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

It is currently 25 Oct 2014, 04:46

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

The median of the list of positive integers above is 5.5

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
User avatar
Joined: 27 Oct 2011
Posts: 191
Location: United States
Concentration: Finance, Strategy
GMAT 1: Q V
GPA: 3.7
WE: Account Management (Consumer Products)
Followers: 2

Kudos [?]: 45 [0], given: 4

The median of the list of positive integers above is 5.5 [#permalink] New post 25 Mar 2012, 17:46
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

60% (02:07) correct 40% (00:47) wrong based on 163 sessions
8, 5, x, 6

The median of the list of positive integers above is 5.5. Which of the following could be the average (arithmetic mean) of the list?

A. 3
B. 5.5
C. 6.25
D. 7
E. 7.5
[Reveal] Spoiler: OA

_________________

DETERMINED TO BREAK 700!!!

2 KUDOS received
Intern
Intern
avatar
Joined: 22 Jan 2010
Posts: 25
Location: India
Concentration: Finance, Technology
GPA: 3.5
WE: Programming (Telecommunications)
Followers: 0

Kudos [?]: 12 [2] , given: 3

Re: The median of the list of positive integers above is 5.5 [#permalink] New post 27 Mar 2013, 03:26
2
This post received
KUDOS
The median will be the average of the two elements in the middle as the list contains even number of elements.
So,the sum of the two numbers in the middle will be 5.5 * 2 = 11.

With the above data,we can write the list as follows :

x 5 6 8 where 1 < x < 6.
Avg = (x+5+6+8)/4 = (19+x)/4.
So, 5< Avg <6

Hence, B will be the answer.

** Alternatively, we can work out this problem taking options one by one.
_________________

Please press +1 KUDOS if you like my post.

1 KUDOS received
VP
VP
User avatar
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1125
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Followers: 113

Kudos [?]: 1198 [1] , given: 219

GMAT ToolKit User
Re: 8, 5, x, 6 The median of the list of positive integers [#permalink] New post 27 Mar 2013, 02:40
1
This post received
KUDOS
8, 5, x, 6

The median of the list of positive integers above is 5.5. Which of the following could be the average (arithmetic mean) of the list?

If the median is 5.5, then x cannot be >8 ( 5,6,8,9 median 7>5,5). It cannot be > 6 (5,6,7,8 median 6.5>5.5).
So we have found that x<=5

\frac{x+5+6+8}{4}=mean
x=mean*4-19
x is an integer so 4*mean - 19 must be an integer, option (C)6.25 is out.
(D)7 (E)7.5 these options return values of x > 9, so they cannot be right.
Option (A)3 returns a negative integer, but x must be positive.
Option (B)5.5 is correct, and the value of x is 3, which is possible given the initial condition of "The median of the list of positive integers above is 5.5"
_________________

It is beyond a doubt that all our knowledge that begins with experience.

Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]

Senior Manager
Senior Manager
User avatar
Joined: 28 Jun 2009
Posts: 456
Location: United States (MA)
Followers: 15

Kudos [?]: 109 [0], given: 46

Re: Mediating the mean [#permalink] New post 25 Mar 2012, 17:57
Given "The median of the list of positive integers above is 5.5"

So arranging the numbers from lowest to highest, avg of 2 middle terms needs to be 5.5

so the sequence will be x 5 6 8

Lets say x = 4, which gives us mean = sum/4 = 5.5

B is correct
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23411
Followers: 3614

Kudos [?]: 28942 [0], given: 2874

Re: Mediating the mean [#permalink] New post 26 Mar 2012, 00:05
Expert's post
piyatiwari wrote:
Given "The median of the list of positive integers above is 5.5"

So arranging the numbers from lowest to highest, avg of 2 middle terms needs to be 5.5

so the sequence will be x 5 6 8

Lets say x = 4, which gives us mean = sum/4 = 5.5

B is correct


8, 5, x, 6

The median of the list of positive integers above is 5.5. Which of the following could be the average (arithmetic mean) of the list?

A. 3
B. 5.5
C. 6.25
D. 7
E. 7.5

Notice that we are told that x is a positive integer.

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

Since given that the median is 5.5 (the average of 5 and 6) then integer x must be less than or equal to 5, in order 5 and 6 to be two middle numbers. So our list in ascending order is: {x, 5, 6, 8}. Now, since x\leq{5} then the maximum sum of the numbers is 5+5+6+8=24, so the maximum average is 24/4=6 (options C, D, and E are out). 3 can not be the average because in thisc ase the sum of the numbers must be 4*3=12, which is less than the sum of just two numbers 6 and 8 (remember here that since x is a positive integer it can not decrease the sum to 12). So we are left only with option B (for x=3 the average is (3+5+6+8)/4=22/4=5.5).

Answer: B.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Director
Director
avatar
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 549
Location: India
GMAT 1: 640 Q43 V34
GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)
Followers: 2

Kudos [?]: 32 [0], given: 562

Re: The median of the list of positive integers above is 5.5 [#permalink] New post 20 Oct 2012, 19:58
This is amazing soln
I solved by plugging in..

(8+5+x+6)/4 . .
plug nos from options 1 by 1..

when ans 5.5 is plugged in,you get x=3. .
so you have 3,5,6,8 as the order which confirms with the given data :lol:
_________________

hope is a good thing, maybe the best of things. And no good thing ever dies.

Who says you need a 700 ?Check this out : http://gmatclub.com/forum/who-says-you-need-a-149706.html#p1201595

My GMAT Journey : end-of-my-gmat-journey-149328.html#p1197992

Senior Manager
Senior Manager
User avatar
Status: struggling with GMAT
Joined: 06 Dec 2012
Posts: 307
Location: Bangladesh
Concentration: Accounting
GMAT Date: 04-06-2013
GPA: 3.65
Followers: 8

Kudos [?]: 117 [0], given: 46

8, 5, x, 6 The median of the list of positive integers [#permalink] New post 27 Mar 2013, 02:23
8, 5, x, 6

The median of the list of positive integers above is 5.5. Which of the following could be the average (arithmetic mean) of the list?
(A)3
(B)5.5
(C)6.25
(D)7
(E)7.5
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23411
Followers: 3614

Kudos [?]: 28942 [0], given: 2874

Re: 8, 5, x, 6 The median of the list of positive integers [#permalink] New post 27 Mar 2013, 03:19
Expert's post
mun23 wrote:
8, 5, x, 6

The median of the list of positive integers above is 5.5. Which of the following could be the average (arithmetic mean) of the list?
(A)3
(B)5.5
(C)6.25
(D)7
(E)7.5


Merging similar topics.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
User avatar
Joined: 24 Nov 2012
Posts: 165
Concentration: Sustainability, Entrepreneurship
GMAT 1: 770 Q50 V44
WE: Business Development (Internet and New Media)
Followers: 19

Kudos [?]: 98 [0], given: 73

Re: 8, 5, x, 6 The median of the list of positive integers [#permalink] New post 03 Aug 2013, 04:43
Zarrolou wrote:
n - 19 must be an integer, option (C)6.25 is out.


The reason c is out is because if the average was 6.25, x = 6 and the media would become 6

(6.25 x 4) = 25

x = 25 - 19
_________________

You've been walking the ocean's edge, holding up your robes to keep them dry. You must dive naked under, and deeper under, a thousand times deeper! - Rumi

http://www.manhattangmat.com/blog/index ... nprep-com/ - This is worth its weight in gold

Economist GMAT Test - 730, Q50, V41 Aug 9th, 2013
Manhattan GMAT Test - 670, Q45, V36 Aug 11th, 2013
Manhattan GMAT Test - 680, Q47, V36 Aug 17th, 2013
GmatPrep CAT 1 - 770, Q50, V44 Aug 24th, 2013
Manhattan GMAT Test - 690, Q45, V39 Aug 30th, 2013
Manhattan GMAT Test - 710, Q48, V39 Sep 13th, 2013
GmatPrep CAT 2 - 740, Q49, V41 Oct 6th, 2013

GMAT - 770, Q50, V44, Oct 7th, 2013
My Debrief - from-the-ashes-thou-shall-rise-770-q-50-v-44-awa-5-ir-162299.html#p1284542

Re: 8, 5, x, 6 The median of the list of positive integers   [#permalink] 03 Aug 2013, 04:43
    Similar topics Author Replies Last post
Similar
Topics:
8 Experts publish their posts in the topic In list L above, there are 3 positive integers, where each MOKSH 6 17 Dec 2012, 15:41
Experts publish their posts in the topic If the median of the numbers in list I above is equal to the Walkabout 3 13 Dec 2012, 09:03
11 Experts publish their posts in the topic In list L above, there are 3 positive integers, where each o bschool83 5 19 Jul 2011, 14:45
1 Experts publish their posts in the topic List S and List T each contain 5 positive integers, and for alimad 6 30 Aug 2006, 12:05
1 Experts publish their posts in the topic The median value of a set of 9 positive integers is 6. If anirban16 19 24 Feb 2005, 17:27
Display posts from previous: Sort by

The median of the list of positive integers above is 5.5

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| 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®.