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

It is currently 16 Sep 2014, 09:32

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: 29641
Followers: 3488

Kudos [?]: 26210 [0], given: 2706

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: 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

Senior Manager
Senior Manager
avatar
Joined: 15 Aug 2013
Posts: 280
Followers: 0

Kudos [?]: 11 [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.
Re: Largest possible range in Set R   [#permalink] 27 May 2014, 15:24
    Similar topics Author Replies Last post
Similar
Topics:
18 Experts publish their posts in the topic A set of numbers contains 7 integers and has an average Joy111 19 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
15 Experts publish their posts in the topic The Range of Set A is R. A number having equal value to R akhileshgupta05 13 30 May 2011, 20:04
4 Experts publish their posts in the topic The range of set A is R. A number having a value equal to R nusmavrik 9 23 Aug 2010, 06:55
The range of a set A is R. A number having a value equal to vikramm 10 19 Oct 2005, 20:51
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  

Go to page   Previous    1   2   [ 22 posts ] 



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®.