Last visit was: 18 May 2024, 01:51 It is currently 18 May 2024, 01:51
Decision Tracker
My Rewards
Unanswered
Active Topics
New posts
New comers' posts
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

In Set T, the average (arithmetic mean) equals the median. Which of th

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93334
Own Kudos [?]: 624605 [20]
Given Kudos: 81899
Send PM
CAT Tests Forum Quiz Mode
In Set T, the average (arithmetic mean) equals the median. Which of th [#permalink] In Set T, the average (arithmetic mean) equals the median. Which of th   10 Feb 2015, 08:42
2
Kudos
18
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

55% (hard)

Question Stats:

51% (01:19) correct 49% (01:17) wrong based on 350 sessions
Hide Show timer Statistics
In Set T, the average (arithmetic mean) equals the median. Which of the following must be true?

I. Set T consists of evenly spaced numbers.
II. Set T consists of an odd number of terms.
III. Set T has no mode.
IV. None of the above.

A. I only
B. I and II
C. II and III
D. I, II, and III
E. IV only

Kudos for a correct solution.
ShowHide Answer
Official Answer
E
Most Helpful Reply
User avatar
gmat6nplus1
Manager
Manager
Joined: 04 Oct 2013
Posts: 141
Own Kudos [?]: 591 [9]
Given Kudos: 29
Concentration: Finance, Leadership
GMAT 1: 590 Q40 V30
GMAT 2: 730 Q49 V40
WE:Project Management (Entertainment and Sports)
Send PM
Re: In Set T, the average (arithmetic mean) equals the median. Which of th [#permalink] In Set T, the average (arithmetic mean) equals the median. Which of th   10 Feb 2015, 09:06
3
Kudos
6
Bookmarks
Bunuel wrote:
In Set T, the average (arithmetic mean) equals the median. Which of the following must be true?

I. Set T consists of evenly spaced numbers.
II. Set T consists of an odd number of terms.
III. Set T has no mode.
IV. None of the above.

A. I only
B. I and II
C. II and III
D. I, II, and III
E. IV only

Kudos for a correct solution.


I. consider T (1, 2, 3) median=mean=2. Consider T (5, 9, 2, 19, 10) median=mean=9
II. Consider T (1, 2, 3) median=mean=2. Consider T (1, 1, 1, 1) median=mean=1
III. Consider T (1, 2, 3) mean=median=2 and there is no mode. Consider T (1, 1, 1) median=mean=1 and mode is 1.

Answer E.
General Discussion
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93334
Own Kudos [?]: 624605 [3]
Given Kudos: 81899
Send PM
CAT Tests Forum Quiz Mode
Re: In Set T, the average (arithmetic mean) equals the median. Which of th [#permalink] In Set T, the average (arithmetic mean) equals the median. Which of th   16 Feb 2015, 05:45
3
Kudos
Expert Reply
Bunuel wrote:
In Set T, the average (arithmetic mean) equals the median. Which of the following must be true?

I. Set T consists of evenly spaced numbers.
II. Set T consists of an odd number of terms.
III. Set T has no mode.
IV. None of the above.

A. I only
B. I and II
C. II and III
D. I, II, and III
E. IV only

Kudos for a correct solution.


VERITAS PREP OFFICIAL SOLUTION

Correct Answer: E

None of the proposed statements must be true; to prove this, you might consider a hypothetical: Set T could be [1,1, 3, 3], in which the average and median are both 2. This set proves I, II, and III wrong. (Note: This set has two modes, 1 and 3)
avatar
Alchemist14
Intern
Intern
Joined: 09 Dec 2014
Posts: 41
Own Kudos [?]: 58 [0]
Given Kudos: 833
GMAT 1: 600 Q42 V32
GMAT 2: 710 Q48 V38
GPA: 3.7
Send PM
Reviews Badge
Re: In Set T, the average (arithmetic mean) equals the median. Which of th [#permalink] In Set T, the average (arithmetic mean) equals the median. Which of th   29 Dec 2015, 19:50
Bunuel wrote:
In Set T, the average (arithmetic mean) equals the median. Which of the following must be true?

I. Set T consists of evenly spaced numbers.
II. Set T consists of an odd number of terms.
III. Set T has no mode.
IV. None of the above.

A. I only
B. I and II
C. II and III
D. I, II, and III
E. IV only

Kudos for a correct solution.


This is a very good 'trap question'.

Consider Set A= { 0,0,0,0 } Mean=Median=Mode=0- Eliminates 1,2 and 3 OR
Consider Set B= {1,2,2,3 } Mean=Median=Mode=2- Eliminates 1,2 and 3

If you think that only in 'consecutive integers' the average is equal to the median you might fall for 'D'.

Ans: E
User avatar
D
stonecold
Alum
Joined: 12 Aug 2015
Posts: 2279
Own Kudos [?]: 3164 [0]
Given Kudos: 893
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Send PM
GMAT ToolKit User
In Set T, the average (arithmetic mean) equals the median. Which of th [#permalink] In Set T, the average (arithmetic mean) equals the median. Which of th   18 Dec 2016, 13:45
This is an Excellent Question.
Here is my take on this one =>


Firstly,
Quote:
For any evenly spaced set => Mean = Median = Average of the first and the last term.

Also =>
Quote:
Sum of deviations around the mean = Zero


Now We are told that a Set T is such that its mean = median
We are asked which of the statements must be true.

Statement 1-->
T is evenly Spaced

Consider two sets => 5,6,7,8,9,10,11
Mean = Median=8
Now Removing 7 and 9 wont affect the mean as 8-7 will be balanced by 8-9 and the sum of deviations around 8 will still be zero.
Hence 5,6,8,10,11 => Mean = 8 and Median = 8
But the above set isn't every spaced.

Hence this statement is not always true.
Statement 2=>

Consider a set => 7,7,7,7
Here => Mean=Median=7
And the number of terms is even.
Hence this statement also isn't always true.

Statement 3-->
Consider a set => 7,7,7,7
Here Mode = 7
Hence Set T will can have a mode=> The statement isn't always true.
Statement 4--> None of the above => TRUE.


Hence E
User avatar
G
ashikaverma13
Manager
Manager
Joined: 19 Aug 2016
Posts: 129
Own Kudos [?]: 296 [0]
Given Kudos: 59
Location: India
Schools: ISB '20 (WD) Schulich Sept 18 Intake (A) Rotman '20 (S)
GMAT 1: 640 Q47 V31
GPA: 3.82
Send PM
Reviews Badge
Re: In Set T, the average (arithmetic mean) equals the median. Which of th [#permalink] In Set T, the average (arithmetic mean) equals the median. Which of th   10 Aug 2017, 02:01
Bunuel wrote:
Bunuel wrote:
In Set T, the average (arithmetic mean) equals the median. Which of the following must be true?

I. Set T consists of evenly spaced numbers.
II. Set T consists of an odd number of terms.
III. Set T has no mode.
IV. None of the above.

A. I only
B. I and II
C. II and III
D. I, II, and III
E. IV only

Kudos for a correct solution.


VERITAS PREP OFFICIAL SOLUTION

Correct Answer: E

None of the proposed statements must be true; to prove this, you might consider a hypothetical: Set T could be [1,1, 3, 3], in which the average and median are both 2. This set proves I, II, and III wrong. (Note: This set has two modes, 1 and 3)


So, in conclusion we can takeway from this question that for an evenly spaced set mean=median does not necessarily mean that the vice versa is true. Just because for a set mean = median does not render the set as an evenly spaced one.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93334
Own Kudos [?]: 624605 [0]
Given Kudos: 81899
Send PM
CAT Tests Forum Quiz Mode
Re: In Set T, the average (arithmetic mean) equals the median. Which of th [#permalink] In Set T, the average (arithmetic mean) equals the median. Which of th   10 Aug 2017, 02:18
Expert Reply
ashikaverma13 wrote:
Bunuel wrote:
Bunuel wrote:
In Set T, the average (arithmetic mean) equals the median. Which of the following must be true?

I. Set T consists of evenly spaced numbers.
II. Set T consists of an odd number of terms.
III. Set T has no mode.
IV. None of the above.

A. I only
B. I and II
C. II and III
D. I, II, and III
E. IV only

Kudos for a correct solution.


VERITAS PREP OFFICIAL SOLUTION

Correct Answer: E

None of the proposed statements must be true; to prove this, you might consider a hypothetical: Set T could be [1,1, 3, 3], in which the average and median are both 2. This set proves I, II, and III wrong. (Note: This set has two modes, 1 and 3)


So, in conclusion we can takeway from this question that for an evenly spaced set mean=median does not necessarily mean that the vice versa is true. Just because for a set mean = median does not render the set as an evenly spaced one.

_______________
Yes, that's true.
User avatar
L
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18873
Own Kudos [?]: 22260 [1]
Given Kudos: 285
Location: United States (CA)
Send PM
Re: In Set T, the average (arithmetic mean) equals the median. Which of th [#permalink] In Set T, the average (arithmetic mean) equals the median. Which of th   15 Aug 2017, 10:56
1
Bookmarks
Expert Reply
Bunuel wrote:
In Set T, the average (arithmetic mean) equals the median. Which of the following must be true?

I. Set T consists of evenly spaced numbers.
II. Set T consists of an odd number of terms.
III. Set T has no mode.
IV. None of the above.

A. I only
B. I and II
C. II and III
D. I, II, and III
E. IV only

Kudos for a correct solution.


Let’s analyze each Roman numeral statement.

I. Set T consists of evenly spaced numbers.

This is not necessarily true. For example, if set T = {1, 2, 4, 4, 9}, we see that average = median, but T is not an evenly spaced set.

II. Set T consists of an odd number of terms.

This is not necessarily true. For example, if set T = {3, 3}, we see that average = median, but T has an even number of terms.

III. Set T has no mode.

This is not necessarily true. For example, if we use the same set T as in Roman numeral I, we see that average = median, but T does have a mode.

Answer: E
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 33057
Own Kudos [?]: 828 [0]
Given Kudos: 0
Send PM
Re: In Set T, the average (arithmetic mean) equals the median. Which of th [#permalink] In Set T, the average (arithmetic mean) equals the median. Which of th   20 Sep 2023, 03:48
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: In Set T, the average (arithmetic mean) equals the median. Which of th [#permalink]
20 Sep 2023, 03:48
Moderators:
Bunuel
Math Expert
93334 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts