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

 It is currently 14 Oct 2019, 01:44 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

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.  In a set of data, the average (arithmetic mean) equals the median. Whi

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

Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 58312
In a set of data, the average (arithmetic mean) equals the median. Whi  [#permalink]

Show Tags 00:00

Difficulty:   55% (hard)

Question Stats: 48% (01:04) correct 52% (01:01) wrong based on 120 sessions

HideShow timer Statistics

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

_________________
Manager  S
Joined: 24 Dec 2016
Posts: 95
Location: India
Concentration: Finance, General Management
WE: Information Technology (Computer Software)
In a set of data, the average (arithmetic mean) equals the median. Whi  [#permalink]

Show Tags

Bunuel wrote:
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

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.
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9697
Location: Pune, India
Re: In a set of data, the average (arithmetic mean) equals the median. Whi  [#permalink]

Show Tags

1
Bunuel wrote:
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.

_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9697
Location: Pune, India
Re: In a set of data, the average (arithmetic mean) equals the median. Whi  [#permalink]

Show Tags

VeritasPrepKarishma wrote:
Bunuel wrote:
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.

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?

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
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Target Test Prep Representative G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2817
Re: In a set of data, the average (arithmetic mean) equals the median. Whi  [#permalink]

Show Tags

Bunuel wrote:
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

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.

_________________

Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Non-Human User Joined: 09 Sep 2013
Posts: 13083
Re: In a set of data, the average (arithmetic mean) equals the median. Whi  [#permalink]

Show Tags

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.
_________________ Re: In a set of data, the average (arithmetic mean) equals the median. Whi   [#permalink] 30 Sep 2018, 06:35
Display posts from previous: Sort by

In a set of data, the average (arithmetic mean) equals the median. Whi

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

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