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

 It is currently 04 May 2016, 07:47

### 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:

### Hide Tags

Manager
Joined: 25 Jul 2010
Posts: 141
Followers: 1

Kudos [?]: 274 [6] , given: 29

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

### Show Tags

02 Oct 2010, 12:23
6
KUDOS
25
This post was
BOOKMARKED
00:00

Difficulty:

85% (hard)

Question Stats:

55% (03:25) correct 45% (02:33) wrong based on 449 sessions

### HideShow timer Statictics

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?

A. 78
B. 77 1/5
C. 66 1/7
D. 55 1/7
E. 52
[Reveal] Spoiler: OA

Last edited by Bunuel on 10 Jun 2012, 01:25, edited 1 time in total.
Edited the question and added the OA
Math Expert
Joined: 02 Sep 2009
Posts: 32613
Followers: 5651

Kudos [?]: 68603 [16] , given: 9815

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

### Show Tags

02 Oct 2010, 12:42
16
KUDOS
Expert's post
9
This post was
BOOKMARKED
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: {$$a_1$$, $$a_1$$, $$55$$, $$55$$, $$3a_1+20$$} --> $$a_1+a_1+55+55+3a_1+20=275$$ --> $$a_1=29$$ --> $$Range=2a_1+20=78$$

_________________
Director
Status: Matriculating
Affiliations: Chicago Booth Class of 2015
Joined: 03 Feb 2011
Posts: 920
Followers: 13

Kudos [?]: 289 [4] , given: 123

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

### Show Tags

07 Mar 2011, 21:06
4
KUDOS
1
This post was
BOOKMARKED
Backsolving : Range = 2a + 20 where a = first number.

Hence the answer is even and highest options. It should be A.
Manager
Joined: 01 Oct 2010
Posts: 71
Followers: 4

Kudos [?]: 92 [2] , given: 19

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

### Show Tags

03 Oct 2010, 13:21
2
KUDOS
I took the set to be m, m, 55, 55, 3m+20. (second value has to be minimum possible - m, and fourth value has to be minimum possible - 55).

now average is 55 so 55 = (6m + 130)/5 which gives m = 29, and 3m+20=107

so range is largest - smallest = 107-29 = 78
_________________
SVP
Joined: 16 Nov 2010
Posts: 1673
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 34

Kudos [?]: 434 [2] , given: 36

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

### Show Tags

07 Mar 2011, 20:20
2
KUDOS
Let smallest # = x, Largest = 3x + 20

So range = 2x + 20

x, x, 55, 55, 3x+20, For Max range lowest should be as low as possible and highest should be as high as possible

also, the 2nd value has to be minimized, so it is x, the fourth value also ahs to be kept at minimum, so it is 55

3x + 20 + 110 + 2x = 275

=> 5x = 275 - 130 = 145 => x = 29 , so range = 29*2 + 20 = 78

_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

Senior Manager
Joined: 06 Aug 2011
Posts: 405
Followers: 2

Kudos [?]: 151 [1] , given: 82

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

### Show Tags

02 Nov 2012, 06:13
1
KUDOS
Thanks alot Bunuel..now i got that ..

i think in REAL GMAT these type of question cum frequenlty..!!.
_________________

Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !

Current Student
Joined: 27 Jun 2012
Posts: 418
Concentration: Strategy, Finance
Followers: 68

Kudos [?]: 625 [1] , given: 183

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

### Show Tags

24 Jan 2013, 13:29
1
KUDOS
Sachin9 wrote:
Hi ,

Here's how I did..

smallest no: s
largest no: 3s+20

since mean = median,

thought that numbers are in AP.

so average= (last no+first no)/2

therefore 55=(s+3s+20)/2
=> s=22.5

now l=20+3s
=> l=87.25

range =l-s=65..
Please let me know where I am going wrong.

Sachin, you assumed that the numbers are in AP, but problem doesn't state that.
This set S = {29, 29, 55, 55, 107} has the maximum range i.e. 78 and mean/median 55.

Note that these numbers are not in AP/sequence. Hence you cannot take average of last & first to find the mean.
_________________

Thanks,
Prashant Ponde

Tough 700+ Level RCs: Passage1 | Passage2 | Passage3 | Passage4 | Passage5 | Passage6 | Passage7
VOTE: vote-best-gmat-practice-tests-excluding-gmatprep-144859.html
PowerScore CR Bible - Official Guide 13 Questions Set Mapped: Click here

Manager
Joined: 03 Aug 2010
Posts: 106
GMAT Date: 08-08-2011
Followers: 1

Kudos [?]: 47 [0], given: 63

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

### Show Tags

08 Mar 2011, 15:51
gmat1220 wrote:
Backsolving : Range = 2a + 20 where a = first number.

Hence the answer is even and highest options. It should be A.

That's an awesome application of number properties to solve this question is seconds.
Kudos
Math Expert
Joined: 02 Sep 2009
Posts: 32613
Followers: 5651

Kudos [?]: 68603 [0], given: 9815

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

### Show Tags

08 Mar 2011, 16:06
Expert's post
Yalephd wrote:
gmat1220 wrote:
Backsolving : Range = 2a + 20 where a = first number.

Hence the answer is even and highest options. It should be A.

That's an awesome application of number properties to solve this question is seconds.
Kudos

That's not correct. Yes, the range equals to 2a+20 but without any further calculation we cannot say whether it must be even, for example if a is not an integer then 2a+20 can be odd or not an integer at all. Also the answer is not necessarily the highest option, it just happened to be so in this particular case.
_________________
Manager
Joined: 03 Aug 2010
Posts: 106
GMAT Date: 08-08-2011
Followers: 1

Kudos [?]: 47 [0], given: 63

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

### Show Tags

08 Mar 2011, 16:19
Bunuel wrote:
Yalephd wrote:
gmat1220 wrote:
Backsolving : Range = 2a + 20 where a = first number.

Hence the answer is even and highest options. It should be A.

That's an awesome application of number properties to solve this question is seconds.
Kudos

That's not correct. Yes, the range equals to 2a+20 but without any further calculation we can not say whether it must be even, for example if a is not an integer then 2a+20 can be odd or not an integer at all. Also the answer is not necessarily the highest option, it just happened to be so in this particular case.

Thanks. Assuming that A is an integer is where I erred.
Director
Status: Matriculating
Affiliations: Chicago Booth Class of 2015
Joined: 03 Feb 2011
Posts: 920
Followers: 13

Kudos [?]: 289 [0], given: 123

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

### Show Tags

08 Mar 2011, 17:54
I was back solving - to confirm the answer.

x^2 = 4
Implies x is not necessarily 2. It can be -2
VP
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1353
Followers: 16

Kudos [?]: 201 [0], given: 10

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

### Show Tags

01 May 2011, 23:15
max range will be when 55*3 = 165 will give 110 as range.But the value isn't present.
Hence go for two small numbers , 55*2 and largest number combination.
thus 2x+110 + 3x+20 = 275
will give, x= 29 and 3x+20 = 97.
Range = 78.
_________________

Visit -- http://www.sustainable-sphere.com/
Promote Green Business,Sustainable Living and Green Earth !!

VP
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1353
Followers: 16

Kudos [?]: 201 [0], given: 10

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

### Show Tags

01 May 2011, 23:16
max range will be when 55*3 = 165 will give 110 as range.But the value isn't present.
Hence go for two small numbers , 55*2 and largest number combination.
thus 2x+110 + 3x+20 = 275
will give, x= 29 and 3x+20 = 97.
Range = 78.
_________________

Visit -- http://www.sustainable-sphere.com/
Promote Green Business,Sustainable Living and Green Earth !!

Manager
Joined: 25 May 2011
Posts: 157
Followers: 2

Kudos [?]: 53 [0], given: 71

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

### Show Tags

18 Nov 2011, 04:18
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: {$$a_1$$, $$a_1$$, $$55$$, $$55$$, $$3a_1+20$$} --> $$a_1+a_1+55+55+3a_1+20=275$$ --> $$a_1=29$$ --> $$Range=2a_1+20=78$$

my approach was like yours, but it took me 6 min!!!
Senior Manager
Joined: 06 Aug 2011
Posts: 405
Followers: 2

Kudos [?]: 151 [0], given: 82

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

### Show Tags

01 Nov 2012, 08:01
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: {$$a_1$$, $$a_1$$, $$55$$, $$55$$, $$3a_1+20$$} --> $$a_1+a_1+55+55+3a_1+20=275$$ --> $$a_1=29$$ --> $$Range=2a_1+20=78$$

Bunuel sir..

few questions that cums in my mnd like ..y did bunuel take A1 is equal to A2..and y didnt he take a2=55 instead of A4=55?

i got lots of questions like this and i cant give ans correctly..

_________________

Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !

Math Expert
Joined: 02 Sep 2009
Posts: 32613
Followers: 5651

Kudos [?]: 68603 [0], given: 9815

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

### Show Tags

02 Nov 2012, 05:17
Expert's post
2
This post was
BOOKMARKED
sanjoo 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: {$$a_1$$, $$a_1$$, $$55$$, $$55$$, $$3a_1+20$$} --> $$a_1+a_1+55+55+3a_1+20=275$$ --> $$a_1=29$$ --> $$Range=2a_1+20=78$$

Bunuel sir..

few questions that cums in my mnd like ..y did bunuel take A1 is equal to A2..and y didnt he take a2=55 instead of A4=55?

i got lots of questions like this and i cant give ans correctly..

After some steps we have that our set in ascending order is {$$a_1$$, $$a_2$$, $$55$$, $$a_4$$, $$3a_1+20$$} and $$Range=2a_1+20$$.

We need to maximize $$Range=2a_1+20$$, thus we need to maximize $$a_1$$ and to maximize $$a_1$$ we should minimize all other terms so $$a_2$$ and $$a_4$$ (remember the sum of the terms is fixed, so we cannot just make $$a_1$$ as large as we want).

Now, since the set is in ascending order min possible value of $$a_2$$ is $$a_1$$ (it cannot be less than the first term) and min possible value of $$a_4$$ is $$median=a_3=55$$ (it cannot be less than the third term).

Similar questions to practice:
if-the-average-of-5-positive-integers-is-40-and-the-127038.html
the-average-arithmetic-mean-of-the-5-positive-integers-k-107059.html
a-certain-city-with-population-of-132-000-is-to-be-divided-76217.html
five-peices-of-wood-have-an-average-length-of-124-inches-and-123513.html
three-boxes-of-supplies-have-an-average-arithmetic-mean-105819.html
a-set-of-25-different-integers-has-a-median-of-50-and-a-129345.html
three-people-each-took-5-tests-if-the-ranges-of-their-score-127935.html
each-senior-in-a-college-course-wrote-a-thesis-the-lengths-126964.html
in-a-certain-set-of-five-numbers-the-median-is-128514.html
shaggy-has-to-learn-the-same-71-hiragana-characters-and-126948.html

Other min/max questions:
PS: search.php?search_id=tag&tag_id=63
DS: search.php?search_id=tag&tag_id=42

Hope it helps.
_________________
Director
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 547
Location: India
GMAT 1: 640 Q43 V34
GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)
Followers: 3

Kudos [?]: 49 [0], given: 562

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

### Show Tags

24 Jan 2013, 03:38
Hi ,

Here's how I did..

smallest no: s
largest no: 3s+20

since mean = median,

thought that numbers are in AP.

so average= (last no+first no)/2

therefore 55=(s+3s+20)/2
=> s=22.5

now l=20+3s
=> l=87.25

range =l-s=65..
Please let me know where I am going wrong.
_________________

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

Director
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 547
Location: India
GMAT 1: 640 Q43 V34
GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)
Followers: 3

Kudos [?]: 49 [0], given: 562

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

### Show Tags

24 Jan 2013, 17:22
PraPon wrote:
Sachin9 wrote:
Hi ,

Here's how I did..

smallest no: s
largest no: 3s+20

since mean = median,

thought that numbers are in AP.

so average= (last no+first no)/2

therefore 55=(s+3s+20)/2
=> s=22.5

now l=20+3s
=> l=87.25

range =l-s=65..
Please let me know where I am going wrong.

Sachin, you assumed that the numbers are in AP, but problem doesn't state that.
This set S = {29, 29, 55, 55, 107} has the maximum range i.e. 78 and mean/median 55.

Note that these numbers are not in AP/sequence. Hence you cannot take average of last & first to find the mean.

Thanks mate..
I thought that the numbers would be in AP since their median and mean were same.

I now understand that if the nos are in AP , then their median and mean will be same but the vice versa is not necessarily true.
_________________

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

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 9278
Followers: 455

Kudos [?]: 115 [0], given: 0

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

### Show Tags

07 Feb 2014, 15:01
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.
_________________
Senior Manager
Joined: 15 Aug 2013
Posts: 328
Followers: 0

Kudos [?]: 37 [0], given: 23

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

### Show Tags

26 May 2014, 13:17
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?
Re: Largest possible range in Set R   [#permalink] 26 May 2014, 13:17

Go to page    1   2    Next  [ 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
10 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