Author 
Message 
Current Student
Joined: 28 Dec 2004
Posts: 3357
Location: New York City
Schools: Wharton'11 HBS'12

Is the mean of a nonempty set S bigger than its median? 1. All members of S are consecutive multiples of 3 2. The sum of all members of S equals 75 Source: GMAT Club Tests  hardest GMAT questions however i think it should be E.. how do we know all the elements in S are positive? what if we have 3, 6, 9, 0, 3, etc?



SVP
Joined: 17 Jun 2008
Posts: 1547

Re: m08#23 [#permalink]
Show Tags
04 Nov 2008, 23:20
1
This post received KUDOS
fresinha12 wrote: Is the mean of a nonempty set S bigger than its median?
1. All members of S are consecutive multiples of 3 2. The sum of all members of S equals 75
OA is A..
however i think it should be E..
how do we know all the elements in S are positive? what if we have 3, 6, 9, 0, 3, etc? Stmt1 simply says that the members of S are in arithmatic series and hence mean and median will be the same.



Intern
Affiliations: Phi Theta Kappa, Dean's list, Chancelors list, Who's Who award, ASCPA
Joined: 16 May 2011
Posts: 25
WE 1: Tax

Re: m08#23 [#permalink]
Show Tags
29 Aug 2011, 05:51
1
This post received KUDOS
Answer: A
Median will equal mean in consecutive integers Not B because it does give any information about the numbers in question.



Math Expert
Joined: 02 Sep 2009
Posts: 39672

Re: m08#23 [#permalink]
Show Tags
29 Aug 2012, 08:01
FN wrote: Is the mean of a nonempty set S bigger than its median? 1. All members of S are consecutive multiples of 3 2. The sum of all members of S equals 75 Source: GMAT Club Tests  hardest GMAT questions however i think it should be E.. how do we know all the elements in S are positive? what if we have 3, 6, 9, 0, 3, etc? REVISED VERSION OF THIS QUESTION IS BELOW: Is the mean of set S greater than its median?(1) Set S consist of consecutive multiples of 3 > set S is evenly spaced. One of the most important properties of evenly spaced set (aka arithmetic progression) is: in any evenly spaced set the arithmetic mean (average) is equal to the median. So, the mean of S = the median of S. Sufficient. (2) The sum of all terms of set S is 75 > if S={75} then mean=median but if S={0, 0, 75} then (mean=25)>(0=median). Not sufficient. Answer: A.
_________________
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? Extrahard Quant Tests with Brilliant Analytics



SVP
Joined: 29 Aug 2007
Posts: 2473

Re: m08#23 [#permalink]
Show Tags
02 Nov 2008, 16:43
fresinha12 wrote: Is the mean of a nonempty set S bigger than its median?
1. All members of S are consecutive multiples of 3 2. The sum of all members of S equals 75
OA is A..
however i think it should be E..
how do we know all the elements in S are positive? what if we have 3, 6, 9, 0, 3, etc? I think OA is ok. 9, 6, 3, 0, 3, sum = 15 mean = 15/5 = 3 median = 3
_________________
Verbal: http://gmatclub.com/forum/newtotheverbalforumpleasereadthisfirst77546.html Math: http://gmatclub.com/forum/newtothemathforumpleasereadthisfirst77764.html Gmat: http://gmatclub.com/forum/everythingyouneedtoprepareforthegmatrevised77983.html
GT



Intern
Joined: 30 Jan 2010
Posts: 13

Re: m08#23 [#permalink]
Show Tags
24 Aug 2010, 07:27
1
This post was BOOKMARKED
Statement 1 : Evenly spaced sets means MEDIAN = MEAN, so > sufficient
Statement 2: You are only given the sum of numbers in set, they could be (1, 75) or (1, 5, 70) so, > not sufficient.
Answer is A.



Verbal Forum Moderator
Joined: 31 Jan 2010
Posts: 488
WE 1: 4 years Tech

Re: m08#23 [#permalink]
Show Tags
24 Aug 2010, 23:57
what if there is an even number of elements in the Set S,For example 27,30,33,36 Mean=31.5 Median=30 or 33 then?
_________________
My Post Invites Discussions not answers Try to give back something to the Forum.I want your explanations, right now ! Please let me know your opinion about the Chandigarh Gmat Centrehttp://gmatclub.com/forum/gmatexperienceatchandigarhindiacentre111830.html



CIO
Joined: 02 Oct 2007
Posts: 1218

Re: m08#23 [#permalink]
Show Tags
25 Aug 2010, 01:04
The median will equal the mean then. Here's a quote from Wikipedia Quote: If there is an even number of observations, then there is no single middle value; the median is then usually defined to be the mean of the two middle values mundasingh123 wrote: what if there is an even number of elements in the Set S,For example 27,30,33,36 Mean=31.5 Median=30 or 33 then?
_________________
Welcome to GMAT Club! Want to solve GMAT questions on the go? GMAT Club iPhone app will help. Please read this before posting in GMAT Club Tests forum Result correlation between real GMAT and GMAT Club Tests Are GMAT Club Test sets ordered in any way? Take 15 free tests with questions from GMAT Club, Knewton, Manhattan GMAT, and Veritas.
GMAT Club Premium Membership  big benefits and savings



Intern
Joined: 11 Nov 2009
Posts: 27

Re: m08#23 [#permalink]
Show Tags
29 Aug 2011, 07:02
A looks good....bu can any one give example of B where Mean is bigger than Median....



Intern
Affiliations: Phi Theta Kappa, Dean's list, Chancelors list, Who's Who award, ASCPA
Joined: 16 May 2011
Posts: 25
WE 1: Tax

Re: m08#23 [#permalink]
Show Tags
29 Aug 2011, 07:53
gsd85 wrote: A looks good....bu can any one give example of B where Mean is bigger than Median.... 15+2+1/3 = 18/3 = 6 Mean of 6 > Median of 2



Director
Joined: 21 Dec 2009
Posts: 583
Concentration: Entrepreneurship, Finance

Re: m08#23 [#permalink]
Show Tags
29 Aug 2011, 08:21
for consecutive integers: mean = median Also, equals (max + min)/2 example: 7, 8, 9, 10, and 11 mean = (7+11)/2 = 9 median = 9 By the same token, for 12, 14, 16, and 18 mean = (12 + 18)/2 = 15 median also = average of 14 and 16 = 15 Hope this helps.
_________________
KUDOS me if you feel my contribution has helped you.



Intern
Joined: 11 Nov 2009
Posts: 27

Re: m08#23 [#permalink]
Show Tags
29 Aug 2011, 09:35
I want to know for no's whose sum =75 is there any combination where mean > median........ for e.g 25+25+25 ..........mean= median for 25 +25+16+9 ............mean < median... so i want to know a combination where mean > median........i could not figure out ....so just need help



Manager
Joined: 14 Mar 2011
Posts: 83

Re: m08#23 [#permalink]
Show Tags
29 Aug 2011, 09:54
Lets take some examples 1. Let set is two number (3,6) mean=4.5, median=4.5 now let take 3 nos. (15, 18, 21) mean=18, Median=18 now lets take a bigger set (12, 9,6,3,0,3,6,9) Median = 1.5, Mean = 12/8= 3/2 = 1.5 A is answer Golden rule for Consecutive integers is already explained just a addition Regards Jagdeep



Manager
Joined: 11 Feb 2011
Posts: 74

Re: m08#23 [#permalink]
Show Tags
29 Aug 2011, 11:21
simple one..A is the answer



Senior Manager
Joined: 19 Oct 2010
Posts: 261
Location: India
GPA: 3

Re: m08#23 [#permalink]
Show Tags
03 Sep 2011, 09:27
celluloidandroid wrote: Answer: A
Median will equal mean in consecutive integers Not B because it does give any information about the numbers in question. Good information. Thank you.
_________________
petrifiedbutstanding



Current Student
Joined: 07 Sep 2011
Posts: 74
GMAT 1: 660 Q41 V40 GMAT 2: 720 Q49 V39
WE: Analyst (Mutual Funds and Brokerage)

Re: m08#23 [#permalink]
Show Tags
29 Aug 2012, 07:15
Remember that evenly spaced sets, the mean = median. Regardless of # of items.
A) Sufficient b) Insufficient



Director
Status: Final Countdown
Joined: 17 Mar 2010
Posts: 537
Location: India
GPA: 3.82
WE: Account Management (Retail Banking)

Re: m08#23 [#permalink]
Show Tags
29 Aug 2012, 11:21
True, as Bunuel said, Mean=Median or evenly spaced sets, so (i) sufficient in (ii) the sets have a sum of 75 ; we can have many combinations to do so (0,0,75),(25,25,25), etc..insufficient (A)wins
_________________
" Make more efforts " Press Kudos if you liked my post










