Author 
Message 
TAGS:

Hide Tags

Senior Manager
Status: 750+ or Burst !
Joined: 01 May 2011
Posts: 361
Location: India
Concentration: General Management, Strategy
GPA: 3.5

The Range of Set A is R. A number having equal value to R
[#permalink]
Show Tags
30 May 2011, 21:04
Question Stats:
19% (02:31) correct 81% (02:11) wrong based on 702 sessions
HideShow timer Statistics
The Range of Set A is R. A number having equal value to R, is added to set A. Will the range of Set A increase ? (1) All numbers in Set A are positive. (2) The mean of the new set is smaller than R. Source: 800Score Tests.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
GMAT done  a mediocre score but I still have a lot of grit in me
The last 20 days of my GMAT journey




Math Expert
Joined: 02 Sep 2009
Posts: 50000

Re: The Range of Set A is R. A number having equal value to R
[#permalink]
Show Tags
13 Oct 2012, 12:52
akhileshgupta05 wrote: The Range of Set A is R. A number having equal value to R, is added to set A. Will the range of Set A increase ?
(1) All numbers in Set A are positive. (2) The mean of the new set is smaller than R.
Source: 800Score Tests. I think we all agree that neither statement is sufficient alone. Now, let's consider the statements together. Since {Range}={Largest}{Smallest}, then the range will increase if R is either the smallest or the largest element of the new set. Now, can R be the smallest element of the new set? If it is, then according to the second statement, we would have that the mean of the new set is smaller than the smallest element of the set, which is not possible: the mean of a set cannot be smaller than its smallest element. Next, can R be the largest element of the new set? We are given that for set A, the range, R={Largest}{Smallest}. Since from the first statement we know that all numbers in Set A are positive, then R must be less than the largest element of set A, hence R cannot be the largest element of the new set. So, we have that R is neither the smallest nor the largest element of the set. Therefore, the range of the new set will not be greater than the range of set A. Sufficient. Answer: C. Hope it's clear.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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? Extrahard Quant Tests with Brilliant Analytics




Senior Manager
Status: 750+ or Burst !
Joined: 01 May 2011
Posts: 361
Location: India
Concentration: General Management, Strategy
GPA: 3.5

Re: Range & Mean
[#permalink]
Show Tags
01 Jun 2011, 00:02
Yes it was pretty difficult. I had to guess on this question. Official Explanation: Disclosure: The following explanation has been typed word to word from an 800score practise test.The range of a set is the difference between the largest and smallest elements of the set. Let's denote e and E as the smallest and largest element of the set, respectively. (if there is only one element, or if all elements are same, then e=E) R, the range of the set = Ee The questions asks whether the range of the Set A will increase when R becomes a member of the set. If R is less than the smallest member,e, or greater than the largest number,E, then the range will increase. However, if E>R>e, then adding R to the set won't increase the range of the set. Statement (1) Tells us that all the members of the set are positive, Since R= Ee and both E and e are positve then R must be less than E.This makes it possible for R to be either between e and E, or less than e. In former case, the range of the new set won't increase but in the latter case it will. (see my example) Thus Statement 1 is insufficient.Statement 2 tells us that the mean of the new set is smaller than R.The mean of the original set A = Sum of elements /number of elements Since the new set is just A plus the addition of R, there will be one addition element in the new set. Thus mean of new set = (sum of elements of A + R) / Number of elements +1 Since R> mean of new set. R> (sum of A + R) / (number of elements +1) Multiplying both sides of the equation by (number of elements + 1) (Number of elements +1) (R) > Sum of A + R, which is equal to (Number of elements)(R) + (R) > Sum of A + R, subtracting R from both sides. (Number of elements)(R)>Sum of A, dividing both sides by (number of elements) R> Sum of A/number of elements, thus R> mean of A Thus if know that the mean of the new set is smaller than R, we also know that the mean of the old set is smaller than R.Furthermore, we know that the mean of any group of numbers is at least as largest as the smallest number so the mean of the old set is greater than of equal to e. So, statment 2 tells us the R>mean of A>e. This is insufficient because R might be greater than E and, and increase the range, or it might be between e and E.Combined two statements are sufficient. Statement (1) tells us that R is less than E and Statement (2) tells us that R is greater than e. This implies that adding R to the set will not increase the range of the set. Final answer : (C)
_________________
GMAT done  a mediocre score but I still have a lot of grit in me
The last 20 days of my GMAT journey




Senior Manager
Joined: 24 Mar 2011
Posts: 371
Location: Texas

Re: Range & Mean
[#permalink]
Show Tags
30 May 2011, 21:10
i thought each statement is sufficient to answer the question.



Senior Manager
Status: 750+ or Burst !
Joined: 01 May 2011
Posts: 361
Location: India
Concentration: General Management, Strategy
GPA: 3.5

Re: Range & Mean
[#permalink]
Show Tags
30 May 2011, 22:01
agdimple333 wrote: i thought each statement is sufficient to answer the question. Statement 1 cannot be sufficient. Range = Highest  Lowest Let, Set A =[2,3,4,5,6] Thus, Range = 62 = 4 . New Set A = [2,3,4,4,5,6]. Range doesn't increase. But if, Set A = [8,9,10] Range = 108=2. New Set A= [2,8,9,10] New Range = 102=8. Range increases. Thus statement 1 is insufficient. I am little confused with statement 2.
_________________
GMAT done  a mediocre score but I still have a lot of grit in me
The last 20 days of my GMAT journey



Retired Moderator
Joined: 16 Nov 2010
Posts: 1436
Location: United States (IN)
Concentration: Strategy, Technology

Re: Range & Mean
[#permalink]
Show Tags
31 May 2011, 05:02
I'm getting E as answer. Let Set A = {1,2,3} => Range = 2 If we add x = R = 2, then the range remain the same Let Set A = {1,1,1} Range = 0 If we add x = R = 0 in this set, then the range become 10 = 1 So (1) is Insufficient (2) In case 2 above, if we add x = 0, then mean is lesser and the Range increases. Again, let A = {1,1,2} then if we add x = 1, the new mean = 5/4 < original mean = 4/3, but the range remains same. So Insufficient (1) + (2) includes all cases above Answer  E
_________________
Formula of Life > Achievement/Potential = k * Happiness (where k is a constant)
GMAT Club Premium Membership  big benefits and savings



Manager
Joined: 04 Apr 2010
Posts: 136

Re: Range & Mean
[#permalink]
Show Tags
31 May 2011, 09:58
I think E should be the answer. For 'Yes' (Range will increase) try (1,1,1) For 'No' (Range will not increase) try (1,1,2) Above listed 2 sets give 'Yes' n 'No' answer for both the statements.
_________________
Consider me giving KUDOS, if you find my post helpful. If at first you don't succeed, you're running about average. ~Anonymous



Retired Moderator
Joined: 20 Dec 2010
Posts: 1835

Re: Range & Mean
[#permalink]
Show Tags
31 May 2011, 12:08
akhileshgupta05 wrote: The Range of Set A is R. A number having equal value to R, is added to set A. Will the range of Set A increase ?
(1)All numbers in Set A are positive. (2)The mean of the new set is smaller than R.
Please explain your answer. Source: 800Score Tests. 1. CaseI: A={1,1,1} R:11=0 New Set: {0,1,1,1} New Range=10=1 Range Increased. CaseII: A={5,10} R=105=5 New Set={5,5,10} New Range=105=5 Range Unchanged. Not Sufficient. 2. Case I: A={10,5} R=5(10)=5 New Set={10,5,5} New Mean = 3.XX; Mean<R New Range: 5(10)=15 Range Increased. Case II: A={0,20} R=200=20 New Set={0,20,20} New Mean=40/3=13.XX. Mean<R New Range=200=20. Range Unchanged. Not Sufficient. Combining both; A={1,101} R=100 New Set={1,101,100} New Mean=202/3=67 Approx < R New Range=100 Range Not Changed. A={1,2,3,4,5} R=4 New Set={1,2,3,4,4,5} New Mean=19/6=3.X<R New Range=4 Range Not Changed. **************************** Ans: "C" ********************** This is a difficult question. Can the author please post the Official Explanation because substitution does not appear full proof. Thanks.
_________________
~fluke
GMAT Club Premium Membership  big benefits and savings



VP
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1055

Re: Range & Mean
[#permalink]
Show Tags
14 Jun 2011, 22:44
a A (1,1) gives (0,1,1) range increases. (1,2) gives (1,1,2) range remains same. Not sufficient.
b A(2,1) gives (2,1,1) range increases always for negative values.
A(1,5) gives (1,4,5) range remains same. Not sufficient.
a+b (1,5) giving (1,4,5) range remaining same. Hence C.



Intern
Joined: 13 May 2012
Posts: 28

Re: The Range of Set A is R . A number having equal value to R ,
[#permalink]
Show Tags
13 Oct 2012, 11:41
If set is (50, 54) then the range is 4. When 4 is added to the set, the mean decreases but range increases.
Consider set (3,7) range is 4. When 4 is added to the set the mean decreases but range remains the same.
So both statements together not sufficient. E?
Posted from my mobile device



Director
Joined: 22 Mar 2011
Posts: 601
WE: Science (Education)

Re: The Range of Set A is R. A number having equal value to R
[#permalink]
Show Tags
13 Oct 2012, 13:11
akhileshgupta05 wrote: The Range of Set A is R. A number having equal value to R, is added to set A. Will the range of Set A increase ?
(1) All numbers in Set A are positive. (2) The mean of the new set is smaller than R.
Source: 800Score Tests. Because we are given a set of numbers, we can assume that all numbers are distinct, and that we have at least two numbers. Let's denote by \(M\) the largest value of the set, and by \(m\) its smallest value. Then the range is \(R = M  m\). The given question can be reformulated as "Is \(R < m\) or \(R>M\)?" If \(m\leq{R}\leq{M},\) the range of the set A will remain the same after adding \(R.\) (1) If \(R=Mm<m,\) then \(\,\,M<2m.\) If \(R=Mm>{m},\) then \(\,\,M>{2m}.\) All the numbers in the set A being positive, both inequalities are possible. In addition, \(R=Mm<M.\) So, \(R\) can be smaller or greater than the smallest element in the set, but for sure, it is smaller than the largest element. Not sufficient. (2) Let's denote by \(A_n\) the average of the set A before we add \(R\) to it. Then \(\frac{A_n\cdot{n}+R}{n+1}<R,\) from which \(A_n\cdot{n}+R<nR+R\), or \(A_n<R.\) Since the average \(A_n\geq{m}\) we can deduce that \(R>m.\) But if \(m\) is negative, \(R=Mm>M\). If \(m\) is positive, then necessarily \(R=Mm<M.\) Not sufficient. (1) and (2) together: from the above analysis, we can see that if \(m>0,\) then \(R\) is between \(m\) and \(M,\) and the range will remain the same. Sufficient. Answer C.
_________________
PhD in Applied Mathematics Love GMAT Quant questions and running.



Intern
Joined: 13 Jan 2013
Posts: 4
Location: India
Concentration: General Management, Marketing

Re: The Range of Set A is R. A number having equal value to R
[#permalink]
Show Tags
30 Dec 2013, 03:58
is zero a positive number ? can we consider zero in set A having all positive number ?



Math Expert
Joined: 02 Sep 2009
Posts: 50000

Re: The Range of Set A is R. A number having equal value to R
[#permalink]
Show Tags
30 Dec 2013, 04:08



Manager
Joined: 14 Apr 2014
Posts: 63

Re: The Range of Set A is R. A number having equal value to R
[#permalink]
Show Tags
16 Sep 2014, 10:06
Bunuel wrote: akhileshgupta05 wrote: The Range of Set A is R. A number having equal value to R, is added to set A. Will the range of Set A increase ?
(1) All numbers in Set A are positive. (2) The mean of the new set is smaller than R.
Source: 800Score Tests. I think we all agree that neither statement is sufficient alone. Now, let's consider the statements together. Since {Range}={Largest}{Smallest}, then the range will increase if R is either the smallest or the largest element of the new set. Now, can R be the smallest element of the new set? If it is, then according to the second statement, we would have that the mean of the new set is smaller than the smallest element of the set, which is not possible: the mean of a set cannot be smaller than its smallest element. Next, can R be the largest element of the new set? We are given that for set A, the range, R={Largest}{Smallest}. Since from the first statement we know that all numbers in Set A are positive, then R must be less than the largest element of set A, hence R cannot be the largest element of the new set. So, we have that R is neither the smallest nor the largest element of the set. Therefore, the range of the new set will not be greater than the range of set A. Sufficient. Answer: C. Hope it's clear. Hi Bunnel, I am getting ans E . Can you please have a look. Given : Suppose: A = {52,53,54} Range = 2 New Set A = {2,52,53,54} Stat 1 says: All numbers in Set A are positive. So Suppose: A = {52,53,54} Range = 2 New Set A = {2,52,53,54} Range = 52 means increased Now suppose A {2,3,4} Range = 2 New Set A = {2,2,3,4} Range = 2 [same range] Hence A is NS Stat 2 : The mean of the new set is smaller than R. Suppose: A = {52,53,54} Range = 2 Mean = 159/3 =53 New Set A = {2,52,53,54} Mean = 161/4 = 40.25 [which is less than previous set] but Range = 52 means increased Now suppose A {2,3,4} Mean = 3 Range = 2 New Set A = {2,2,3,4} Mean = 11/4 = 2.7 Range = 2 [same range] So even if I am trying to combine 1 + 2 I can't say range is increased. Can you please clear my doubt ?



Math Expert
Joined: 02 Sep 2009
Posts: 50000

Re: The Range of Set A is R. A number having equal value to R
[#permalink]
Show Tags
16 Sep 2014, 14:17
ajaym28 wrote: Bunuel wrote: akhileshgupta05 wrote: The Range of Set A is R. A number having equal value to R, is added to set A. Will the range of Set A increase ?
(1) All numbers in Set A are positive. (2) The mean of the new set is smaller than R.
Source: 800Score Tests. I think we all agree that neither statement is sufficient alone. Now, let's consider the statements together. Since {Range}={Largest}{Smallest}, then the range will increase if R is either the smallest or the largest element of the new set. Now, can R be the smallest element of the new set? If it is, then according to the second statement, we would have that the mean of the new set is smaller than the smallest element of the set, which is not possible: the mean of a set cannot be smaller than its smallest element. Next, can R be the largest element of the new set? We are given that for set A, the range, R={Largest}{Smallest}. Since from the first statement we know that all numbers in Set A are positive, then R must be less than the largest element of set A, hence R cannot be the largest element of the new set. So, we have that R is neither the smallest nor the largest element of the set. Therefore, the range of the new set will not be greater than the range of set A. Sufficient. Answer: C. Hope it's clear. Hi Bunnel, I am getting ans E . Can you please have a look. Given : Suppose: A = {52,53,54} Range = 2 New Set A = {2,52,53,54} Stat 1 says: All numbers in Set A are positive. So Suppose: A = {52,53,54} Range = 2 New Set A = {2,52,53,54} Range = 52 means increased Now suppose A {2,3,4} Range = 2 New Set A = {2,2,3,4} Range = 2 [same range] Hence A is NS Stat 2 : The mean of the new set is smaller than R. Suppose: A = {52,53,54} Range = 2 Mean = 159/3 =53 New Set A = {2,52,53,54} Mean = 161/4 = 40.25 [which is less than previous set] but Range = 52 means increased Now suppose A {2,3,4} Mean = 3 Range = 2 New Set A = {2,2,3,4} Mean = 11/4 = 2.7 Range = 2 [same range] So even if I am trying to combine 1 + 2 I can't say range is increased. Can you please clear my doubt ? In your examples the mean of new set is NOT less than R.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 14 Apr 2014
Posts: 63

The Range of Set A is R. A number having equal value to R
[#permalink]
Show Tags
16 Sep 2014, 20:02
ooops thanks for catching this, next time I will be more careful.



NonHuman User
Joined: 09 Sep 2013
Posts: 8457

Re: The Range of Set A is R. A number having equal value to R
[#permalink]
Show Tags
02 Nov 2017, 14:15
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: The Range of Set A is R. A number having equal value to R &nbs
[#permalink]
02 Nov 2017, 14:15






