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M17-33

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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.
[Reveal] Spoiler: OA

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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
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Re: M17-33 [#permalink]

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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.

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New post 12 Oct 2014, 04:27
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.
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Re: M17-33 [#permalink]

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New post 23 Oct 2014, 05:34
:) Shudn the answer be A?

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Re: M17-33 [#permalink]

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New post 07 Feb 2015, 18:25
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"

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Re: M17-33 [#permalink]

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New post 11 Mar 2015, 18:44
I think this question is not helpful.
answer B says that mean will not change-so the answer should be A?(mean decrease)

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New post 11 Mar 2015, 18:51
Viktorijakm wrote:
I think this question is not helpful.
answer B says that mean will not change-so 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...
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New post 01 Jun 2015, 00:38
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]

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New post 01 Jun 2015, 01:08
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: set-s-consists-of-positive-numbers-if-1-is-added-151019.html
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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

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Re: M17-33 [#permalink]

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New post 27 Oct 2015, 19:34
I think this is a poor-quality question and I agree with explanation. the solution doesnt align with the answer marked as correct. D is the correct answer.

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New post 27 Oct 2015, 22:22

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Re: M17-33 [#permalink]

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New post 26 Nov 2015, 13:23
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..

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Re: M17-33 [#permalink]

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New post 11 Apr 2016, 09:16
the ans marked is wrong. the correct one is A

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Re: M17-33 [#permalink]

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New post 11 Apr 2016, 09:16
I don't agree with the explanation.

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New post 11 Apr 2016, 09:26

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Re: M17-33 [#permalink]

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New post 11 Apr 2016, 11:18
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.

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Re: M17-33 [#permalink]

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New post 29 Jun 2017, 03:58
I think this is a poor-quality 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)

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Re: M17-33 [#permalink]

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New post 19 Nov 2017, 11:49
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?)

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Re: M17-33   [#permalink] 19 Nov 2017, 11:49

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