Author 
Message 
TAGS:

Hide Tags

Current Student
Joined: 11 May 2008
Posts: 551

The mean of four integers will not change if all the integer [#permalink]
Show Tags
11 Sep 2008, 22:10
2
This post received KUDOS
12
This post was BOOKMARKED
Question Stats:
43% (00:55) correct 57% (00:55) wrong based on 371 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
Official Answer and Stats are available only to registered users. Register/ Login.



SVP
Joined: 29 Aug 2007
Posts: 2437

Re: always true [#permalink]
Show Tags
11 Sep 2008, 23:08
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/newtotheverbalforumpleasereadthisfirst77546.html Math: http://gmatclub.com/forum/newtothemathforumpleasereadthisfirst77764.html Gmat: http://gmatclub.com/forum/everythingyouneedtoprepareforthegmatrevised77983.html
GT



Intern
Joined: 13 Aug 2008
Posts: 17

Re: always true [#permalink]
Show Tags
11 Sep 2008, 23:35
IMO I only. the 4 integers could be 0,0,0,0 Hence III ruled out!



SVP
Joined: 29 Aug 2007
Posts: 2437

Re: always true [#permalink]
Show Tags
12 Sep 2008, 09:51
ankush83gupta wrote: IMO I only. the 4 integers could be 0,0,0,0 Hence III ruled out! are they four integers? however the question doesnot say four different integers!
_________________
Verbal: http://gmatclub.com/forum/newtotheverbalforumpleasereadthisfirst77546.html Math: http://gmatclub.com/forum/newtothemathforumpleasereadthisfirst77764.html Gmat: http://gmatclub.com/forum/everythingyouneedtoprepareforthegmatrevised77983.html
GT



VP
Joined: 17 Jun 2008
Posts: 1490

Re: always true [#permalink]
Show Tags
14 Sep 2008, 23:00
[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
Status: Final Lap Up!!!
Affiliations: NYK Line
Joined: 21 Sep 2012
Posts: 1036
Location: India
GMAT 1: 410 Q35 V11 GMAT 2: 530 Q44 V20 GMAT 3: 630 Q45 V31
GPA: 3.84
WE: Engineering (Transportation)

Re: The mean of four integers will not change if all the [#permalink]
Show Tags
03 Feb 2013, 15:27
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.....



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8026
Location: Pune, India

Re: The mean of four integers will not change if all the [#permalink]
Show Tags
03 Feb 2013, 22:28
7
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



Intern
Joined: 20 Jan 2013
Posts: 45
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.42

Re: The mean of four integers will not change if all the integer [#permalink]
Show Tags
01 Mar 2014, 05:25
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/collectionofthebestgmatresources167295.html#p1329720
May we all emerge victorious



Math Expert
Joined: 02 Sep 2009
Posts: 44566

Re: The mean of four integers will not change if all the integer [#permalink]
Show Tags
01 Mar 2014, 07:11
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: Ultimate GMAT Quantitative Megathread  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? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 02 May 2013
Posts: 24

Re: The mean of four integers will not change if all the integer [#permalink]
Show Tags
Updated on: 01 Mar 2014, 08:53
2
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.
Originally posted by pocoyama on 01 Mar 2014, 08:35.
Last edited by pocoyama on 01 Mar 2014, 08:53, edited 2 times in total.



Manager
Joined: 23 Sep 2015
Posts: 87
Concentration: General Management, Finance
GMAT 1: 680 Q46 V38 GMAT 2: 690 Q47 V38
GPA: 3.5

Re: The mean of four integers will not change if all the integer [#permalink]
Show Tags
07 Nov 2015, 22:51
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



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11489
Location: United States (CA)
GRE 1: 340 Q170 V170

Re: The mean of four integers will not change if all the integer [#permalink]
Show Tags
23 Feb 2018, 13:02
Hi All, In Roman Numeral questions, it's often easiest to DISPROVE the Roman Numerals, if possible (so that you can eliminate answer choices). Here, we're told that the MEAN of 4 integers will NOT change if each integer is multiplied by the same (re: ANY) constant. We're asked which of the Roman Numerals is ALWAYS TRUE. We can TEST VALUES to eliminate options.... II. The sum of the largest and smallest is 0 IF...the set is {3, 0, 1, 2} then the mean would stay the same, but the sum of the largest and smallest is NOT 0. Roman Numeral II is NOT true. Eliminate Answers B, D and E III. The set contains BOTH positive AND negative numbers IF....the set is {0, 0, 0, 0} then the mean would stay the same and the set does NOT contain both positive and negative numbers. Roman Numeral III is NOT true. Eliminate Answer C. There's only one answer left.... Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************



Intern
Joined: 01 Feb 2018
Posts: 4

The mean of four integers will not change if all the integer [#permalink]
Show Tags
21 Mar 2018, 14:14
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
A. I only B. II only C. III only D. I and II only E. I, II, and III Here's what I used, mostly because I suck at plugging in values 4 integers w,x,y,z Average = (w+x+y+z)/4 The Mean does not change when multiplied by any constant so, (w+x+y+z)/4 = a(w+x+y+z)/4 ; a is the constant here => (w+x+y+z)(1a)=0 And so we get that either the constant a is 1 or (w+x+y+z) = 0; I is true because w+x+y+z=0 and therefore the mean is 0 II there is no reason for this to be true III Not always true since {0,0,0,0} satisfies the parameters of the question




The mean of four integers will not change if all the integer
[#permalink]
21 Mar 2018, 14:14






