|
Author |
Message |
|
TAGS:
|
|
|
Manager
Joined: 25 Jul 2010
Posts: 147
Followers: 1
Kudos [?]:
13
[0], given: 29
|
Set R contains five numbers that have an average value of 55 [#permalink]
 02 Oct 2010, 12:23
Question Stats:
50% (04:05) correct
50% (02:41) wrong based on 78 sessions
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
Last edited by Bunuel on 10 Jun 2012, 01:25, edited 1 time in total.
Edited the question and added the OA
|
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 12099
Followers: 1876
Kudos [?]:
10098
[3] , given: 959
|
Re: Largest possible range in Set R [#permalink]
02 Oct 2010, 12:42
3
This post received
KUDOS
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=78Answer: A.
_________________
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
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. NEW!!! ,11 Mixed Questions NEW!!!, 12 Fresh Meat NEW!!!
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. NEW!!!, 11 New DS set. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
Director
Status: Matriculating
Affiliations: Chicago Booth
Joined: 03 Feb 2011
Posts: 947
Followers: 10
Kudos [?]:
144
[3] , given: 123
|
Re: Largest possible range in Set R [#permalink]
07 Mar 2011, 21:06
3
This post received
KUDOS
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 [?]:
45
[1] , given: 19
|
Re: Largest possible range in Set R [#permalink]
03 Oct 2010, 13:21
1
This post received
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
_________________
Some other posts by me...
My GMAT Journey
Timer Tool for Google spreadsheet
Quant Flash Cards/Pages
700 (Q:49 V:35) - Thanks GMATClub - Test Center experience
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 12099
Followers: 1876
Kudos [?]:
10098
[1] , given: 959
|
Re: Largest possible range in Set R [#permalink]
02 Nov 2012, 05:17
1
This post received
KUDOS
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=78Answer: A. 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.. Thank u in advance bunuel.. 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.htmlthe-average-arithmetic-mean-of-the-5-positive-integers-k-107059.htmla-certain-city-with-population-of-132-000-is-to-be-divided-76217.htmlfive-peices-of-wood-have-an-average-length-of-124-inches-and-123513.htmlthree-boxes-of-supplies-have-an-average-arithmetic-mean-105819.htmla-set-of-25-different-integers-has-a-median-of-50-and-a-129345.htmlthree-people-each-took-5-tests-if-the-ranges-of-their-score-127935.htmleach-senior-in-a-college-course-wrote-a-thesis-the-lengths-126964.htmlin-a-certain-set-of-five-numbers-the-median-is-128514.htmlshaggy-has-to-learn-the-same-71-hiragana-characters-and-126948.htmlOther min/max questions:PS: search.php?search_id=tag&tag_id=63DS: search.php?search_id=tag&tag_id=42Hope it helps.
_________________
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
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. NEW!!! ,11 Mixed Questions NEW!!!, 12 Fresh Meat NEW!!!
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. NEW!!!, 11 New DS set. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
Senior Manager
Joined: 27 Jun 2012
Posts: 413
Followers: 25
Kudos [?]:
200
[1] , given: 174
|
Re: Set R contains five numbers that have an average value of 55 [#permalink]
24 Jan 2013, 13:29
1
This post received
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,
PraPon
VOTE: vote-best-gmat-practice-tests-excluding-gmatprep-144859.html
Tough RCs: Passage1 | Passage2 | Passage3 | Passage4 | Passage5 | Passage6 | Passage7
|
|
|
|
|
|
Manager
Joined: 26 Mar 2007
Posts: 89
Concentration: General Management, Leadership
Followers: 1
Kudos [?]:
11
[0], given: 8
|
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 How to solve it in 2 mins? 
Last edited by kannn on 07 Mar 2011, 08:48, edited 1 time in total.
|
|
|
|
|
|
SVP
Joined: 16 Nov 2010
Posts: 1719
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 26
Kudos [?]:
229
[0], given: 35
|
Re: Largest possible range in Set R [#permalink]
07 Mar 2011, 20:20
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 So answer is A.
_________________
Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
Manager
Joined: 03 Aug 2010
Posts: 111
GMAT Date: 08-08-2011
Followers: 1
Kudos [?]:
12
[0], given: 63
|
Re: Largest possible range in Set R [#permalink]
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
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 12099
Followers: 1876
Kudos [?]:
10098
[0], given: 959
|
Re: Largest possible range in Set R [#permalink]
08 Mar 2011, 16:06
|
|
|
|
|
|
Manager
Joined: 03 Aug 2010
Posts: 111
GMAT Date: 08-08-2011
Followers: 1
Kudos [?]:
12
[0], given: 63
|
Re: Largest possible range in Set R [#permalink]
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
Joined: 03 Feb 2011
Posts: 947
Followers: 10
Kudos [?]:
144
[0], given: 123
|
Re: Largest possible range in Set R [#permalink]
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: 1395
Followers: 8
Kudos [?]:
86
[0], given: 10
|
Re: Largest possible range in Set R [#permalink]
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: 1395
Followers: 8
Kudos [?]:
86
[0], given: 10
|
Re: Largest possible range in Set R [#permalink]
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: 170
Followers: 1
Kudos [?]:
17
[0], given: 71
|
Re: Largest possible range in Set R [#permalink]
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=78Answer: A. my approach was like yours, but it took me 6 min!!!  
|
|
|
|
|
|
Senior Manager
Joined: 12 Oct 2011
Posts: 283
Followers: 0
Kudos [?]:
13
[0], given: 110
|
Re: Largest possible range in Set R [#permalink]
05 Jan 2012, 02:30
Yup. Same approach. But it took me 5.5 minutes. A is the answer.
_________________
Consider KUDOS if you feel the effort's worth it
|
|
|
|
|
|
Manager
Joined: 22 Apr 2011
Posts: 224
Schools: Mccombs business school, Mays business school, Rotman Business School,
Followers: 0
Kudos [?]:
10
[0], given: 18
|
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 any shortcut method
_________________
some people are successful, because they have been fortunate enough and some people earn success, because they have been determined.....
please press kudos if you like my post.... i am begging for kudos...lol
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 12099
Followers: 1876
Kudos [?]:
10098
[0], given: 959
|
|
|
|
|
|
|
Senior Manager
Joined: 06 Aug 2011
Posts: 261
Followers: 2
Kudos [?]:
22
[0], given: 42
|
Re: Largest possible range in Set R [#permalink]
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=78Answer: A. 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.. Thank u in advance bunuel..
|
|
|
|
|
|
Senior Manager
Joined: 06 Aug 2011
Posts: 261
Followers: 2
Kudos [?]:
22
[0], given: 42
|
Re: Set R contains five numbers that have an average value of 55 [#permalink]
02 Nov 2012, 06:13
Thanks alot Bunuel..now i got that  .. i think in REAL GMAT these type of question cum frequenlty..!!.
|
|
|
|
|
|
|
Re: Set R contains five numbers that have an average value of 55
[#permalink]
02 Nov 2012, 06:13
|
|
|
|
|
|
|
|
|
|
|
close
