Set S consists of positive numbers. If -1 is added : GMAT Problem Solving (PS)
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# Set S consists of positive numbers. If -1 is added

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16 Apr 2013, 18:38
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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.
[Reveal] Spoiler: OA

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Last edited by Bunuel on 16 Apr 2013, 23:25, edited 2 times in total.
Edited the question.
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Re: Set S consists of positive numbers. If -1 is added [#permalink]

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16 Apr 2013, 21:58
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Consider set $$S={2,2}$$
Median=2 Mean=2 Range=0 stDev=0

Now $$S={2,2,-1}$$
After I've put -1: median=2 mean=1 Range=3 Std>0

A.The mean will decrease but median will not change.(Possible)
B.The median will decrease but mean will not change.
C.The range will increase but median will not change.(Possible)
D.The range will increase but mean will decrease.(Possible)
E.The standard deviation will increase but mean will decrease.(Possible)

IMO B
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Re: Set S consists of positive numbers. If -1 is added [#permalink]

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16 Apr 2013, 22:22
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Expert's post
sujit2k7 wrote:
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.

OA after some discussion...
OA: B

Must be B because of the mean not changing. The only way the mean can't change is if the new element is equal to the existing mean. Since the set is comprised only of positive numbers, the entry -1 must necessarily be less than the mean and therefore decrease the mean.

Without the word "positive" any of these could be possible, so keep in mind precision in language elements on test day.

Hope this helps!
-Ron
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Re: Set S consists of positive numbers. If -1 is added [#permalink]

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16 Apr 2013, 22:36
Thanks a Lot Zarrolou and Ron

BTW seems like GMAT is a playground for all RONs ( Previously It was Manhattan Ron , Now Vertisas Ron) ...I am definitely going give my son's name RON..hehehhehe( i m still unmarried )

Jokes apart can someone tell me when are the below conditions become false.... (these changes in mean , median really bug me up)

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.
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Re: Set S consists of positive numbers. If -1 is added [#permalink]

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16 Apr 2013, 23:26
m17 q33

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 $$\frac{less \ sum}{more \ terms}=\frac{less \ sum}{n+1}$$, which will be less than $$\frac{sum}{n}$$. Hence the mean must decrease.

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Re: Set S consists of positive numbers. If -1 is added [#permalink]

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17 Apr 2013, 06:41
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Expert's post
sujit2k7 wrote:
Thanks a Lot Zarrolou and Ron

BTW seems like GMAT is a playground for all RONs ( Previously It was Manhattan Ron , Now Vertisas Ron) ...I am definitely going give my son's name RON..hehehhehe( i m still unmarried )

Jokes apart can someone tell me when are the below conditions become false.... (these changes in mean , median really bug me up)

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.

Hey sujit2k7, thanks for the compliment about the Rons! I'll pass it on to my parents. I tell them it stands for "Really Outstanding Name"

As for your question about when these changes become false, Zarrolou's post gives a good example of how these conditions can change with the set 2,2. All four other options (A, C, D, E) could occur in that situation. In general terms, the introduction of a new term will change the mean of a set unless the new term is exactly that mean. However a median can remain the same even if scores of new numbers are introduced.

Consider a set consisting of ten 5's {5,5,5,5,5,5,5,5,5,5}. You could add -1's until the number of terms in this set went from 10 to 19 and the set would then be {-1,-1,-1,-1,-1,-1,-1,-1,-1, 5,5,5,5,5,5,5,5,5,5}, in which case the middle term would still be 5, so the mean would remain unchanged. However as soon as you add a single -1 the mean will drop from 5 to 4.5 or so. It helps when looking at these abstract questions to try real numbers and then draw logical conclusions from your observations.

Hope this helps!
-Ron
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Re: Set S consists of positive numbers. If -1 is added [#permalink]

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11 Dec 2015, 00:26
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Re: Set S consists of positive numbers. If -1 is added   [#permalink] 11 Dec 2015, 00:26
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