at least one non-zero element in S, then the sum will be negative (because S doesn't contain any positive numbers). The range is always a non-negative number, so it will be greater than the mean (which is negative).

Therefore statement (1) gives us two possible answers to the main question. Statement (1) by itself is NOT sufficient.

From Statement (2) we know that the mean is negative. Any range is a non-negative number. Therefore the range is greater than the mean. Statement (2) by itself is sufficient.

Since Statement (1) is insufficient and Statement (2) is sufficient, the correct answer is choice (B).

If this seems too abstract, it helps to pick some numbers, like the set {-5, -4, 2}, to see how the range will be greater than the mean. The mean is negative, and the range is 2 – (-5) = 7.
-------------

I believe the answer should be E. Statement 2 should be insufficient, because what if the set is {-10,-15,-20}. The range would be -10 and the mean would be -15. In this case the mean is LARGER than its range..


Top
 Profile  
 
 Post subject: Re: GMAT Sets
PostPosted: Mon Sep 10, 2012 11:09 am 
Offline

Joined: Thu Jul 05, 2012 11:55 am
Posts: 64
Quote:
I believe the answer should be E. Statement 2 should be insufficient, because what if the set is {-10,-15,-20}. The range would be -10 and the mean would be -15. In this case the mean is LARGER than its range..
Let us analyze the proposed set (-10,-15,-20) first.

It's range is -10 – (-20) = -10 + 20 = 10.
It's mean is ((-10) + (-15) + (-20)) / 3 = -45/3 = -15

10 > -15

The range is greater than the mean.

The range shows how far are the greatest and the least elements apart. Note, that range is always a NON-NEGATIVE number, i.e. positive or zero. And it equals zero only if all elements in a set are equal.


Top
 Profile  
 
 Post subject: Re: GMAT Sets
PostPosted: Mon Sep 10, 2012 11:10 am 
Offline
User avatar

Joined: Tue Apr 13, 2010 8:48 am
Posts: 477
I don't seem to understand the explanation.
In statement 1, every element of S is negative.
If S = {-1, -1}, range = 0 and mean = -1. So range > mean
If S = {-1, -3}, range = 2 and mean = -2. So range > mean
How can the mean be zero if every element of S is always negative?


Top
 Profile  
 
 Post subject: Re: GMAT Sets
PostPosted: Mon Sep 10, 2012 11:26 am 
Offline

Joined: Thu Jul 05, 2012 11:55 am
Posts: 64
Quote:
In statement 1, every element of S is negative.
Statement (1) tells us that S contains no positive elements, but it still can contain 0, as 0 is an integer and it is neither positive, nor negative.
So S can be {0, 0, …, 0}.


Top
 Profile  
 
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 4 posts ] 

All times are UTC - 7 hours


Who is online

Users browsing this forum: No registered users and 2 guests


You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum

Search for:
Jump to:  
cron
Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group
Template made by DEVPPL -
phpBB SEO
 
GMAT(TM) and GMAT CAT (TM) are registered trademarks of the Graduate Management Admission Council(TM). The Graduate Management Admission Council(TM) does not endorse, nor is affiliated in any way with the owner or any content of this site.