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M10-10

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M10-10  [#permalink]

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New post 16 Sep 2014, 00:41
11
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

42% (01:05) correct 58% (00:59) wrong based on 161 sessions

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Re M10-10  [#permalink]

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New post 16 Sep 2014, 00:41
Official Solution:


Notice that the range of ANY set is more than or equal to zero.

(1) All elements of set \(S\) are negative. The mean of a set with all negative elements is certainly negative so less than its range (which as discussed is always non-negative). Sufficient.

(2) The median of set \(S\) is negative. So, there is at least one negative term is the set. Now, consider two cases:

A. If all elements in set \(S\) are negative then we have the same scenario as above so \(Range \gt Mean\);

B. If not all elements in set \(S\) are negative then \(Range=Largest-Smallest\), which will mean that \(\text{Range} \gt \text{Largest Element}\) (that's because the smallest element in set \(S\) is negative. For example consider the following set {-1, -1, 2}: the range of that set is \(Range=2-(-1)=3 \gt 2)\). For the same reason the mean will be less than the largest element, so \(Range \gt Largest \gt Mean\).

So, in any case \(Range \gt Mean\). Sufficient.


Answer: D
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M10-10  [#permalink]

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New post 31 Jul 2015, 00:00
Bunuel wrote:
Official Solution:


Notice that the range of ANY set is more than or equal to zero.

(1) All elements of set \(S\) are negative. The mean of a set with all negative elements is certainly negative so less than its range (which as discussed is always non-negative). Sufficient.

(2) The median of set \(S\) is negative. So, there is at least one negative term is the set. Now, consider two cases:

A. If all elements in set \(S\) are negative then we have the same scenario as above so \(Range \gt Mean\);

B. If not all elements in set \(S\) are negative then \(Range=Largest-Smallest\), which will mean that \(\text{Range} \gt \text{Largest Element}\) (that's because the smallest element in set \(S\) is negative. For example consider the following set {-1, -1, 2}: the range of that set is \(Range=2-(-1)=3 \gt 2)\). For the same reason the mean will be less than the largest element, so \(Range \gt Largest \gt Mean\).

So, in any case \(Range \gt Mean\). Sufficient.


Answer: D


What if the set has only one number Set: {x}. Can we rule out this option saying that range is not defined for set consisting of one number? Or range is 0 for this set?
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New post 31 Jul 2015, 01:13
popov wrote:
Bunuel wrote:
Official Solution:


Notice that the range of ANY set is more than or equal to zero.

(1) All elements of set \(S\) are negative. The mean of a set with all negative elements is certainly negative so less than its range (which as discussed is always non-negative). Sufficient.

(2) The median of set \(S\) is negative. So, there is at least one negative term is the set. Now, consider two cases:

A. If all elements in set \(S\) are negative then we have the same scenario as above so \(Range \gt Mean\);

B. If not all elements in set \(S\) are negative then \(Range=Largest-Smallest\), which will mean that \(\text{Range} \gt \text{Largest Element}\) (that's because the smallest element in set \(S\) is negative. For example consider the following set {-1, -1, 2}: the range of that set is \(Range=2-(-1)=3 \gt 2)\). For the same reason the mean will be less than the largest element, so \(Range \gt Largest \gt Mean\).

So, in any case \(Range \gt Mean\). Sufficient.


Answer: D


What if the set has only one number Set: {x}. Can we rule out this option saying that range is not defined for set consisting of one number? Or range is 0 for this set?


The range of a single element set is 0.
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New post 18 Jul 2016, 09:15
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. Hi,

what would be the range for a set (-1, -2,-3,-4)? would it be -3 or 3? Why range is always positive?
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New post 18 Jul 2016, 09:18
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Re: M10-10  [#permalink]

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New post 12 Oct 2016, 07:14
Bunuel wrote:
Saurav Arora wrote:
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. Hi,

what would be the range for a set (-1, -2,-3,-4)? would it be -3 or 3? Why range is always positive?


The range is the difference between the largest and smallest elements of a set. The range of {-1, -2, -3, -4} is therefore -1 - (-4) = 3.



Hi

what about the following scenario

Elements : { -8,-9,-10 }
Range = -2
Mean = -9

Range > Mean

Elements : { -1,-2,-3,-4 ...... -10 }
Range= -9
Mean = -5

Mean > Range

Hence Statement 1 is insufficient .
Please let me know if otherwise
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New post 12 Oct 2016, 07:49
rt1601 wrote:
Bunuel wrote:
Saurav Arora wrote:
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. Hi,

what would be the range for a set (-1, -2,-3,-4)? would it be -3 or 3? Why range is always positive?


The range is the difference between the largest and smallest elements of a set. The range of {-1, -2, -3, -4} is therefore -1 - (-4) = 3.



Hi

what about the following scenario

Elements : { -8,-9,-10 }
Range = -2
Mean = -9

Range > Mean

Elements : { -1,-2,-3,-4 ...... -10 }
Range= -9
Mean = -5

Mean > Range

Hence Statement 1 is insufficient .
Please let me know if otherwise


The correct answer to the question is D, so there MUST be something wrong with your solution...

Let's see: the range is the difference between the largest and smallest elements of a set. The range CANNOT be negative. The range of {-8, -9, -10} is -8 - (-10) = 2 and the range of {-1, -2, -3, -4 ...... -10} is -1 - (-10) = 9.
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Re: M10-10  [#permalink]

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New post 30 Jul 2018, 14:35
This question is quite tricky but a really good one! I fell for A only as I did not consider the negative numbers and itsimplications on the range to a sufficient degree.
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New post 26 Oct 2018, 13:30
I think this is a high-quality question and I agree with explanation. is range always greater than mean and median... if not, in which case?
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New post 27 Oct 2018, 02:31
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Re: M10-10   [#permalink] 27 Oct 2018, 02:31
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