The mean of four integers will not change if all the integer : GMAT Problem Solving (PS)
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

It is currently 06 Dec 2016, 10:21
GMAT Club Tests

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

The mean of four integers will not change if all the integer

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

2 KUDOS received
Current Student
User avatar
Joined: 11 May 2008
Posts: 556
Followers: 8

Kudos [?]: 167 [2] , given: 0

The mean of four integers will not change if all the integer [#permalink]

Show Tags

New post 11 Sep 2008, 21:10
2
This post received
KUDOS
8
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

38% (01:58) correct 62% (00:58) wrong based on 276 sessions

HideShow timer Statistics

The mean of four integers will not change if all the integers are multiplied by any constant. What is always true about this set of numbers?

I. The mean of the set is 0
II. The sum of the largest member and the smallest member of the set is 0
III. The set contains both positive and negative integers

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III
[Reveal] Spoiler: OA
1 KUDOS received
SVP
SVP
User avatar
Joined: 29 Aug 2007
Posts: 2492
Followers: 67

Kudos [?]: 728 [1] , given: 19

Re: always true [#permalink]

Show Tags

New post 11 Sep 2008, 22:08
1
This post received
KUDOS
arjtryarjtry wrote:
The mean of four integers will not change if all the integers are multiplied by any constant. What is always true about this set of numbers?

I. The mean of the set is 0
II. The sum of the largest member and the smallest member of the set is 0
III. The set contains both positive and negative integers

I only
II only
III only
I and II only
I, II, and III


I. The mean of the set is 0. true.

II. The sum of the largest member and the smallest member of the set is 0.

set 1: -2, -1, 1, 2. true
set 2: -3, -2, -1, 6. false.

III. The set contains both positive and negative integers.

set 1: -2, -1, 1, 2. true
set 2: -3, -2, -1, 6. true

So D. I and III.
_________________

Verbal: http://gmatclub.com/forum/new-to-the-verbal-forum-please-read-this-first-77546.html
Math: http://gmatclub.com/forum/new-to-the-math-forum-please-read-this-first-77764.html
Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html


GT

Intern
Intern
avatar
Joined: 13 Aug 2008
Posts: 17
Followers: 0

Kudos [?]: 3 [0], given: 0

Re: always true [#permalink]

Show Tags

New post 11 Sep 2008, 22:35
IMO I only. the 4 integers could be 0,0,0,0 Hence III ruled out!
SVP
SVP
User avatar
Joined: 29 Aug 2007
Posts: 2492
Followers: 67

Kudos [?]: 728 [0], given: 19

Re: always true [#permalink]

Show Tags

New post 12 Sep 2008, 08:51
ankush83gupta wrote:
IMO I only. the 4 integers could be 0,0,0,0 Hence III ruled out!



are they four integers? :roll:

however the question doesnot say four different integers!
_________________

Verbal: http://gmatclub.com/forum/new-to-the-verbal-forum-please-read-this-first-77546.html
Math: http://gmatclub.com/forum/new-to-the-math-forum-please-read-this-first-77764.html
Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html


GT

SVP
SVP
avatar
Joined: 17 Jun 2008
Posts: 1569
Followers: 11

Kudos [?]: 245 [0], given: 0

Re: always true [#permalink]

Show Tags

New post 14 Sep 2008, 22:00
[quote="GMAT TIGER]

I. The mean of the set is 0. true.

II. The sum of the largest member and the smallest member of the set is 0.

set 1: -2, -1, 1, 2. true
set 2: -3, -2, -1, 6. false.

III. The set contains both positive and negative integers.

set 1: -2, -1, 1, 2. true
set 2: -3, -2, -1, 6. true

So D. I and III.
[/quote]

I do see a problem here.
What if set 3 = -1, -1, 0, 5?

IMO A.
VP
VP
avatar
Status: Final Lap Up!!!
Affiliations: NYK Line
Joined: 21 Sep 2012
Posts: 1096
Location: India
GMAT 1: 410 Q35 V11
GMAT 2: 530 Q44 V20
GMAT 3: 630 Q45 V31
GPA: 3.84
WE: Engineering (Transportation)
Followers: 37

Kudos [?]: 518 [0], given: 70

Re: The mean of four integers will not change if all the [#permalink]

Show Tags

New post 03 Feb 2013, 14:27
I have a doubt in this question
If we consider a set {1,2,3,4}, when multiplied with a constant we take that constant as 1 and multiply resulting set will contain the same numbers as the original. so how can the answer be I only.....
Expert Post
3 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 7069
Location: Pune, India
Followers: 2086

Kudos [?]: 13283 [3] , given: 222

Re: The mean of four integers will not change if all the [#permalink]

Show Tags

New post 03 Feb 2013, 21:28
3
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
Archit143 wrote:
I have a doubt in this question
If we consider a set {1,2,3,4}, when multiplied with a constant we take that constant as 1 and multiply resulting set will contain the same numbers as the original. so how can the answer be I only.....


The question tells you that 'The mean of four integers will not change if all the integers are multiplied by any constant.'

This means that when you multiply all the four integers by any constant e.g. 1 or 2 or 5 or 100 or -20 etc, you will always get the same mean.
In case of (1, 2, 3, 4}, the mean stays the same only when you multiple each number by 1. When you multiply each number by some other number e.g. 2, the mean changes. So {1, 2, 3, 4} doesn't satisfy our condition.

If the mean is 0, all the numbers will add up to 0.
a+b+c+d = 0
When you multiply this sum by any constant, the sum will remain 0 and hence the new mean will remain 0.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 12882
Followers: 561

Kudos [?]: 158 [0], given: 0

Premium Member
Re: The mean of four integers will not change if all the integer [#permalink]

Show Tags

New post 23 Feb 2014, 02:40
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Intern
Intern
avatar
Joined: 20 Jan 2013
Posts: 48
Location: India
Concentration: Finance, Entrepreneurship
GMAT 1: 740 Q49 V41
GPA: 3.42
Followers: 1

Kudos [?]: 19 [0], given: 70

GMAT ToolKit User Reviews Badge
Re: The mean of four integers will not change if all the integer [#permalink]

Show Tags

New post 01 Mar 2014, 04:25
The possible sets are-
{0,0,0,0,0} and {... -2,-1,0,1,2...}

The question asks "What is always true about this set of numbers". Statement 2 seems to fit the criteria as well. Can someone please explain why statement 2 is not being considered just because there can be sets that satisfy S2 but not the required set {0,0,0,0,0} and {... -2,-1,0,1,2...}?

The question asks "What is always true about this set of numbers". Statement 2 is always true about this set of numbers. Or is there some other possible set for the answer that S2 does not satisfy?
_________________

Best GMAT Resources downloads-
http://gmatclub.com/forum/collection-of-the-best-gmat-resources-167295.html#p1329720

May we all emerge victorious :)

Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 35910
Followers: 6846

Kudos [?]: 89982 [1] , given: 10396

Re: The mean of four integers will not change if all the integer [#permalink]

Show Tags

New post 01 Mar 2014, 06:11
1
This post received
KUDOS
Expert's post
anindame wrote:
The possible sets are-
{0,0,0,0,0} and {... -2,-1,0,1,2...}

The question asks "What is always true about this set of numbers". Statement 2 seems to fit the criteria as well. Can someone please explain why statement 2 is not being considered just because there can be sets that satisfy S2 but not the required set {0,0,0,0,0} and {... -2,-1,0,1,2...}?

The question asks "What is always true about this set of numbers". Statement 2 is always true about this set of numbers. Or is there some other possible set for the answer that S2 does not satisfy?


How is {..., -2, -1, 0, 1, 2, ...} a possible set? We are told that the set consists of 4 integers and if all the integers are multiplied by ANY constant, the mean won't change. Does your set satisfy this?
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | 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.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

1 KUDOS received
Intern
Intern
avatar
Joined: 02 May 2013
Posts: 25
Followers: 0

Kudos [?]: 17 [1] , given: 76

Reviews Badge
Re: The mean of four integers will not change if all the integer [#permalink]

Show Tags

New post 01 Mar 2014, 07:35
1
This post received
KUDOS
anindame wrote:
The possible sets are-
{0,0,0,0,0} and {... -2,-1,0,1,2...}

The question asks "What is always true about this set of numbers". Statement 2 seems to fit the criteria as well. Can someone please explain why statement 2 is not being considered just because there can be sets that satisfy S2 but not the required set {0,0,0,0,0} and {... -2,-1,0,1,2...}?

The question asks "What is always true about this set of numbers". Statement 2 is always true about this set of numbers. Or is there some other possible set for the answer that S2 does not satisfy?



consider this, {-3, 0, 1, 2}. The sum of the largest and the smallest is not 0 (-3 + 2 = 1).

However, the mean of the set is still 0, and multiplying any constant to the set will not change the mean of the set.

If you doubt that, consider -3=x, 1=y, 2=z.
x = y + z
Multiplying ANY constant C to the numbers, the sum of the positives and the negatives will not change.
xC = yC + zC = C(y + z)

Hope this helps that II is not ALWAYS true.

Last edited by pocoyama on 01 Mar 2014, 07:53, edited 2 times in total.
Intern
Intern
avatar
Joined: 20 Jan 2013
Posts: 48
Location: India
Concentration: Finance, Entrepreneurship
GMAT 1: 740 Q49 V41
GPA: 3.42
Followers: 1

Kudos [?]: 19 [0], given: 70

GMAT ToolKit User Reviews Badge
Re: The mean of four integers will not change if all the integer [#permalink]

Show Tags

New post 01 Mar 2014, 07:44
Bunuel wrote:
anindame wrote:
The possible sets are-
{0,0,0,0,0} and {... -2,-1,0,1,2...}

The question asks "What is always true about this set of numbers". Statement 2 seems to fit the criteria as well. Can someone please explain why statement 2 is not being considered just because there can be sets that satisfy S2 but not the required set {0,0,0,0,0} and {... -2,-1,0,1,2...}?

The question asks "What is always true about this set of numbers". Statement 2 is always true about this set of numbers. Or is there some other possible set for the answer that S2 does not satisfy?


How is {..., -2, -1, 0, 1, 2, ...} a possible set? We are told that the set consists of 4 integers and if all the integers are multiplied by ANY constant, the mean won't change. Does your set satisfy this?



Sorry.. my bad.. missed the "4 integers" part :(
_________________

Best GMAT Resources downloads-
http://gmatclub.com/forum/collection-of-the-best-gmat-resources-167295.html#p1329720

May we all emerge victorious :)


Last edited by anindame on 01 Mar 2014, 07:54, edited 1 time in total.
Intern
Intern
avatar
Joined: 20 Jan 2013
Posts: 48
Location: India
Concentration: Finance, Entrepreneurship
GMAT 1: 740 Q49 V41
GPA: 3.42
Followers: 1

Kudos [?]: 19 [0], given: 70

GMAT ToolKit User Reviews Badge
Re: The mean of four integers will not change if all the integer [#permalink]

Show Tags

New post 01 Mar 2014, 07:52
cssmarimo wrote:
bumpbot wrote:
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.


consider this, {-3, 0, 1, 2}. The sum of the largest and the smallest is not 0 (-3 + 2 = 1).

However, the mean of the set is still 0, and multiplying any constant to the set will not change the mean of the set.

If you doubt that, consider -3=x, 1=y, 2=z.
x = y + z
Multiplying ANY constant C to the numbers, the sum of the positives and the negatives will not change.
xC = yC + zC = C(y + z)

Hope this helps that II is not ALWAYS true.


Right!! Thanks :)
_________________

Best GMAT Resources downloads-
http://gmatclub.com/forum/collection-of-the-best-gmat-resources-167295.html#p1329720

May we all emerge victorious :)

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 12882
Followers: 561

Kudos [?]: 158 [0], given: 0

Premium Member
Re: The mean of four integers will not change if all the integer [#permalink]

Show Tags

New post 06 Sep 2015, 19:03
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Manager
Manager
User avatar
Joined: 23 Sep 2015
Posts: 95
Concentration: General Management, Finance
GMAT 1: 680 Q46 V38
GMAT 2: 690 Q47 V38
GPA: 3.5
Followers: 0

Kudos [?]: 13 [0], given: 213

Re: The mean of four integers will not change if all the integer [#permalink]

Show Tags

New post 07 Nov 2015, 21:51
i tested with sets

{-2 -1 1 2}
{0 0 0 0}
{-3 -2 -1 6}

able to eliminate all but A, in each case the mean is 0
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 12882
Followers: 561

Kudos [?]: 158 [0], given: 0

Premium Member
Re: The mean of four integers will not change if all the integer [#permalink]

Show Tags

New post 04 Dec 2016, 05:31
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: The mean of four integers will not change if all the integer   [#permalink] 04 Dec 2016, 05:31
    Similar topics Author Replies Last post
Similar
Topics:
16 Experts publish their posts in the topic What is the sum of all four digit integers formed using the digits 1, Bunuel 7 24 Feb 2016, 03:18
5 Experts publish their posts in the topic The average (arithmetic mean) of four distinct positive integers is 10 goodyear2013 4 06 Oct 2014, 06:30
38 Experts publish their posts in the topic There are 24 different four-digit integers than can be Maxswe 17 04 Nov 2012, 09:39
43 Experts publish their posts in the topic E is a collection of four ODD integers and the greatest nusmavrik 23 25 Aug 2010, 06:41
1 What is the greatest number of four-digit integers whose dancinggeometry 5 15 Sep 2008, 03:15
Display posts from previous: Sort by

The mean of four integers will not change if all the integer

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.