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# M10: Q10 - DS

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Manager
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M10: Q10 - DS [#permalink]

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22 Aug 2008, 15:34
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Is the range of a non-empty set $$S$$ bigger than its mean?

1. All members of $$S$$ are negative
2. The median of set $$S$$ is negative

[Reveal] Spoiler: OA
D

Source: GMAT Club Tests - hardest GMAT questions
GMAT Tutor
Joined: 24 Jun 2008
Posts: 1179
Re: M10: Q10 - DS [#permalink]

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22 Aug 2008, 16:18
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The range can't be negative, but if all members of a set are negative, the mean is certainly negative. So 1) should be sufficient.

If the median of a set is negative, at least one of the elements of the set is negative. If all of the elements in the set are negative, the range must be larger than the mean, because the range can't be negative. If there is a positive element in the set, then there is a largest positive element- call it x. The mean must be less than x- unless all elements are equal, the mean will certainly be smaller than the largest element. The range must be larger than x, since x is positive and the smallest element is negative. So the range is larger than the mean, and 2) should be sufficient.

Nice question. Answer is D.
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Manager
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Re: M10: Q10 - DS [#permalink]

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20 Jan 2010, 07:19
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1. All members of are negative
a)if all members are same then range will be 0 which is greater than mean
b)if all members are different then range will be > than 0 which is > than mean

either way range is > than mean
so choice 1 alone is sufficient

2. The median of set is negative
if median is negative then range is definitely positive and greater than mean

so choice 2 alone is sufficient

so my choice is D
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Re: M10: Q10 - DS [#permalink]

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07 Oct 2009, 17:24
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tejal777 wrote:
Ian,
What if the set contains only ONE element>?
According to stmt 1 that one no. will be -ive.Then won't the mean and range both be zero?
Confused:(

If the set is something like {-3}, then the range is zero, but the mean is -3. So in that case the range is still bigger than the mean.
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Re: M10: Q10 - DS [#permalink]

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07 Oct 2009, 19:56
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tejal777 wrote:
REALLY?Thanks man!Is there a link where such stuff is posted?
I always get confused..Lemme try and get it together:

If the set is {-3}
Mean: -3 >>I always thought this was Zero.(Mean is the average so -3/1 =-3 )
Median:0 (There is only one element so no middle value)
Mode: 0 (Since no value is repeating)

Range: 0 (No highest or lowest value)
Standard deviation: O (how far are the values dispersed from the mean)

If the set is made up of identical values {1,1,1,1,1}
Range= 0,Standard deviation=0

INPUTS?

Median:-3
Mode: 0? 0 cannot be 0 is not in the set. So it could be -3 or none.
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Joined: 18 Jan 2010
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Re: M10: Q10 - DS [#permalink]

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19 Jan 2010, 04:53
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Mode - numbers appearing most frequently...

hence

For set (-3) -

Mode = -3
Median - For a set with odd numbered elements median is the middle nuber...

Median = -3
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Posts: 39702
Re: M10: Q10 - DS [#permalink]

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28 Jan 2013, 07:06
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KingReuben9 wrote:
A "range" can never be negative and if all the members of the set are negative, then the mean will definitely be negative.
Statement 1 only is sufficient
The median only provide no information about the mean nor the range.
Statement 2 only is insufficient

So I will go ans A

The correct answer is D, not A. Check here: m10-q10-ds-69229.html#p510263 or m10-q10-ds-69229.html#p1174482

Hope it helps.
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Re: M10: Q10 - DS [#permalink]

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22 Aug 2008, 15:38
I'm not sure if I understand the question but I would have to guess E because both answers give no indication of where the mean is, and for all we know there is only one number in set S that is equal to the mean, or there could be 5 or 6.
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Re: M10: Q10 - DS [#permalink]

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23 Aug 2008, 10:32
yeah nvrmnd not sure what I was thinking there. good one.
Director
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Location: Kolkata,India
Re: M10: Q10 - DS [#permalink]

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07 Oct 2009, 16:53
Ian,
What if the set contains only ONE element>?
According to stmt 1 that one no. will be -ive.Then won't the mean and range both be zero?
Confused:(
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Director
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Re: M10: Q10 - DS [#permalink]

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07 Oct 2009, 19:48
REALLY?Thanks man!Is there a link where such stuff is posted?
I always get confused..Lemme try and get it together:

If the set is {-3}
Mean: -3 >>I always thought this was Zero.(Mean is the average so -3/1 =-3 )
Median:0 (There is only one element so no middle value)
Mode: 0 (Since no value is repeating)
Range: 0 (No highest or lowest value)
Standard deviation: O (how far are the values dispersed from the mean)

If the set is made up of identical values {1,1,1,1,1}
Range= 0,Standard deviation=0

INPUTS?
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Director
Joined: 25 Oct 2008
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Re: M10: Q10 - DS [#permalink]

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07 Oct 2009, 20:09
GMAT TIGER wrote:
tejal777 wrote:
REALLY?Thanks man!Is there a link where such stuff is posted?
I always get confused..Lemme try and get it together:

If the set is {-3}
Mean: -3 >>I always thought this was Zero.(Mean is the average so -3/1 =-3 )
Median:0 (There is only one element so no middle value)
Mode: 0 (Since no value is repeating)

Range: 0 (No highest or lowest value)
Standard deviation: O (how far are the values dispersed from the mean)

If the set is made up of identical values {1,1,1,1,1}
Range= 0,Standard deviation=0

INPUTS?

Median:-3
Mode: 0? 0 cannot be 0 is not in the set. So it could be -3 or none.

Could you please explain the median??How is it -3?
Mode: hmm..ya i get how that is -3 thanks!!
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Manager
Joined: 04 Dec 2009
Posts: 70
Location: INDIA
Re: M10: Q10 - DS [#permalink]

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19 Jan 2010, 20:05
Ans : D

S1: case-1. S(-1,-1,-1) then Mean=-1 Range=0 so, 0>-1
case-2 S(-1,-2,-3) then mean=-2 range=2 so,2>-2. Sufficient
S2: If the median of a set is negative, at least one of the elements of the set is negative or all elements can be nagative,and range cannot be negative so, same cane be explaine as S1.
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Re: M10: Q10 - DS [#permalink]

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20 Jan 2010, 09:54
Either should be sufficient. (Don't remember which that is.) The mean should be negative for both regardless of the size of the set. So the range would be 0 for only one member (or sets containing the same number) and > 0 for more than one distinct member. So 0 is always > than a negative number.
Manager
Joined: 20 Oct 2009
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Re: M10: Q10 - DS [#permalink]

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23 Jan 2010, 22:42
balboa wrote:
Is the range of a non-empty set $$S$$ bigger than its mean?

1. All members of $$S$$ are negative
2. The median of set $$S$$ is negative

[Reveal] Spoiler: OA
D

Source: GMAT Club Tests - hardest GMAT questions

1) range >=0 and the means are negative - sufficient
2) several cases:
a)negative element only -> refer to 1) - sufficient
b)more than 1 element - 1) identical elements range=0, median = the element and average = the element => range>mean.
2) non-identical elements range >0, median = negative number, average < the range b.1 and b.2 yields the same result=> 2 is also sufficient

P.S explanation on b.2 as why average is less than range in this case :

If median is negative, that means the left side of the elements ( whether the median is one number or average of two numbers) are less than or equal to the median (or the less of the two numbers) and the right sides are more than or equal to the median( or the bigger of the two numbers). range = Sn-S1 ( S1<0) => range > Sn. Average = Sum (S1, S2, S3....Sn)/ n < Sn. If it is hard to understand, try an example such as { -2, -1, 0, 8} range = 10 >8 and Average = 5/4 < 8

answer is D
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Manager
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Re: M10: Q10 - DS [#permalink]

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24 Jan 2011, 06:44
D.

Rephrasing: Is Range [S] > avg[S]
S1: Range is always positive as its the difference between extreme points in the set.
avg will be -ve as all points are -ve
Suff
S2: Median being -ve means that mean will be less than range as for eg -32, -31, -30 mean is -31 less then range = 2
-32, -31, 8 mean is -ve which is less then range = 40
Math Expert
Joined: 02 Sep 2009
Posts: 39702
Re: M10: Q10 - DS [#permalink]

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28 Jan 2013, 06:15
balboa wrote:
Is the range of a non-empty set $$S$$ bigger than its mean?

1. All members of $$S$$ are negative
2. The median of set $$S$$ is negative

[Reveal] Spoiler: OA
D

Source: GMAT Club Tests - hardest GMAT questions

Below is revised version of this question:

Is the range of set S greater than its mean?

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

So, in any case Range>Mean. Sufficient.

Answer: D.
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Re: M10: Q10 - DS [#permalink]

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28 Jan 2013, 07:02
A "range" can never be negative and if all the members of the set are negative, then the mean will definitely be negative.
Statement 1 only is sufficient
The median only provide no information about the mean nor the range.
Statement 2 only is insufficient

So I will go ans A
Re: M10: Q10 - DS   [#permalink] 28 Jan 2013, 07:02
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