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# M17-33

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 01:02
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45% (medium)

Question Stats:

64% (01:12) correct 36% (01:08) wrong based on 283 sessions

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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.

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16 Sep 2014, 01:02
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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.

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12 Oct 2014, 03:54
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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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12 Oct 2014, 05:27
1
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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23 Oct 2014, 06:34
Math Expert
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23 Oct 2014, 07:06
risch wrote:
:) Shudn the answer be A?

The question asks which of the following is impossible. It's not possible mean not to change so the answer is B.
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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"
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11 Mar 2015, 19:44
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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11 Mar 2015, 19:51
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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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.

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.

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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.

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.

[/quote]

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27 Oct 2015, 20:34
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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27 Oct 2015, 23:22
rish422007 wrote:
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.

Hope it helps.
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26 Nov 2015, 14:23
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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11 Apr 2016, 10:16
the ans marked is wrong. the correct one is A
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11 Apr 2016, 10:16
I don't agree with the explanation.
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11 Apr 2016, 10:26
garvpal wrote:
the ans marked is wrong. the correct one is A

Please read the discussion above and elaborate why do you think that the answer must be A.
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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.

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29 Jun 2017, 04:58
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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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?)
Re: M17-33 &nbs [#permalink] 19 Nov 2017, 12:49

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# M17-33

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