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# Set S contains more than one element. Is the range S bigger

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Director
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Set S contains more than one element. Is the range S bigger [#permalink]  27 Oct 2005, 18:25
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Set S contains more than one element. Is the range S bigger than its mean?

A. Set S does not contain positive elements
B. The median of the set S is negative
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I would say D.

Statement 1 tells us we are dealing with negative numbers. Lets plug some in.

-2 and -6

Range 4, mean -4

-0.5 and -1

Range 0.5, mean -0.75

and so forth.
The mean will always be negative since we are dealing with negative numbers, the range is always going to be positive as it is a measure of distance between two numbers.

Statement 2 tells us median is negative.

If we have a negative number, we know that the range will always be greater than the mean.
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Re: DS - Mean/Range [#permalink]  27 Oct 2005, 20:01
B.

from i, set S could include {0,0}, or {0,-1}. first set has median=range. second set has range>median.

from ii, set S could include {-4,-3,-2,-1,0}, or {-5,-4,-3,-2,-1}. first set has range>median. second set has also range>median. in short, most importantly, range cannot be -ve because range = highest - lowest. so (ii) is suff.

So B is correct.....
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Re: DS - Mean/Range [#permalink]  27 Oct 2005, 20:19
rahulraao wrote:
Set S contains more than one element. Is the range S bigger than its mean?

A. Set S does not contain positive elements
B. The median of the set S is negative

D

A) suff.
Range is always positive. If no positive numbers, then mean is -ve.
B) suff.
If there are both -ve and +ve numbers, R>M is True
If all negative numbers, then it follows same explanation as A.
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Re: DS - Mean/Range [#permalink]  28 Oct 2005, 01:51
rahulraao wrote:
Set S contains more than one element. Is the range S bigger than its mean?

A. Set S does not contain positive elements
B. The median of the set S is negative

I've got to go with B.

The first statement could mean that both the range and the mean are 0, or that the range is bigger than the mean. The only thing we know for sure from this statement is that the range cannot be smaller than the mean. Insufficient.

The second statement tells us only that the median is negative. The mean could still be positive. However, if the mean is positive it would still be less than the highest value in the set. Thus, the range will be greater than the mean. Sufficient.
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I understood "elements" to mean that you need different numbers. Ie 2 zeros is only one element twice, while 0 and -1 are two elements.

Tricky stuff!
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Re: DS - Mean/Range [#permalink]  28 Oct 2005, 03:45
I agree with B.

The key here is to include zero in the set. When we say not positive numbers, we tend to overlook and miss zero from this set. Zero is neither a positive or a negative integer.
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Re: DS - Mean/Range [#permalink]  28 Oct 2005, 11:04
rahulraao wrote:
Set S contains more than one element. Is the range S bigger than its mean?

A. Set S does not contain positive elements
B. The median of the set S is negative

D. Range = (max - min)

A. If all are -ve numbers then Mean has to be -ve. Range is always +ve. So suff. R > M

B. If we have a set of -ve and +ve such as -2, -1, 48 in that case range would be greater than the max number and mean will be less.
R > M.
If all negative then as per stmnt A - R > M so R > M.
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Rahul,

if number is non positive it can be zero or negative. So answer can't be be D. it has to be B.
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Re: DS - Mean/Range [#permalink]  28 Oct 2005, 17:01
gsr wrote:
Range is always positive.

range could be zero, which is not +ve, too. however range cannot be -ve.
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Well, the OA is D!!
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rahulraao wrote:
Well, the OA is D!!

any OE???????????? what if set S contains only zeros (0). how this is sufficient?
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Quote:
understood "elements" to mean that you need different numbers. Ie 2 zeros is only one element twice, while 0 and -1 are two elements.

Tricky stuff!

elements is plural hence more than one number. It also means there are different numbers (as the statement hints towards it), even if one number is 0, there must be one that isnt, and we know it is negative.
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xennie wrote:

Quote:
understood "elements" to mean that you need different numbers. Ie 2 zeros is only one element twice, while 0 and -1 are two elements.

Tricky stuff!

elements is plural hence more than one number. It also means there are different numbers (as the statement hints towards it), even if one number is 0, there must be one that isnt, and we know it is negative.

Agreed.
Generally, when the question says a set S has 5 positive numbers, IMO it cannot all be the same.
S={1,1,1,1,1} is equal to set {1}. This way it will have only one number.
or even S={1,1,1,2,2} = {1,2}
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