It is currently 20 Nov 2017, 23:46

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

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

M28-47

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42275

Kudos [?]: 132870 [0], given: 12389

M28-47 [#permalink]

Show Tags

New post 16 Sep 2014, 02:51
Expert's post
6
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

49% (00:37) correct 51% (01:05) wrong based on 37 sessions

HideShow timer Statistics

What is the value of the median of set A?


(1) No number in set A is less than the average (arithmetic mean) of set A.

(2) The average (arithmetic mean) of set A is equal to the range of set A.
[Reveal] Spoiler: OA

_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 132870 [0], given: 12389

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42275

Kudos [?]: 132870 [1], given: 12389

Re M28-47 [#permalink]

Show Tags

New post 16 Sep 2014, 02:51
1
This post received
KUDOS
Expert's post
Official Solution:


(1) No number in set A is less than the average (arithmetic mean) of set A.

Since no number is less than the average, then no number is more than the average, which implies that the list contains identical elements: \(A=\{x, \ x, \ x, \ ...\}\). From this it follows that (the average)=(the median). But we don't know the value of \(x\), thus this statement is NOT sufficient.

(2) The average (arithmetic mean) of set A is equal to the range of set A.

Not sufficient: if \(A=\{0, \ 0, \ 0, \ 0\}\), then (the median)=0, but if \(A=\{1, \ 2, \ 2, \ 3\}\), then (the median)=2.

(1)+(2) From (1) we have that the list contains identical elements. The range of all such sets is 0. Therefore, from (2) we have that (the average)=(the range)=0 and since from (1) we also know that (the average)=(the median), then (the median)=0. Sufficient.


Answer: C
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 132870 [1], given: 12389

Manager
Manager
avatar
Joined: 14 Jul 2014
Posts: 97

Kudos [?]: 32 [0], given: 49

Re: M28-47 [#permalink]

Show Tags

New post 11 Mar 2015, 10:45
Bunuel wrote:
Official Solution:


(1) No number in set A is less than the average (arithmetic mean) of set A.

Since no number is less than the average, then no number is more than the average, which implies that the list contains identical elements: \(A=\{x, \ x, \ x, \ ...\}\). From this it follows that (the average)=(the median). But we don't know the value of \(x\), thus this statement is NOT sufficient.

(2) The average (arithmetic mean) of set A is equal to the range of set A.

Not sufficient: if \(A=\{0, \ 0, \ 0, \ 0\}\), then (the median)=0, but if \(A=\{1, \ 2, \ 2, \ 3\}\), then (the median)=2.

(1)+(2) From (1) we have that the list contains identical elements. The range of all such sets is 0. Therefore, from (2) we have that (the average)=(the range)=0 and since from (1) we also know that (the average)=(the median), then (the median)=0. Sufficient.


Answer: C


Hi Bunuel

How can you derive the highlighted part above? (i.e. then no number is more than the average) - I think this is possible

Eg A= { 2 } - Here, Median = Mean = 2
A = { 2, 2, 2, 3} - Here, Median = 2, Mean = 2.25 ..... What Im trying to say is that we can have a number > Mean

Either ways, I agree that this is Insufficient.

Pls clarify my doubt

Thanks

Kudos [?]: 32 [0], given: 49

1 KUDOS received
Intern
Intern
avatar
Joined: 23 Apr 2016
Posts: 22

Kudos [?]: 10 [1], given: 39

Location: Finland
Concentration: General Management, International Business
GPA: 3.65
Premium Member
Re: M28-47 [#permalink]

Show Tags

New post 11 Nov 2016, 15:05
1
This post received
KUDOS
The question says, no number is less than average, NOT some number is less than average.
For example take a set of number 2,2,2 here no number is more than the average
now if we add say 3 to this set... to bring the average of this new set (2,2,2,3), we needs some value which will bring back the average of 3 and that number back to 2, so we will have to add a to the set.

So what Bunuel is basically saying that if something is more than average, than there must be some number less than average OR if nothing is more than average, than nothing should be less than average as well.

Kudos [?]: 10 [1], given: 39

Manager
Manager
avatar
G
Joined: 14 Oct 2012
Posts: 182

Kudos [?]: 54 [0], given: 962

Premium Member Reviews Badge CAT Tests
M28-47 [#permalink]

Show Tags

New post 16 Apr 2017, 20:28
My 2 cents,
Elaborating further on what thapliya said:
Initially, set = {2,2,2} mean = median = 2
Now, set = {2,2,2,3} mean = 11/4 = 2.25 & Median = 2
To bring the mean of the set back to 2 we need to remove the additional portion of 2 (8+2, i hope this is clear. if not leave a message!!!) added to the mean by entering 3 in the set.
Set = {-1,2,2,2,3} => Mean = (11-1)/5 = 10/5 = 2.
Thus we again get Mean = Median = 2.

Coming back to the problem:
S-1 - "No number in set A is less than the average (arithmetic mean) of set A."
But in our case we CANNOT add any value which is smaller than mean. Thus we CANNOT add any new value to the set which is either greater than or less than mean of set, as we CANNOT add any smaller value to balance out higher value in our set. Thus ALL the values in the set NEED to be equal.
I hope this helps!!!

Kudos [?]: 54 [0], given: 962

Manager
Manager
avatar
S
Joined: 02 Jun 2015
Posts: 189

Kudos [?]: 316 [0], given: 390

Location: Ghana
Premium Member
Re: M28-47 [#permalink]

Show Tags

New post 28 Jun 2017, 06:49
Bunuel wrote:
What is the value of the median of set A?


(1) No number in set A is less than the average (arithmetic mean) of set A.

(2) The average (arithmetic mean) of set A is equal to the range of set A.


Hi Bunuel,

Kindly help me to understand this: why can't set A be a one-element set?

Thanks
_________________

Kindly press kudos if you find my post helpful

Kudos [?]: 316 [0], given: 390

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42275

Kudos [?]: 132870 [1], given: 12389

Re: M28-47 [#permalink]

Show Tags

New post 28 Jun 2017, 09:56
1
This post received
KUDOS
Expert's post
duahsolo wrote:
Bunuel wrote:
What is the value of the median of set A?


(1) No number in set A is less than the average (arithmetic mean) of set A.

(2) The average (arithmetic mean) of set A is equal to the range of set A.


Hi Bunuel,

Kindly help me to understand this: why can't set A be a one-element set?

Thanks


The number of x's in the solution can be any. So, we can have one-element set but we'll still get the same answer. One element set for (1)+(2) will be {0}.
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 132870 [1], given: 12389

Intern
Intern
avatar
B
Joined: 24 Jun 2017
Posts: 3

Kudos [?]: 0 [0], given: 6

CAT Tests
Re: M28-47 [#permalink]

Show Tags

New post 31 Oct 2017, 02:00
From Statement 2, cant we have single element set {1} . In this set, Range of single element set is 1 and average is 1. Is this right??? then we dont have solution for this?

Kudos [?]: 0 [0], given: 6

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42275

Kudos [?]: 132870 [0], given: 12389

Re: M28-47 [#permalink]

Show Tags

New post 31 Oct 2017, 02:08
Bhadri1199 wrote:
From Statement 2, cant we have single element set {1} . In this set, Range of single element set is 1 and average is 1. Is this right??? then we dont have solution for this?


(The range) = (Largest element) - (Smallest element).

Now, since a single-element set (Largest element) = (Smallest element), then (The range of a single-element set) = (Largest element) - (Smallest element) = 0.
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 132870 [0], given: 12389

Re: M28-47   [#permalink] 31 Oct 2017, 02:08
Display posts from previous: Sort by

M28-47

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

Moderators: Bunuel, chetan2u



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

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

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®.