Find all School-related info fast with the new School-Specific MBA Forum

It is currently 01 May 2016, 03:00
GMAT Club Tests

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

What is the median of the numbers 4, 5, 6, 7, 9, and x?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Manager
Manager
avatar
Joined: 10 Sep 2012
Posts: 150
Followers: 2

Kudos [?]: 113 [0], given: 17

What is the median of the numbers 4, 5, 6, 7, 9, and x? [#permalink]

Show Tags

New post 01 Nov 2012, 15:43
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

51% (02:12) correct 49% (01:08) wrong based on 136 sessions

HideShow timer Statictics

What is the median of the numbers 4, 5, 6, 7, 9, and x?

(1) x > 7
(2) The mean of the six numbers is equal to their median.

[Reveal] Spoiler:
The solution states that the answer is A but in my opinion the answer is D.

The mean of a sequence is equal to the median of that sequence. Which means that x can only be 8 according to Stat(2)- (in order to make the mean of that set the same as the median). The numbers that the solution cites, to me, seems invalid. For example, the solution states x<5. Let's take 4 then. If x=4, the mean becomes 5.83, but the median is 5.5, which doesn't satisfy Stat(2). Could someone clarify this?

Here is the official solution:
This is a "what is the value of..." DS question. In this type of question, a statement will be sufficient only if it leads to a single value of the variable (or expression) that you're asked about.

Remember:

The median is the middle number in a set of numbers, arranged in ascending or descending order.
To find the median consider the number of elements:
If the number of elements is odd, the median is the middle number.
If the number of elements is even the median is the average of the middle two elements.
Together with x, there are 6 numbers; therefore, the median will be calculated as the average of the two middle numbers. Therefore, the real issue of the question is the values of the two middle numbers.

According to Stat. (2),

The average of 4,5,6,7,9, and x is equal to the median. The median, which is also the average, will vary according to the value of x:

If x<5, the median is equal to the average of the two middle numbers --> 5 and 6 = 5.5. But,

If x>7, the median is equal to the average of the two middle numbers --> 6 and 7 = 6.5. No single value can be determined for the median of the set, so Stat.(2)->IS.
[Reveal] Spoiler: OA

Last edited by Bunuel on 01 Nov 2012, 15:47, edited 1 time in total.
Renamed the topic and edited the question.
Expert Post
2 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 32549
Followers: 5633

Kudos [?]: 68346 [2] , given: 9797

Re: What is the median of the numbers 4, 5, 6, 7, 9, and x? [#permalink]

Show Tags

New post 01 Nov 2012, 16:10
2
This post received
KUDOS
Expert's post
What is the median of the numbers 4, 5, 6, 7, 9, and x?

The median of a set with even number of terms is the average of two middle terms when arranged in ascending/descending order.

(1) x > 7 --> two middle terms are 6 and 7, thus median=(6+7)/2=6.5. Sufficient.

(2) The mean of the six numbers is equal to their median.

If \(x\leq{5}\), then two middle terms are 5 and 6, thus median=(5+6)/2=5.5. In this case mean=(4+5+6+7+9+x)/6=5.5 --> x=2. Possible scenario.
If \(x\geq{7}\), then two middle terms are 6 and 7, thus median=(6+7)/2=6.5. In this case mean=(4+5+6+7+9+x)/6=6.5 --> x=8. Possible scenario.
Not sufficient.

Answer: A.

P.S. For (2): if \(5<x<7\), then two middle terms are x and 6, thus median=(x+6)/2. In this case mean=median=(4+5+6+7+9+x)/6=(x+6)/2 --> x=6.5. Also, possible scenario.
_________________

New to the Math Forum?
Please read this: 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

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 32549
Followers: 5633

Kudos [?]: 68346 [0], given: 9797

Re: What is the median of the numbers 4, 5, 6, 7, 9, and x? [#permalink]

Show Tags

New post 01 Nov 2012, 16:13
Expert's post
anon1 wrote:
What is the median of the numbers 4, 5, 6, 7, 9, and x?

(1) x > 7
(2) The mean of the six numbers is equal to their median.

[Reveal] Spoiler:
The solution states that the answer is A but in my opinion the answer is D.

The mean of a sequence is equal to the median of that sequence. Which means that x can only be 8 according to Stat(2)- (in order to make the mean of that set the same as the median). The numbers that the solution cites, to me, seems invalid. For example, the solution states x<5. Let's take 4 then. If x=4, the mean becomes 5.83, but the median is 5.5, which doesn't satisfy Stat(2). Could someone clarify this?

Here is the official solution:
This is a "what is the value of..." DS question. In this type of question, a statement will be sufficient only if it leads to a single value of the variable (or expression) that you're asked about.

Remember:

The median is the middle number in a set of numbers, arranged in ascending or descending order.
To find the median consider the number of elements:
If the number of elements is odd, the median is the middle number.
If the number of elements is even the median is the average of the middle two elements.
Together with x, there are 6 numbers; therefore, the median will be calculated as the average of the two middle numbers. Therefore, the real issue of the question is the values of the two middle numbers.

According to Stat. (2),

The average of 4,5,6,7,9, and x is equal to the median. The median, which is also the average, will vary according to the value of x:

If x<5, the median is equal to the average of the two middle numbers --> 5 and 6 = 5.5. But,

If x>7, the median is equal to the average of the two middle numbers --> 6 and 7 = 6.5. No single value can be determined for the median of the set, so Stat.(2)->IS.


Similar questions to practice:
if-set-s-consists-of-the-numbers-1-5-2-8-and-n-is-132570.html
what-is-the-value-of-n-in-the-list-above-137225.html
if-the-range-of-the-set-containing-the-numbers-x-y-and-z-127089.html
the-sum-of-the-integers-in-list-s-is-the-same-as-the-sum-of-127755.html
given-the-ascending-set-of-positive-integers-a-b-c-d-e-115675.html

Hope it helps.
_________________

New to the Math Forum?
Please read this: 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: 10 Sep 2012
Posts: 150
Followers: 2

Kudos [?]: 113 [0], given: 17

Re: What is the median of the numbers 4, 5, 6, 7, 9, and x? [#permalink]

Show Tags

New post 01 Nov 2012, 16:33
Intern
Intern
avatar
Joined: 04 Mar 2012
Posts: 6
Followers: 0

Kudos [?]: 0 [0], given: 8

GMAT ToolKit User
Re: What is the median of the numbers 4, 5, 6, 7, 9, and x? [#permalink]

Show Tags

New post 24 Oct 2013, 07:21
Bunuel wrote:
What is the median of the numbers 4, 5, 6, 7, 9, and x?

The median of a set with even number of terms is the average of two middle terms when arranged in ascending/descending order.

(1) x > 7 --> two middle terms are 6 and 7, thus median=(6+7)/2=6.5. Sufficient.

(2) The mean of the six numbers is equal to their median.

If \(x\leq{5}\), then two middle terms are 5 and 6, thus median=(5+6)/2=5.5. In this case mean=(4+5+6+7+9+x)/6=5.5 --> x=2. Possible scenario.
If \(x\geq{7}\), then two middle terms are 6 and 7, thus median=(6+7)/2=6.5. In this case mean=(4+5+6+7+9+x)/6=6.5 --> x=8. Possible scenario.
Not sufficient.

Answer: A.

P.S. For (2): if \(5<x<7\), then two middle terms are x and 6, thus median=(x+6)/2. In this case mean=median=(4+5+6+7+9+x)/6=(x+6)/2 --> x=6.5. Also, possible scenario.




why have you taken mean =median i.e 5.5 and 6.5 .
Mean =Median is only in evenly spaced sets.
Please explain?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 32549
Followers: 5633

Kudos [?]: 68346 [0], given: 9797

Re: What is the median of the numbers 4, 5, 6, 7, 9, and x? [#permalink]

Show Tags

New post 24 Oct 2013, 07:35
Expert's post
kop wrote:
Bunuel wrote:
What is the median of the numbers 4, 5, 6, 7, 9, and x?

The median of a set with even number of terms is the average of two middle terms when arranged in ascending/descending order.

(1) x > 7 --> two middle terms are 6 and 7, thus median=(6+7)/2=6.5. Sufficient.

(2) The mean of the six numbers is equal to their median.

If \(x\leq{5}\), then two middle terms are 5 and 6, thus median=(5+6)/2=5.5. In this case mean=(4+5+6+7+9+x)/6=5.5 --> x=2. Possible scenario.
If \(x\geq{7}\), then two middle terms are 6 and 7, thus median=(6+7)/2=6.5. In this case mean=(4+5+6+7+9+x)/6=6.5 --> x=8. Possible scenario.
Not sufficient.

Answer: A.

P.S. For (2): if \(5<x<7\), then two middle terms are x and 6, thus median=(x+6)/2. In this case mean=median=(4+5+6+7+9+x)/6=(x+6)/2 --> x=6.5. Also, possible scenario.




why have you taken mean =median i.e 5.5 and 6.5 .
Mean =Median is only in evenly spaced sets.
Please explain?


That's not true. Consider: {0, 1, 1, 2} --> mean=1=median.

So, if a set is evenly spaced, then mean=median, but if mean=median, then it's not necessary the set to be evenly spaced.

Does this make sense?
_________________

New to the Math Forum?
Please read this: 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

Intern
Intern
avatar
Joined: 04 Mar 2012
Posts: 6
Followers: 0

Kudos [?]: 0 [0], given: 8

GMAT ToolKit User
Re: What is the median of the numbers 4, 5, 6, 7, 9, and x? [#permalink]

Show Tags

New post 24 Oct 2013, 10:36
Bunuel wrote:
kop wrote:
Bunuel wrote:
What is the median of the numbers 4, 5, 6, 7, 9, and x?

The median of a set with even number of terms is the average of two middle terms when arranged in ascending/descending order.

(1) x > 7 --> two middle terms are 6 and 7, thus median=(6+7)/2=6.5. Sufficient.

(2) The mean of the six numbers is equal to their median.

If \(x\leq{5}\), then two middle terms are 5 and 6, thus median=(5+6)/2=5.5. In this case mean=(4+5+6+7+9+x)/6=5.5 --> x=2. Possible scenario.
If \(x\geq{7}\), then two middle terms are 6 and 7, thus median=(6+7)/2=6.5. In this case mean=(4+5+6+7+9+x)/6=6.5 --> x=8. Possible scenario.
Not sufficient.

Answer: A.

P.S. For (2): if \(5<x<7\), then two middle terms are x and 6, thus median=(x+6)/2. In this case mean=median=(4+5+6+7+9+x)/6=(x+6)/2 --> x=6.5. Also, possible scenario.




why have you taken mean =median i.e 5.5 and 6.5 .
Mean =Median is only in evenly spaced sets.
Please explain?


That's not true. Consider: {0, 1, 1, 2} --> mean=1=median.

So, if a set is evenly spaced, then mean=median, but if mean=median, then it's not necessary the set to be evenly spaced.

Does this make sense?




Thanks Bunnel. I understood it now.
Re: What is the median of the numbers 4, 5, 6, 7, 9, and x?   [#permalink] 24 Oct 2013, 10:36
    Similar topics Author Replies Last post
Similar
Topics:
2 Experts publish their posts in the topic 2, 4, 5, 5, 9, m For the list of numbers above, what is the median? Bunuel 4 10 Jun 2015, 04:09
11 Experts publish their posts in the topic If 2 < x < 4, what is the median of the numbers 0, 5, x, 1, bgribble 11 30 Nov 2013, 11:54
3 Experts publish their posts in the topic Is the range of the integers 4, 7, x, 6, 5, y greater than 9 HBSdetermined 3 01 Sep 2013, 05:25
2 Experts publish their posts in the topic What is the median of a certain set of 7 numbers? zz0vlb 4 28 Apr 2010, 12:42
If a is equal to one of the numbers 5/11, 7/12,9/13 what is vishalranka 3 06 Apr 2010, 01:36
Display posts from previous: Sort by

What is the median of the numbers 4, 5, 6, 7, 9, and x?

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.