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# mean/median ds

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Director
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mean/median ds [#permalink]  13 Jan 2006, 04:55
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A list contains 3 diferent numbers. Does the median of the 3 numbers equal the arithmetic mean of the 3 numbers?

1) The range of the 3 numbers is equal to twice the difference betwenn the greatest number and the median

2) the sum of the 3 numbers is equal to 3 times one of the numbers
Director
Joined: 17 Dec 2005
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Location: Germany
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[#permalink]  13 Jan 2006, 08:50
As far as I can see it's D

1)

The only way the range is equal to twice the difference betwenn the greatest number and the median is when the three numbers are equal.

Consider some ex.

[123] Median=2 Range=1, => out
[125] M=2 R=4 => out
[222] M=2 R=0 fits

Sufficient

2)
[-1,0,1] fits
[222] also
[125]nope
[-2,0,3]nope
Sufficient

This is a stupid method and it's inaccurate too, maybe I've overseen a set.
Hope you provide a more elegant way to answer this.
VP
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[#permalink]  13 Jan 2006, 09:11
allabout wrote:
As far as I can see it's D

1)

The only way the range is equal to twice the difference betwenn the greatest number and the median is when the three numbers are equal.

Consider some ex.

[123] Median=2 Range=1, => out
[125] M=2 R=4 => out
[222] M=2 R=0 fits

Sufficient

2)
[-1,0,1] fits
[222] also
[125]nope
[-2,0,3]nope
Sufficient

This is a stupid method and it's inaccurate too, maybe I've overseen a set.
Hope you provide a more elegant way to answer this.

allabout, The question asks whether median = mean.

It should be A?

Let {x1,x2,x3} be the numbers

Q: Is x2 = (x1+x2+x3)/3 ? or
is x2 = (x1+x3)/2 ?

(1) Given x3-x1 = 2(x3-x2)
or x2 = (x1+x3)/2
SUFFICIENT.
(2) INSUFFICIENT, since the sum can equal any of the numbers x1,x2 or x3.

Hence A.
_________________

"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."

- Bernard Edmonds

Director
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Posts: 548
Location: Germany
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[#permalink]  13 Jan 2006, 09:19
giddi77 wrote:
allabout wrote:
As far as I can see it's D

1)

The only way the range is equal to twice the difference betwenn the greatest number and the median is when the three numbers are equal.

Consider some ex.

[123] Median=2 Range=1, => out
[125] M=2 R=4 => out
[222] M=2 R=0 fits

Sufficient

2)
[-1,0,1] fits
[222] also
[125]nope
[-2,0,3]nope
Sufficient

This is a stupid method and it's inaccurate too, maybe I've overseen a set.
Hope you provide a more elegant way to answer this.

allabout, The question asks whether median = mean.

It should be A?

Let {x1,x2,x3} be the numbers

Q: Is x2 = (x1+x2+x3)/3 ? or
is x2 = (x1+x3)/2 ?

(1) Given x3-x1 = 2(x3-x2)
or x2 = (x1+x3)/2
SUFFICIENT.
(2) INSUFFICIENT, since the sum can equal any of the numbers x1,x2 or x3.

Hence A.

Don't know; the sum of the three numbers is equal to three times one number. Do you know a set that fullfills this condition (2) but in which the mean isn't equal to the median?
VP
Joined: 21 Sep 2003
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[#permalink]  13 Jan 2006, 10:59
allabout wrote:

Don't know; the sum of the three numbers is equal to three times one number. Do you know a set that fullfills this condition (2) but in which the mean isn't equal to the median?

Hmm. I understand it now sir/madam(?) THANK YOU!!

It will work only if the numbers are of the form you mentioned.
(-n,0,n) or (n,n,n). Hence SUFFICIENT.

Therefor D.

Another classic case of "Answer Biasing" as duttsit would like to call it. I just rejected (2) because I didn't like it
_________________

"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."

- Bernard Edmonds

CEO
Joined: 20 Nov 2005
Posts: 2910
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
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[#permalink]  13 Jan 2006, 12:32
D it is.

Say numbers are x,y,z and these are in ascending order, So median here is y

Range = z-x

St1:

Range = 2 * (z-y)

so z-x = 2z-2y
-x = z-2y
0 = z+x -2y
y = z+x -2y + y
i.e 3y = x+y+z
y = (x+y+z)/3

So median = mean SUFF

St2:
this have three cases

1. x+y+z = 3x
x + (x +a) + (x+b) = 3x
so a + b = 0 (Remember that a and b are +ve)
This means all must be equal to x i.e mean = median
2. x+y+z = 3y
(y-a) + y + y(+b) = 3y
so b-a = 0 i.e a = b (Remember that a and b are +ve)
This means all must be equal to y i.e mean = median

3. x+y+z = 3z
(z-a) + (z-b) + z = 3z
so -a-b = 0 i.e a +b = 0 (Remember that a and b are +ve)
This means all must be equal to z i.e mean = median

SUFF
_________________

SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

Director
Joined: 17 Dec 2005
Posts: 548
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[#permalink]  13 Jan 2006, 13:12
En contraire, I'm sorry giddi that I haven't made it clear enough.

dahiyas approach is clearer and intuitive. One should strive always for clarity even when the time ticks.

By the way, I'm male.
Director
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[#permalink]  14 Jan 2006, 00:46
I would go with D

The nos are a, b, c

i) c-a=2(c-b)=>b=(a+c)/2 =>which is AP which means mean=median
so SUFFICIENT
ii) a+b+c=2a/2b/2c=>Again an AP so SUFFICIENT

So ans is D
Director
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[#permalink]  14 Jan 2006, 02:40
the oa is D

great explanation guys

btw how long did it take you to solve?
Director
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[#permalink]  15 Jan 2006, 00:51
Close to 1.5 min..
The real trick was to know that the series is an AP..Once you get that its harly a matter of 2 sec
SVP
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[#permalink]  15 Jan 2006, 23:06
I also got D. Could not fail the second statement. Looks like 3 times one number always means 3 time median.

Last edited by Bhai on 15 Jan 2006, 23:31, edited 1 time in total.
Director
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[#permalink]  15 Jan 2006, 23:25
joemama142000 wrote:
what is an AP?

AP= Arithmetic Progression

example
5 +10 +15 + 20 + 25 +... + 100

AP formula
S = n/2 ((2a + (n-1)*d) = 20/2 (5*2 + 19*5) = 1050
[#permalink] 15 Jan 2006, 23:25
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# mean/median ds

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