GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 23 Jun 2018, 20:40

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

Lists S and T consist of the same number of positive

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

Hide Tags

2 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 12 Mar 2009
Posts: 301
GMAT ToolKit User
Lists S and T consist of the same number of positive [#permalink]

Show Tags

New post Updated on: 12 Jul 2013, 00:58
2
14
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

62% (01:35) correct 38% (01:37) wrong based on 468 sessions

HideShow timer Statistics

Lists S and T consist of the same number of positive integers. Is the median of the integers in S greater than the average (arithmetic mean) of the integers in T?

(1) The integers in S are consecutive even integers, and the integers in T are consecutive odd integers.
(2) The sum of the integers in S is greater than the sum of the integers in T.

Originally posted by vaivish1723 on 17 Jan 2010, 10:45.
Last edited by Bunuel on 12 Jul 2013, 00:58, edited 1 time in total.
Edited the question and added the OA
Expert Post
6 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46297
Re: mean and median [#permalink]

Show Tags

New post 17 Jan 2010, 17:01
6
3
vaivish1723 wrote:
Lists S and T consist of the same number of positive integers. Is the median of the integers in S greater than the average (arithmetic mean) of the integers in T?
(1) The integers in S are consecutive even integers, and the integers in T are consecutive odd integers.
(2) The sum of the integers in S is greater than the sum of the integers in T.

OA is

Pl explain


Q: is \(Median\{S\}>Mean\{T\}\)? Given: {# of terms in S}={# of terms in T}, let's say N.

(1) From this statement we can derive that as set S and set T are evenly spaced their medians equal to their means. So from this statement question becomes is \(Mean\{S\}>Mean\{T\}\)? But this statement is clearly insufficient. As we can have set S{2,4,6} and set T{21,23,25} OR S{20,22,24} and T{1,3,5}.

(2) \(Sum\{S\}>Sum\{T\}\). Also insufficient. As we can have set S{1,1,10} (Median{S}=1) and set T{3,3,3} (Mean{T}=3) OR S{20,20,20} (Median{S}=20) and T{1,1,1} (Mean{T}=1).

(1)+(2) From (1) question became is \(Mean\{S\}>Mean\{T\}\)? --> As there are equal # of term in sets and mean(average)=(Sum of terms)/(# of terms), then we have: is \(\frac{Sum\{S\}}{N}>\frac{Sum\{T\}}{N}\) true? --> Is \(Sum\{S\}>Sum\{T\}\)? This is exactly what is said in statement (2) that \(Sum\{S\}>Sum\{T\}\). Hence 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

Manager
Manager
User avatar
Joined: 22 Jan 2010
Posts: 110
Schools: UCLA, INSEAD
Re: mean and median [#permalink]

Show Tags

New post 24 Jan 2010, 14:24
Good question and good answer.
Intern
Intern
avatar
Joined: 10 Feb 2011
Posts: 49
Re: mean and median [#permalink]

Show Tags

New post 02 Jul 2011, 03:59
I feel there is an ambiguity in the wording of the question itself. The question says that set S and T consist of the same number of positive integers. This statement does not exclude the possibility that Set S and/or T might contain some negative numbers or zero.

Had the question said: " Set S and T consist of only the same number of positive integers then I would have agreed with the solution. What do you guys think? Also, can the original poster mention the source of this question pls?!
Director
Director
User avatar
Joined: 25 Apr 2012
Posts: 702
Location: India
GPA: 3.21
WE: Business Development (Other)
Premium Member Reviews Badge
Re: mean and median [#permalink]

Show Tags

New post 03 Dec 2013, 22:13
Bunuel wrote:
vaivish1723 wrote:
Lists S and T consist of the same number of positive integers. Is the median of the integers in S greater than the average (arithmetic mean) of the integers in T?
(1) The integers in S are consecutive even integers, and the integers in T are consecutive odd integers.
(2) The sum of the integers in S is greater than the sum of the integers in T.

OA is

Pl explain


Q: is \(Median\{S\}>Mean\{T\}\)? Given: {# of terms in S}={# of terms in T}, let's say N.

(1) From this statement we can derive that as set S and set T are evenly spaced their medians equal to their means. So from this statement question becomes is \(Mean\{S\}>Mean\{T\}\)? But this statement is clearly insufficient. As we can have set S{2,4,6} and set T{21,23,25} OR S{20,22,24} and T{1,3,5}.

(2) \(Sum\{S\}>Sum\{T\}\). Also insufficient. As we can have set S{1,1,10} (Median{S}=1) and set T{3,3,3} (Mean{T}=3) OR S{20,20,20} (Median{S}=20) and T{1,1,1} (Mean{T}=1).

(1)+(2) From (1) question became is \(Mean\{S\}>Mean\{T\}\)? --> As there are equal # of term in sets and mean(average)=(Sum of terms)/(# of terms), then we have: is \(\frac{Sum\{S\}}{N}>\frac{Sum\{T\}}{N}\) true? --> Is \(Sum\{S\}>Sum\{T\}\)? This is exactly what is said in statement (2) that \(Sum\{S\}>Sum\{T\}\). Hence sufficient.

Answer: C.





Hi Bunuel,

In the above Question, it says there are same number of positive integers but does not explicitly rule out negative numbers or fractions etc.

After combining 2 statements and taking the case of negative numbers we can have the following as well

Let us say S= -2,0,2,4,6 and 8, Median will be 3
T= -1,1,3,5 and7, Median will be 3

Clearly there can be 2 cases and ans can be E.

I think the question needs to mention that the list contains only positive integers

Please confirm
_________________


“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Intern
Intern
avatar
Joined: 15 Jul 2014
Posts: 10
Re: Lists S and T consist of the same number of positive [#permalink]

Show Tags

New post 04 Dec 2014, 20:07
hey Bunuel.

in your explanation for (1) and (2) combined, you derived a relationship for the Means of the two sets from statement (1). can you please explain how you got that. Statement (1) only tells us that one set has even consecutive integers and one odd. so how do you know that Mean of S > Mean of T?
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46297
Lists S and T consist of the same number of positive [#permalink]

Show Tags

New post 05 Dec 2014, 04:33
kritiu wrote:
hey Bunuel.

in your explanation for (1) and (2) combined, you derived a relationship for the Means of the two sets from statement (1). can you please explain how you got that. Statement (1) only tells us that one set has even consecutive integers and one odd. so how do you know that Mean of S > Mean of T?


From (1) we don't know whether \(Mean\{S\}>Mean\{T\}\).

From (1) the question became "is \(Mean\{S\}>Mean\{T\}\)?"" Meaning that based on the information given in (1), the original question "is \(Median\{S\}>Mean\{T\}\)?" could be rephrased "is \(Mean\{S\}>Mean\{T\}\)?".

Please re-read the solution.

Hope it helps.
_________________

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

Manager
Manager
avatar
Joined: 22 Aug 2014
Posts: 174
Re: Lists S and T consist of the same number of positive [#permalink]

Show Tags

New post 03 Apr 2015, 04:12
Lists S and T consist of the same number of positive integers. Is the median of the integers in S greater than the average (arithmetic mean) of the integers in T?

(1) The integers in S are consecutive even integers, and the integers in T are consecutive odd integers.
(2) The sum of the integers in S is greater than the sum of the integers in T.[/quote]


Hey Bunuel,
PLease explain this.When I take below sets I get answer E.

Set S=(6,8,10)...Median=8
Set T=(1,3,5)...Mean=4.5
Median of S>mean of t


If Set s=(2,4,6)...Median=4
Set T=(1,3,5)...Mean=4.5

Here,Median of S IS NOT GREATER THAN mean of T
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46297
Lists S and T consist of the same number of positive [#permalink]

Show Tags

New post 03 Apr 2015, 04:40
ssriva2 wrote:
Lists S and T consist of the same number of positive integers. Is the median of the integers in S greater than the average (arithmetic mean) of the integers in T?

(1) The integers in S are consecutive even integers, and the integers in T are consecutive odd integers.
(2) The sum of the integers in S is greater than the sum of the integers in T.

Hey Bunuel,
PLease explain this.When I take below sets I get answer E.

Set S=(6,8,10)...Median=8
Set T=(1,3,5)...Mean=4.5
Median of S>mean of t


If Set s=(2,4,6)...Median=4
Set T=(1,3,5)...Mean=4.5

Here,Median of S IS NOT GREATER THAN mean of T


The median/mean of {1, 3, 5} is 3, not 4.5.
_________________

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

Manager
Manager
avatar
Joined: 22 Aug 2014
Posts: 174
Re: Lists S and T consist of the same number of positive [#permalink]

Show Tags

New post 03 Apr 2015, 05:05
Oh mean is 3,that was indeed a silly question!
Director
Director
User avatar
S
Affiliations: CrackVerbal
Joined: 03 Oct 2013
Posts: 518
Location: India
GMAT 1: 780 Q51 V46
Re: Lists S and T consist of the same number of positive [#permalink]

Show Tags

New post 03 Apr 2015, 23:37
Hi All,
Given: List S and T have same no. of elements.
Median of S > average of T?
Statement 1 is insufficient:
Whenever it is consecutive median is always equal to mean.
Let S =2 ,4 ,6 median is 4.
Let T = 1,3,5 median(mean) is 3.
Answer to the question is YES.
Let S =2 ,4 ,6 median is 4.
Let T = 3,5,7 median(mean) is 5.
Answer to the question is NO.
So not sufficient.
Statement 2 is insufficient:
Sum of the integers in S is greater than T(here the list not necessarily be consecutive).
Let S =1 ,2 ,3 median is 2.
Let T = 0,1,2 median(mean) is 1.
Answer to the question is YES.
Let S =1 ,5 ,20 median is 5.
Let T = 5,6,7 median(mean) is 6.
Answer to the question is NO.
So not sufficient.
Together it is sufficient.
Since the S and T are consecutive even and odd and Sum of S is greater than T.
Then median of S is always greater than mean(median) of T .
So answer is together sufficient .
_________________

Register for CrackVerbal MBA Achiever's Summit here -
http://crackverbal.com/mba-summit-2018

Enroll for our GMAT Trial Course here -
http://gmatonline.crackverbal.com/

For more info on GMAT and MBA, follow us on @AskCrackVerbal

Current Student
avatar
B
Joined: 22 Sep 2016
Posts: 198
Location: India
GMAT 1: 710 Q50 V35
GPA: 4
Lists S and T consist of the same number of positive [#permalink]

Show Tags

New post Updated on: 06 Aug 2017, 06:33
Bunuel wrote:
vaivish1723 wrote:
Lists S and T consist of the same number of positive integers. Is the median of the integers in S greater than the average (arithmetic mean) of the integers in T?
(1) The integers in S are consecutive even integers, and the integers in T are consecutive odd integers.
(2) The sum of the integers in S is greater than the sum of the integers in T.

OA is

Pl explain


Q: is \(Median\{S\}>Mean\{T\}\)? Given: {# of terms in S}={# of terms in T}, let's say N.

(1) From this statement we can derive that as set S and set T are evenly spaced their medians equal to their means. So from this statement question becomes is \(Mean\{S\}>Mean\{T\}\)? But this statement is clearly insufficient. As we can have set S{2,4,6} and set T{21,23,25} OR S{20,22,24} and T{1,3,5}.

(2) \(Sum\{S\}>Sum\{T\}\). Also insufficient. As we can have set S{1,1,10} (Median{S}=1) and set T{3,3,3} (Mean{T}=3) OR S{20,20,20} (Median{S}=20) and T{1,1,1} (Mean{T}=1).

(1)+(2) From (1) question became is \(Mean\{S\}>Mean\{T\}\)? --> As there are equal # of term in sets and mean(average)=(Sum of terms)/(# of terms), then we have: is \(\frac{Sum\{S\}}{N}>\frac{Sum\{T\}}{N}\) true? --> Is \(Sum\{S\}>Sum\{T\}\)? This is exactly what is said in statement (2) that \(Sum\{S\}>Sum\{T\}\). Hence sufficient.

Answer: C.


I'm sorry, but I disagree. The question says that "the lists S and T consist of SAME NUMBER OF POSITIVE INTEGERS".
Now you just know that the number of positive integers are same on both lists. What if there are some negative integers as well? or infact zero?
I didn't interpret the question to say that there are same number of terms.
_________________

Desperately need 'KUDOS' !!


Originally posted by rekhabishop on 04 Aug 2017, 18:32.
Last edited by rekhabishop on 06 Aug 2017, 06:33, edited 1 time in total.
Manager
Manager
User avatar
B
Joined: 12 Sep 2016
Posts: 76
Location: India
GMAT 1: 700 Q50 V34
GPA: 3.15
Reviews Badge
Re: Lists S and T consist of the same number of positive [#permalink]

Show Tags

New post 05 Aug 2017, 12:27
We cannot assume that set A and set B do not contain negative numbers.
Either the question needs to be edited to "same number of integers" or the OA needs to be changed to E.
Expert Post
1 KUDOS received
Manhattan Prep Instructor
User avatar
S
Joined: 04 Dec 2015
Posts: 529
GMAT 1: 790 Q51 V49
GRE 1: 340 Q170 V170
Re: Lists S and T consist of the same number of positive [#permalink]

Show Tags

New post 05 Aug 2017, 14:06
1
darn wrote:
We cannot assume that set A and set B do not contain negative numbers.
Either the question needs to be edited to "same number of integers" or the OA needs to be changed to E.


We actually can assume that! The question itself says "S and T consist of the same number of positive integers." If it said "contain the same number of positive integers", your argument would be correct. But when a GMAT problem tells you that a set 'consists of' something, you know they've told you about everything that's in the set. Since the question uses the word 'consist' and says 'positive integers', you know that both sets consist of only positive integers.
_________________

Image

Chelsey Cooley | Manhattan Prep Instructor | Seattle and Online

My upcoming GMAT trial classes | GMAT blog archive

Re: Lists S and T consist of the same number of positive   [#permalink] 05 Aug 2017, 14:06
Display posts from previous: Sort by

Lists S and T consist of the same number of positive

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


cron

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.