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

 It is currently 26 May 2016, 11:46

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

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

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 33023
Followers: 5758

Kudos [?]: 70567 [0], given: 9849

Re: Largest possible range in Set R [#permalink]

### Show Tags

27 May 2014, 01:16
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.
_________________
Senior Manager
Joined: 15 Aug 2013
Posts: 328
Followers: 0

Kudos [?]: 38 [0], given: 23

Re: Largest possible range in Set R [#permalink]

### Show Tags

27 May 2014, 16:24
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
Joined: 09 Sep 2013
Posts: 9638
Followers: 465

Kudos [?]: 120 [0], given: 0

Re: Set R contains five numbers that have an average value of 55 [#permalink]

### Show Tags

28 May 2015, 08:24
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.
_________________
Re: Set R contains five numbers that have an average value of 55   [#permalink] 28 May 2015, 08:24

Go to page   Previous    1   2   [ 23 posts ]

Similar topics Replies Last post
Similar
Topics:
Set S contains exactly 10 numbers and has an average (arithmetic mean) 2 29 Mar 2016, 03:24
8 List R contains five numbers that have an average value of 55. If the 3 03 Jan 2016, 06:38
11 The average of a set of five distinct integers is 300. 8 09 Aug 2014, 03:43
36 A set of numbers contains 7 integers and has an average 25 15 May 2012, 01:36
2 R is a set containing 8 different numbers. S is a set 4 25 Feb 2012, 05:06
Display posts from previous: Sort by

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

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

 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®.