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Is the range of set \(S\) greater than its mean? (1) All elements of set \(S\) are negative (2) The median of set \(S\) is negative
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Re M1010
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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 nonnegative). 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 \(Range=LargestSmallest\), 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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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 nonnegative). 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 \(Range=LargestSmallest\), 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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Re: M1010
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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 nonnegative). 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 \(Range=LargestSmallest\), 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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Re M1010
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18 Jul 2016, 09:15
I think this is a highquality 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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Re: M1010
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18 Jul 2016, 09:18
Saurav Arora wrote: I think this is a highquality 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.
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Re: M1010
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12 Oct 2016, 07:14
Bunuel wrote: Saurav Arora wrote: I think this is a highquality 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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Re: M1010
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12 Oct 2016, 07:49
rt1601 wrote: Bunuel wrote: Saurav Arora wrote: I think this is a highquality 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: M1010
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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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Re M1010
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26 Oct 2018, 13:30
I think this is a highquality question and I agree with explanation. is range always greater than mean and median... if not, in which case?



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Re: M1010
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27 Oct 2018, 02:31
zeeniagoyal wrote: I think this is a highquality question and I agree with explanation. is range always greater than mean and median... if not, in which case? No. For example, take {1, 2}. Range = 1, while median = mean = 1.5.
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