Last visit was: 28 Apr 2026, 04:01 It is currently 28 Apr 2026, 04:01
Home
Messages
Tests
Schools
Events
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
Back to Forum
Create Topic
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 28 Apr 2026
Posts: 109,948
Own Kudos:
811,682
 [20]
Given Kudos: 105,927
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,948
Kudos: 811,682
 [20]
In a set of data, the average (arithmetic mean) equals the median. Whi 06 Jun 2017, 11:29
1
Kudos
Add Kudos
19
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

55% (hard)

Question Stats:

54% (01:13) correct 46% (01:11) wrong based on 428 sessions

History

Date
Time
Result
Not Attempted Yet
In a set of data, the average (arithmetic mean) equals the median. Which of the following must be true?

I. The set consists of evenly spaced numbers.
II. The set consists of an odd number of terms.
III. The set has no mode.

A. I only
B. I and II
C. II and III
D. I, II, and III
E. None of the above
ShowHide Answer
Official Answer
E
User avatar
Shruti0805
User avatar
Joined: 24 Dec 2016
Last visit: 02 Sep 2021
Posts: 91
Own Kudos:
49
 [1]
Given Kudos: 145
Location: India
Concentration: Finance, General Management
Schools: Simon '21 (A$) Carlson '21 (A$) McDonough '21 (A)
WE:Information Technology (Computer Software)
Schools: Simon '21 (A$) Carlson '21 (A$) McDonough '21 (A)
Posts: 91
Kudos: 49
 [1]
In a set of data, the average (arithmetic mean) equals the median. Whi 06 Jun 2017, 22:55
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
In a set of data, the average (arithmetic mean) equals the median. Which of the following must be true?

I. The set consists of evenly spaced numbers.
II. The set consists of an odd number of terms.
III. The set has no mode.

A. I only
B. I and II
C. II and III
D. I, II, and III
E. None of the above
Show more

Per question, AM=Median.
Lets take a look at a few sets where the relation is true.

A- {2,4,6,8} -- Here AM= Median and the set is equally spaced
B- {10, 12, 14.5, 16, 20} -- Here also AM=Median= 14.5 but the set isn't equally spaced.
C- {11, 19, 19, 27} -- Here also AM = Median = 19 but the set isnt equally spaced.

Now, lets check the options.
I is incorrect, by sets B and C
II is incorrect by set A and C
III is incorrect by set C.

Answer should be E.
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 27 Apr 2026
Posts: 16,447
Own Kudos:
79,434
 [2]
Given Kudos: 485
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,447
Kudos: 79,434
 [2]
In a set of data, the average (arithmetic mean) equals the median. Whi 07 Jun 2017, 02:52
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
In a set of data, the average (arithmetic mean) equals the median. Which of the following must be true?

I. The set consists of evenly spaced numbers.
II. The set consists of an odd number of terms.
III. The set has no mode.

A. I only
B. I and II
C. II and III
D. I, II, and III
E. None of the above
Show more

We need to find whether the following 'must be true':

I. The set consists of evenly spaced numbers.
Is it necessary? Can we not have a set in which mean = median but the set is not evenly spaced?
Such as 1, 4, 4, 5, 6
Here mean = median = 4, but the set is not evenly spaced.
So this condition is not necessary.

II. The set consists of an odd number of terms.
Is this condition necessary?
3, 4, 4, 5 has an even number of terms but mean = median = 4.
So this condition is also not necessary.

III. The set has no mode.
The example above 3, 4, 4, 5 has a mode but mean = median = 4.
So this condition is also not necessary.

Answer (E)
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 27 Apr 2026
Posts: 16,447
Own Kudos:
79,434
Given Kudos: 485
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,447
Kudos: 79,434
In a set of data, the average (arithmetic mean) equals the median. Whi 10 Jun 2017, 06:43
Kudos
Add Kudos
Bookmarks
Bookmark this Post
VeritasPrepKarishma
Bunuel
In a set of data, the average (arithmetic mean) equals the median. Which of the following must be true?

I. The set consists of evenly spaced numbers.
II. The set consists of an odd number of terms.
III. The set has no mode.

A. I only
B. I and II
C. II and III
D. I, II, and III
E. None of the above

We need to find whether the following 'must be true':

I. The set consists of evenly spaced numbers.
Is it necessary? Can we not have a set in which mean = median but the set is not evenly spaced?
Such as 1, 4, 4, 5, 6
Here mean = median = 4, but the set is not evenly spaced.
So this condition is not necessary.

II. The set consists of an odd number of terms.
Is this condition necessary?
3, 4, 4, 5 has an even number of terms but mean = median = 4.
So this condition is also not necessary.

III. The set has no mode.
The example above 3, 4, 4, 5 has a mode but mean = median = 4.
So this condition is also not necessary.

Answer (E)
Show more

Responding to a pm:

Quote:

Just to confirm, I think logic in this question is inversely true.
Meaning, if a set contains evenly spaced numbers, and have odd number of terms then the mean and median are same. is this always right?
Show more

In an evenly spaced set, mean will be equal to median. It doesn't matter whether the number of elements is even or odd.
1, 3, 5
Mean = median = 3

1, 3, 5, 7
Mean = median = 4
User avatar
JeffTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 04 Mar 2011
Last visit: 05 Jan 2024
Posts: 2,974
Own Kudos:
8,718
Given Kudos: 1,646
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Expert
Expert reply
Posts: 2,974
Kudos: 8,718
In a set of data, the average (arithmetic mean) equals the median. Whi 10 Jun 2017, 07:20
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
In a set of data, the average (arithmetic mean) equals the median. Which of the following must be true?

I. The set consists of evenly spaced numbers.
II. The set consists of an odd number of terms.
III. The set has no mode.

A. I only
B. I and II
C. II and III
D. I, II, and III
E. None of the above
Show more

Let’s analyze each Roman numeral with examples to determine whether it must be true.

I. The set consists of evenly spaced numbers.


This does not have to be true. For example, let’s say the set consists of the following numbers: 1, 2, 4, 6, 7. The mean and median are both 4, but this is not a set of evenly spaced numbers (notice that 2 is one more than 1, but 4 is two more than 2).

II. The set consists of an odd number of terms.

This does not have to be true. For example, let’s say the set consists of the following numbers: 1, 1. The mean and median are both 1, but this set has 2 terms.

III. The set has no mode.

This does not have to be true. For example, let’s say the set consists of the following numbers: 1, 2, 2, 3. The mean and median are both 2, which is also the mode of the set.

Answer: E
User avatar
Adarsh_24
User avatar
Joined: 06 Jan 2024
Last visit: 03 Apr 2025
Posts: 240
Own Kudos:
65
Given Kudos: 2,015
Posts: 240
Kudos: 65
In a set of data, the average (arithmetic mean) equals the median. Whi 18 Oct 2024, 05:56
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Since, mean=median, the frequency distribution graph should be symmetric and we can think of something like 1,1 2,2,3,3 for this particular question.

This could be an easier way to find combinations, may be.
Moderators:
Bunuel
Math Expert
109948 posts
Krunaal
Tuck School Moderator
852 posts