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

It is currently 30 Jul 2015, 22:03
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

Set R contains five numbers that have an average value of 55

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 28780
Followers: 4592

Kudos [?]: 47359 [0], given: 7121

Re: Largest possible range in Set R [#permalink] New post 27 May 2014, 00:16
Expert's post
russ9 wrote:
Bunuel wrote:
Orange08 wrote:
Set R contains five numbers that have an average value of 55. If the median of the set is equal to the mean, and the largest number in the set is equal to 20 more than three times the smallest number, what is the largest possible range for the numbers in the set?


78
77 1/5
66 1/7
55 1/7
52


{\(a_1\), \(a_2\), \(a_3\), \(a_4\), \(a_5\)}
As mean of 5 numbers is 55 then the sum of these numbers is \(5*55=275\);
The median of the set is equal to the mean --> \(mean=median=a_3=55\);
The largest number in the set is equal to 20 more than three times the smallest number --> \(a_5=3a_1+20\).

So our set is {\(a_1\), \(a_2\), \(55\), \(a_4\), \(3a_1+20\)} and \(a_1+a_2+55+a_4+3a_1+20=275\).

The range of a set is the difference between the largest and smallest elements of a set.

\(Range=a_5-a_1=3a_1+20-a_1=2a_1+20\) --> so to maximize the range we should maximize the value of \(a_1\) and to maximize \(a_1\) we should minimize all other terms so \(a_2\) and \(a_4\).

Min possible value of \(a_2\) is \(a_1\) and min possible value of \(a_4\) is \(median=a_3=55\) --> set becomes: {\(a_1\), \(a_1\), \(55\), \(55\), \(3a_1+20\)} --> \(a_1+a_1+55+55+3a_1+20=275\) --> \(a_1=29\) --> \(Range=2a_1+20=78\)

Answer: A.


Hi Bunuel,

Since the statement says that the median = mean, aren't we supposed to assume that it's an evenly spaced set? If so, wouldn't a2 and a4 be different from a1 and a3?


For evenly spaced set mean = median, but the reverse is not necessarily true. Consider {1, 1, 2, 2, 4} --> mean = median = 2, but the set is not evenly spaced.
_________________

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

PLEASE READ AND FOLLOW: 12 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 ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. 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?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Senior Manager
Senior Manager
avatar
Joined: 15 Aug 2013
Posts: 331
Followers: 0

Kudos [?]: 25 [0], given: 23

Re: Largest possible range in Set R [#permalink] New post 27 May 2014, 15:24
Bunuel wrote:
russ9 wrote:

Hi Bunuel,

Since the statement says that the median = mean, aren't we supposed to assume that it's an evenly spaced set? If so, wouldn't a2 and a4 be different from a1 and a3?


For evenly spaced set mean = median, but the reverse is not necessarily true. Consider {1, 1, 2, 2, 4} --> mean = median = 2, but the set is not evenly spaced.


thanks for clarifying.
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 5692
Followers: 322

Kudos [?]: 62 [0], given: 0

Premium Member
Re: Set R contains five numbers that have an average value of 55 [#permalink] New post 28 May 2015, 07:24
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 Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: Set R contains five numbers that have an average value of 55   [#permalink] 28 May 2015, 07:24

Go to page   Previous    1   2   [ 23 posts ] 

    Similar topics Author Replies Last post
Similar
Topics:
4 The average of a set of five distinct integers is 300. WoundedTiger 2 09 Aug 2014, 02:43
27 Experts publish their posts in the topic A set of numbers contains 7 integers and has an average Joy111 22 15 May 2012, 00:36
2 Experts publish their posts in the topic R is a set containing 8 different numbers. S is a set enigma123 4 25 Feb 2012, 04:06
Set A contains all the even numbers..... pzazz12 2 08 Oct 2010, 04:39
4 Experts publish their posts in the topic S is a set containing 9 different numbers. T is a set contai vksunder 4 12 Aug 2008, 10:07
Display posts from previous: Sort by

Set R contains five numbers that have an average value of 55

  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®.