which of the following cannot be the median

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uptowngirl92: Master | Next Rank: 500 Posts; Posts: 447; Joined: Sun Apr 19, 2009 9:08 pm; Location: Kolkata,India; Thanked: 7 times; GMAT Score:670

by uptowngirl92 » Tue Jul 07, 2009 4:25 am

which of the following cannot be the median of the three ordered positive integers x,y and z?
x
z
x+z
x+z/2
x+z/3

I got the correct answer (c) but was thrown off-guard by the word "ordered".What does it mean?At first glance I thought it mens that they are ordered in ascending/descending but i guess not!!Please shed some light.

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ssmiles08: Master | Next Rank: 500 Posts; Posts: 472; Joined: Sun Mar 29, 2009 6:54 pm; Thanked: 56 times

by ssmiles08 » Tue Jul 07, 2009 4:38 am

I think you are right. I think it does mean ordered, but I dont think it is strictly ascending or descending, it could also mean that some variables are the same?

1) 4, 4, 5 works
2) 5, 7, 7 works
3) does not work b/c y is median which should be >= x or <= z.
4) 3, 4, 5 works
5) 3, 3, 6 works

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batman73: Junior | Next Rank: 30 Posts; Posts: 22; Joined: Thu Aug 14, 2008 1:16 pm; Location: silicon valley; Thanked: 1 times; GMAT Score:590

Re: which of the following cannot be the median

by batman73 » Tue Jul 14, 2009 7:38 pm

uptowngirl92 wrote:which of the following cannot be the median of the three ordered positive integers x,y and z?
x
z
x+z
x+z/2
x+z/3

I got the correct answer (c) but was thrown off-guard by the word "ordered".What does it mean?At first glance I thought it mens that they are ordered in ascending/descending but i guess not!!Please shed some light.

According to OG 11, the word "ordered" is not stated in the problem. Does this mean that OG made a mistake, because I did not assume they are ordered because it is not mentioned. Can someone help me with this? Thanks in advance

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tohellandback: Legendary Member; Posts: 752; Joined: Sun May 17, 2009 11:04 pm; Location: Tokyo; Thanked: 81 times; GMAT Score:680

by tohellandback » Tue Jul 14, 2009 9:29 pm

ordered means in order. ascending or descending
but in any case median can only be >= smallest number and <= greatest number
x+z is greater than Z

as for batman73's question, even if they are not ordered, its impossible
lets say 3 numbers x,y and z
IF, x+z is the median
then y must be equal to x+z because thats the only number remaining since neither x nor z is the median.
that means y>=x or x+z>=x-true
but
that also means y<=z or X+Z<=Z- false if all numbers are positive

The powers of two are bloody impolite!!

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