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

 It is currently 22 May 2015, 01:13

### 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

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

Author Message
TAGS:
Math Expert
Joined: 02 Sep 2009
Posts: 27457
Followers: 4303

Kudos [?]: 42074 [0], given: 5945

Re: Largest possible range in Set R [#permalink]  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: {$$a_1$$, $$a_1$$, $$55$$, $$55$$, $$3a_1+20$$} --> $$a_1+a_1+55+55+3a_1+20=275$$ --> $$a_1=29$$ --> $$Range=2a_1+20=78$$

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: 331
Followers: 0

Kudos [?]: 21 [0], given: 23

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

Go to page   Previous    1   2   [ 22 posts ]

Similar topics Replies Last post
Similar
Topics:
24 A set of numbers contains 7 integers and has an average 21 15 May 2012, 00:36
2 R is a set containing 8 different numbers. S is a set 4 25 Feb 2012, 04:06
23 The Range of Set A is R. A number having equal value to R 15 30 May 2011, 20:04
5 The range of set A is R. A number having a value equal to R 9 23 Aug 2010, 06:55
The range of a set A is R. A number having a value equal to 10 19 Oct 2005, 20:51
Display posts from previous: Sort by