Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 44298

Question Stats:
67% (01:11) correct 33% (01:00) wrong based on 224 sessions
HideShow timer Statistics



Math Expert
Joined: 02 Sep 2009
Posts: 44298

Re M1733 [#permalink]
Show Tags
16 Sep 2014, 01:02
2
This post received KUDOS
Expert's post
2
This post was BOOKMARKED
Official Solution:Data set \(S\) consists of positive numbers. If 1 is added as an element to set \(S\), which of the following is NOT possible?A. The mean will decrease but median will not change. B. The median will decrease but mean will not change. C. The range will increase but median will not change. D. The range will increase but mean will decrease. E. The standard deviation will increase but mean will decrease. The mean of set \(S\) is \(\frac{sum}{n}\), where \(n\) is the number of terms in set \(S\). Since set \(S\) consist of positive numbers, then when we add 1 to the set the sum of the numbers in the new set will decrease. So, the new mean will be \(\frac{\text{less sum}}{\text{more terms}}=\frac{\text{less sum}}{n+1}\), which will be less than \(\frac{sum}{n}\). Hence the mean must decrease. Answer: B
_________________
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



Intern
Joined: 04 Sep 2012
Posts: 3

Re: M1733 [#permalink]
Show Tags
12 Oct 2014, 03:54
2
This post received KUDOS
Sure, mean will definitely decrease as explained. However, how is it possible that median can stay the same (as answer choice A suggests) even after 1 has been added to this set of only positive numbers? Can someone come up with an example to show that? Thanks.



Math Expert
Joined: 02 Sep 2009
Posts: 44298

Re: M1733 [#permalink]
Show Tags
12 Oct 2014, 05:27
javzprobz wrote: Sure, mean will definitely decrease as explained. However, how is it possible that median can stay the same (as answer choice A suggests) even after 1 has been added to this set of only positive numbers? Can someone come up with an example to show that? Thanks. If S={1, 1, 1}, then the median is 1. Adding 1 we get S'={1, 1, 1, 1}, the median is still 1.
_________________
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



Intern
Joined: 05 Sep 2014
Posts: 25

Re: M1733 [#permalink]
Show Tags
23 Oct 2014, 06:34
Shudn the answer be A?



Math Expert
Joined: 02 Sep 2009
Posts: 44298

Re: M1733 [#permalink]
Show Tags
23 Oct 2014, 07:06



Intern
Joined: 23 Dec 2014
Posts: 1

Re: M1733 [#permalink]
Show Tags
07 Feb 2015, 19:25
I think this question is good and helpful. I think there is an error in the answer. As the explanation said, the mean must decrease and the answer "B" says that the mean will not change. The correct answer is "D"



Intern
Joined: 16 Sep 2013
Posts: 2
Concentration: Accounting, Finance
GMAT 1: 510 Q29 V21 GMAT 2: 460 Q33 V19
GPA: 3.95

Re: M1733 [#permalink]
Show Tags
11 Mar 2015, 19:44
I think this question is not helpful. answer B says that mean will not changeso the answer should be A?(mean decrease)



Math Expert
Joined: 02 Aug 2009
Posts: 5720

Re: M1733 [#permalink]
Show Tags
11 Mar 2015, 19:51
Viktorijakm wrote: I think this question is not helpful. answer B says that mean will not changeso the answer should be A?(mean decrease) hi the question asks what is not possible? and if you add a negative number to a set of positive number, the mean will decrease... ans B says it will remain the same, which is not possible... therefore ans B...
_________________
Absolute modulus :http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
GMAT online Tutor



Intern
Joined: 06 Jun 2014
Posts: 5

Re: M1733 [#permalink]
Show Tags
01 Jun 2015, 01:38
Hello, for the below question mean will decrease. 1. Range will increase 2. Standard deviation will decrease.
How do we conclude about median for this case?
option E is also impossible.
Please clarify.
Regards, Mahuya
Set \(S\) consists of positive numbers. If 1 is added as an element to set \(S\), which of the following is impossible?
A. The mean will decrease but median will not change. B. The median will decrease but mean will not change. C. The range will increase but median will not change. D. The range will increase but mean will decrease. E. The standard deviation will increase but mean will decrease.
The mean of set \(S\) is \(\frac{sum}{n}\), where \(n\) is the number of terms in set \(S\). Since set \(S\) consist of positive numbers, then when we add 1 to the set the sum of the numbers in the new set will decrease. So, the new mean will be \(\frac{\text{less sum}}{\text{more terms}}=\frac{\text{less sum}}{n+1}\), which will be less than \(\frac{sum}{n}\). Hence the mean must decrease.
Answer: B[/quote]



Math Expert
Joined: 02 Sep 2009
Posts: 44298

Re: M1733 [#permalink]
Show Tags
01 Jun 2015, 02:08
mahuya78 wrote: Hello, for the below question mean will decrease. 1. Range will increase 2. Standard deviation will decrease.
How do we conclude about median for this case?
option E is also impossible.
Please clarify.
Regards, Mahuya
Set \(S\) consists of positive numbers. If 1 is added as an element to set \(S\), which of the following is impossible?
A. The mean will decrease but median will not change. B. The median will decrease but mean will not change. C. The range will increase but median will not change. D. The range will increase but mean will decrease. E. The standard deviation will increase but mean will decrease.
The mean of set \(S\) is \(\frac{sum}{n}\), where \(n\) is the number of terms in set \(S\). Since set \(S\) consist of positive numbers, then when we add 1 to the set the sum of the numbers in the new set will decrease. So, the new mean will be \(\frac{\text{less sum}}{\text{more terms}}=\frac{\text{less sum}}{n+1}\), which will be less than \(\frac{sum}{n}\). Hence the mean must decrease.
Answer: B [/quote] Please check examples here: setsconsistsofpositivenumbersif1isadded151019.html
_________________
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



Intern
Joined: 13 Apr 2015
Posts: 1

Re: M1733 [#permalink]
Show Tags
27 Oct 2015, 20:34
I think this is a poorquality question and I agree with explanation. the solution doesnt align with the answer marked as correct. D is the correct answer.



Math Expert
Joined: 02 Sep 2009
Posts: 44298

Re: M1733 [#permalink]
Show Tags
27 Oct 2015, 23:22



Board of Directors
Joined: 17 Jul 2014
Posts: 2752
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

Re: M1733 [#permalink]
Show Tags
26 Nov 2015, 14:23
what about the SD? the distance between numbers remain the same, thus the SD will not change. only E mentions something about SD, and since SD will not change, E can be a candidate as well. no?
ok, now I see, not 1 to all elements, but 1 added as a new element..yes E can't be true..



Intern
Joined: 26 May 2015
Posts: 4

Re: M1733 [#permalink]
Show Tags
11 Apr 2016, 10:16
the ans marked is wrong. the correct one is A



Intern
Joined: 26 May 2015
Posts: 4

Re: M1733 [#permalink]
Show Tags
11 Apr 2016, 10:16
I don't agree with the explanation.



Math Expert
Joined: 02 Sep 2009
Posts: 44298

Re: M1733 [#permalink]
Show Tags
11 Apr 2016, 10:26



Manager
Joined: 17 Oct 2013
Posts: 56

Re: M1733 [#permalink]
Show Tags
11 Apr 2016, 12:18
I didn't even tried to calculate, answer choices helped me.
Answer A and C say, median will not change. So both can't be answers.
Answer D and E say, mean will decrease. So both can't be answers.
Answer is B.



Intern
Joined: 12 Mar 2017
Posts: 5
Location: India
Anup: Patel
Concentration: Strategy, Economics
GPA: 3
WE: Education (Education)

Re: M1733 [#permalink]
Show Tags
29 Jun 2017, 04:58
I think this is a poorquality question and the explanation isn't clear enough, please elaborate. The statement after but is dubious...so what should we consider as a statement....
Before the "But" whatever is mentioned is true/ false and after it is False/ True in some cases...
so what should we consider, either meaning before But or after but...as it is contradictory....for example...option C says Range will increase (true)...BUT...Median will not change (it will change as the number of items in the set will change)



Intern
Joined: 09 Nov 2017
Posts: 5

Re: M1733 [#permalink]
Show Tags
19 Nov 2017, 12:49
Bunuel wrote: If S={1, 1, 1}, then the median is 1. Adding 1 we get S'={1, 1, 1, 1}, the median is still 1. Is it not the case that a "set" consists of distinct items? (Atleast as the word is used in questions on the GMAT?)







Go to page
1 2
Next
[ 21 posts ]



