February 20, 2019 February 20, 2019 08:00 PM EST 09:00 PM EST Strategies and techniques for approaching featured GMAT topics. Wednesday, February 20th at 8 PM EST February 21, 2019 February 21, 2019 10:00 PM PST 11:00 PM PST Kick off your 2019 GMAT prep with a free 7day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th.
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 06 Apr 2016
Posts: 22

Hello Bunuel,
What if : set S = {1,2,3,4} ; Mean=2.5 subset of S ={1,2} ; Mean =1.5
Then option 2 " All elements in set S are equal" does not fit in. Please let me where am i going wrong.
Thanks, Saba



Math Expert
Joined: 02 Sep 2009
Posts: 52971

Re: M1623
[#permalink]
Show Tags
24 Aug 2017, 11:25



Intern
Joined: 06 Apr 2016
Posts: 22

Bunuel wrote: saba@4010 wrote: Hello Bunuel,
What if : set S = {1,2,3,4} ; Mean=2.5 subset of S ={1,2} ; Mean =1.5
Then option 2 " All elements in set S are equal" does not fit in. Please let me where am i going wrong.
Thanks, Saba "The mean of set \(S\) does not exceed mean of ANY subset of set \(S\)". Your example does not work. Thanks Bunuel ,understood ! Posted from my mobile device



Current Student
Joined: 12 Feb 2015
Posts: 56
Location: India
GPA: 3.84

Re: M1623
[#permalink]
Show Tags
25 Aug 2017, 01:47
Just need to confirm one thing.S={1,2,3} then can the subset be like A={1,1,}



Math Expert
Joined: 02 Sep 2009
Posts: 52971

Re: M1623
[#permalink]
Show Tags
25 Aug 2017, 04:50
himanshukamra2711 wrote: Just need to confirm one thing.S={1,2,3} then can the subset be like A={1,1,} No, you don't have three 1's in S. Subsets of {1, 2, 3} are: {1, 2, 3} {1, 2} {1, 3} {2, 3} {1} {2} {3} {}  an empty set.
_________________
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: 14 May 2017
Posts: 47

Re: M1623
[#permalink]
Show Tags
29 Aug 2017, 05:04
Bunuel wrote: ManSab wrote: 1. Set S contains only one element. Does it mean count of element or value of element? My understanding is that set S has only one element by count not by value... therefore {X,X...} is not possible. Please help understand. Option 1, Set S contains only one element means that there is only one elements in S: {X}. This option is not necessarily true. Please reread the solution. Hi, I am confused with second option. If i didn't misunderstood the question, it state that mean of Set S should be less than mean of its subset. Lets Consider: S =(2,4,6)  mean =4 S'= (4,6)  mean = 5 Here Set S has different values. Please advise. Thanks, Arpit



Math Expert
Joined: 02 Sep 2009
Posts: 52971

Re: M1623
[#permalink]
Show Tags
29 Aug 2017, 05:07
NeverGiveUp Arpit wrote: Bunuel wrote: ManSab wrote: 1. Set S contains only one element. Does it mean count of element or value of element? My understanding is that set S has only one element by count not by value... therefore {X,X...} is not possible. Please help understand. Option 1, Set S contains only one element means that there is only one elements in S: {X}. This option is not necessarily true. Please reread the solution. Hi, I am confused with second option. If i didn't misunderstood the question, it state that mean of Set S should be less than mean of its subset. Lets Consider: S =(2,4,6)  mean =4 S'= (4,6)  mean = 5 Here Set S has different values. Please advise. Thanks, Arpit I'd advice to reread the stem and the solution carefully and go through the discussion once more.
_________________
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: 14 May 2017
Posts: 47

Re: M1623
[#permalink]
Show Tags
29 Aug 2017, 05:56
[quote="Bunuel"
I'd advice to reread the stem and the solution carefully and go through the discussion once more.[/quote]
Got it. Thanks mate.
I overlooked the word 'Any '.
Posted from my mobile device
Posted from my mobile device



Intern
Joined: 07 Oct 2015
Posts: 7

Re: M1623
[#permalink]
Show Tags
18 Sep 2017, 23:48
What is S= 1,2,3,4,5 Mean=3 Median=3 Subset(4,5); Mean =4.5>3 So, Statment 3: False



Math Expert
Joined: 02 Sep 2009
Posts: 52971

Re: M1623
[#permalink]
Show Tags
18 Sep 2017, 23:50



Intern
Joined: 19 Jun 2017
Posts: 4

Re: M1623
[#permalink]
Show Tags
22 Dec 2017, 14:18
Hello ! For case III, let's take an example where the median of set S equals the mean of set S : set S = {1,2,3}, mean=median=2. In that case, {1} is a subset of set S and 2>1. Conclusion: the mean of set S DOES exceed mean of a subset of set S How is III still correct ?



Math Expert
Joined: 02 Sep 2009
Posts: 52971

Re: M1623
[#permalink]
Show Tags
23 Dec 2017, 00:14



Intern
Joined: 22 Aug 2016
Posts: 10

Re: M1623
[#permalink]
Show Tags
20 Jun 2018, 23:03
Hi Bunuel,
"If the mean of set S does not exceed mean of any subset of set S''
Does it have to be true that Mean of S and Mean of any subset of S is equal? What if set S has negative numbers?
For Ex: S= {3,4,5,6,7} and subset of S is {3,4,5,6}. Here mean does not exceed but is lower that its subset.
In above example none of the three statement holds true? Could you please advise.
Thank you.



Math Expert
Joined: 02 Sep 2009
Posts: 52971

Re: M1623
[#permalink]
Show Tags
20 Jun 2018, 23:16
hrishipatil72 wrote: Hi Bunuel,
"If the mean of set S does not exceed mean of any subset of set S''
Does it have to be true that Mean of S and Mean of any subset of S is equal? What if set S has negative numbers?
For Ex: S= {3,4,5,6,7} and subset of S is {3,4,5,6}. Here mean does not exceed but is lower that its subset.
In above example none of the three statement holds true? Could you please advise.
Thank you. The mean of {3, 4, 5, 6, 7} is 2.2. The mean of one of the subset of the above set, {3, 7}, is 2. So, your example is not valid. The stem says: "The mean of set \(S\) does not exceed mean of ANY subset of set \(S\)".
_________________
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: 05 Mar 2018
Posts: 1

Re M1623
[#permalink]
Show Tags
10 Aug 2018, 02:47
I don't agree with the explanation. Statement III. If median of set = mean of set eg. mean {0,1,2} = median {0,1,2} = 1 here, mean exceeds the subset of set which is {2}.
Only II should be the corret answer?



Math Expert
Joined: 02 Sep 2009
Posts: 52971

Re: M1623
[#permalink]
Show Tags
10 Aug 2018, 02:59



Intern
Joined: 10 Dec 2017
Posts: 25
Location: India

Re: M1623
[#permalink]
Show Tags
21 Sep 2018, 00:47
As the question stem says "what must be true"?
let's consider S=(1,2,3,4,5) Subset of S say S'=(3,4,5)
If the mean of set S does not exceed mean of any subset of set S(Given) Mean of the Set= 3 Mean of the subset= 4 Does not exceed means, either the mean of the set is smaller than that of its subset or the mean of the set is equal to that of its subset. 3<4 so the consideration of the numbers is correct.
Here, option 3 is valid, but Could you guys please tell me why the second option is correct as the question specifically given "must be true"????
Thanks,



Intern
Joined: 17 Aug 2017
Posts: 1

Re: M1623
[#permalink]
Show Tags
11 Oct 2018, 00:26
Hi Bunel I am bit confused between statement 1 and 2 statement 1 cannot always be true because stmt 2 is a possibility we can say the same to stmt 2 also right it cannot always be true stmt 1 is also a possibility and what if there was an option that says both statment 1& 3 thanks a lot in advance Bunuel wrote: Official Solution:
If the mean of set \(S\) does not exceed mean of any subset of set \(S\), which of the following must be true about set \(S\)? I. Set \(S\) contains only one element II. All elements in set \(S\) are equal III. The median of set \(S\) equals the mean of set \(S\)
A. none of the three qualities is necessary B. II only C. III only D. II and III only E. I, II, and III
"The mean of set \(S\) does not exceed mean of ANY subset of set \(S\)" implies that set \(S\) could be: A. \(S=\{x\}\)  \(S\) contains only one element (e.g. {7 }); B. \(S=\{x, x, ...\}\)  \(S\) contains more than one element and all elements are equal (e.g. {7,7,7,7 }). Why is that? Because if set \(S\) contains two (or more) different elements, then we can always consider the subset with smallest number and the mean of this subset (mean of subset=smallest number) will be less than mean of entire set (mean of full set\(\gt\)smallest number). Example: if \(S=\{3, 5\}\), then mean of \(S=4\). Pick subset with the smallest number: \(s'=\{3\}\), mean of \(s'=3\). As we see \(3 \lt 4\). Now let's consider the statements: I. Set \(S\) contains only one element  not always true, we can have scenario \(B\) too (\(S=\{x, x, ...\}\)); II. All elements in set \(S\) are equal  true for both \(A\) and \(B\) scenarios, hence always true; III. The median of set \(S\) equals the mean of set \(S\)   true for both \(A\) and \(B\) scenarios, hence always true. So statements II and III are always true.
Answer: D







Go to page
Previous
1 2
[ 38 posts ]



