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# S is a set with at least two numbers. Is the range of s greater than

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Manager
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Joined: 26 Apr 2013
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Concentration: Finance, Strategy
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WE: Consulting (Computer Hardware)
S is a set with at least two numbers. Is the range of s greater than  [#permalink]

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27 Mar 2016, 01:29
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85% (hard)

Question Stats:

50% (02:25) correct 50% (01:43) wrong based on 103 sessions

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S is a set with at least two numbers. Is the range of s greater than its arithmetic mean?

1> The median of the set S is negative
2> The mean and the median are equal

Need help with this question
Math Expert
Joined: 02 Aug 2009
Posts: 7765
S is a set with at least two numbers. Is the range of s greater than  [#permalink]

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27 Mar 2016, 05:12
1
email2vm wrote:
S is a set with at least two numbers. Is the range of s greater than its arithmetic mean?

1> The median of the set S is negative
2> The mean and the median are equal

Need help with this question

Hi,
the Mean can be greater than average when we have set of large numbers, few in number..
say 5,6,7 range = 2, mean= 6...

lets see the statements

1> The median of the set S is negative
Median of set -ive means the MEAN < RANGE
lets try -ive numbers..
-5,-6,-7
Range= -5-(-7)= 2, MEAN= -6
10,7,-1, -2,-3
Range 10-(-3)=13
Mean= 11/5

What is happening is that the RANGE in all these cases is > the largest number
whereas MEAN will always remain< the lesser number

Suff

2> The mean and the median are equal
Insuff

A
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S is a set with at least two numbers. Is the range of s greater than  [#permalink]

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07 Nov 2018, 22:11
chetan2u wrote:
email2vm wrote:
S is a set with at least two numbers. Is the range of s greater than its arithmetic mean?

1> The median of the set S is negative
2> The mean and the median are equal

Need help with this question

Hi,
the Mean can be greater than average when we have set of large numbers, few in number..
say 5,6,7 range = 2, mean= 6...

lets see the statements

1> The median of the set S is negative
Median of set -ive means the MEAN < RANGE
lets try -ive numbers..
-5,-6,-7
Range= -5-(-7)= 2, MEAN= -6
10,7,-1, -2,-3
Range 10-(-3)=13
Mean= 11/5

What is happening is that the RANGE in all these cases is > the largest number
whereas MEAN will always remain< the lesser number

Suff

2> The mean and the median are equal
Insuff

A

Hi chetan2u,
why did you consider only a three element set. With a two element set, the said statement does not satisfy . For example : Let the numbers be a and b
Therefore by statement 1 ----> a+b<0

Our stem asked to comment on if b>3a.

But from statement 1 derivation we cannot sufficiently comment upon the stem.
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Posts: 1437
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Re: S is a set with at least two numbers. Is the range of s greater than  [#permalink]

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07 Nov 2018, 22:29
1
ShankSouljaBoi wrote:
chetan2u wrote:
email2vm wrote:
S is a set with at least two numbers. Is the range of s greater than its arithmetic mean?

1> The median of the set S is negative
2> The mean and the median are equal

Need help with this question

Hi,
the Mean can be greater than average when we have set of large numbers, few in number..
say 5,6,7 range = 2, mean= 6...

lets see the statements

1> The median of the set S is negative
Median of set -ive means the MEAN < RANGE
lets try -ive numbers..
-5,-6,-7
Range= -5-(-7)= 2, MEAN= -6
10,7,-1, -2,-3
Range 10-(-3)=13
Mean= 11/5

What is happening is that the RANGE in all these cases is > the largest number
whereas MEAN will always remain< the lesser number

Suff

2> The mean and the median are equal
Insuff

A

Hi chetan2u,
why did you consider only a three element set. With a two element set, the said statement does not satisfy . For example : Let the numbers be a and b
Therefore by statement 1 ----> a+b<0

Our stem asked to comment on if b>3a.

But from statement 1 derivation we cannot sufficiently comment upon the stem.

Hello

If we take a two element set say a, b - and we consider statement 1 that median is negative: then lets see what it means. For a two element set, median is the arithmetic mean only - so median = arithmetic mean of this set = (a+b)/2.
We are given that (a+b)/2 < 0 or a+b < 0. So arithmetic mean is clearly negative.

BUT - range can never be negative. Even if both numbers are equal (and negative), the range will still be '0'. If the numbers are unequal, then range will be greater than 0. So in any case, range > arithmetic mean for a two element set whose median is negative.
Re: S is a set with at least two numbers. Is the range of s greater than   [#permalink] 07 Nov 2018, 22:29
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