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# the median

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Intern
Joined: 18 Oct 2008
Posts: 5

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Location: Ukraine / UK

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07 Mar 2009, 06:30
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Set S consists of the following unique integers: -2, 17, 3, n, 2, 15, -3, and -27; which of the following could be the median of set S?
A) 1
B) 9
C) 14
D) 17
E) It Cannot Be Determined

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Manager
Joined: 26 Dec 2008
Posts: 58

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Schools: Booth (Admit R1), Sloan (Ding R1), Tuck (R1)
Re: the median [#permalink]

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07 Mar 2009, 11:08
mishak wrote:
Set S consists of the following unique integers: -2, 17, 3, n, 2, 15, -3, and -27; which of the following could be the median of set S?
A) 1
B) 9
C) 14
D) 17
E) It Cannot Be Determined

IMHO E

median = center value once numbers are arranged in increasing or decreasing order

rearrange numbers:

-27, -3, -2, 2, 3, 15, 17 + n somewhere ==> total of 8 numbers ==> median would be average of TWO central values

taking 2 cases:
(1) if n is after 17 then median = avg(2, 3) = 2.5
(2) if n is before -27 then median = avg(-2, 2) = 0

thus, can't be determined

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Manager
Joined: 27 Feb 2009
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Re: the median [#permalink]

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07 Mar 2009, 16:25
the possible values of n could be -2,-1,0,1,2,3

when u arrange it is -27 -3 -2 2 3 15 17. Hence the total no's is 8, n can come between -2, 3.

from this when n = 0, the median is 0+2/2 = 1

Kudos [?]: 28 [0], given: 0

Senior Manager
Joined: 30 Nov 2008
Posts: 485

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Schools: Fuqua
Re: the median [#permalink]

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07 Mar 2009, 18:48
kaushik04 wrote:
the possible values of n could be -2,-1,0,1,2,3

when u arrange it is -27 -3 -2 2 3 15 17. Hence the total no's is 8, n can come between -2, 3.

from this when n = 0, the median is 0+2/2 = 1

How did you know that n can have only the values from -2 to 3?

It is is given that set S contains Unique Integers. So n cannot take the value of 2,3,-2.

Kudos [?]: 360 [0], given: 15

Manager
Joined: 26 Dec 2008
Posts: 58

Kudos [?]: 14 [0], given: 0

Schools: Booth (Admit R1), Sloan (Ding R1), Tuck (R1)
Re: the median [#permalink]

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07 Mar 2009, 21:44
mrsmarthi wrote:
kaushik04 wrote:
the possible values of n could be -2,-1,0,1,2,3

when u arrange it is -27 -3 -2 2 3 15 17. Hence the total no's is 8, n can come between -2, 3.

from this when n = 0, the median is 0+2/2 = 1

How did you know that n can have only the values from -2 to 3?

It is is given that set S contains Unique Integers. So n cannot take the value of 2,3,-2.

just wondering if the question is asking for "any" possible median value.. and when we take n = 0 we get 1 which is one of the answer choices..

..any thoughts?

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VP
Joined: 18 May 2008
Posts: 1258

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Re: the median [#permalink]

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07 Mar 2009, 21:55
I think there is something missing in the statement otherwise it shld be E

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Senior Manager
Joined: 30 Nov 2008
Posts: 485

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Re: the median [#permalink]

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07 Mar 2009, 22:01
ritula wrote:
I think there is something missing in the statement otherwise it shld be E

Nope the question is absolutely fine. It is just a trap to overlook one critical word COULD BE.

Set S consists of the following unique integers: -2, 17, 3, n, 2, 15, -3, and -27; which of the following COULD BE the median of set S?

When could be is asked, need to check for the possibilities. This can best be solved by the Process of Elimination method.

When the numbers are arranged in the order, we have

-27, -3, -2, 2, 3, 15, 17 and n. In total there are 8 terms. Median will be the avg of the two middle terms. One of the middle terms is 2. The other could be based on what the value of n is.

case 1 - N could be greater than 2 in which case median will avg(2 and 3) that is 2.5(There can't be any other integers between 2 and 3). So B, C and D are out of the race.
case 2 - N could be between -2 and 2. If n > -2 and < 2 ie -1,0,1 then n will occur betwee -2 and 2 and will be the other term for median calucation. In these cases, median can be 0.5 or 1 or 1.5 1 is one of the ans choices. Hence it is the ans.
case 3 - N could be less than -2 in which case median will be avg(-2,2) that is 0.

GMAT is all about trapping us. How well can we escape the trap and find the solution is what that proves our score.

Kudos [?]: 360 [0], given: 15

VP
Joined: 18 May 2008
Posts: 1258

Kudos [?]: 527 [0], given: 0

Re: the median [#permalink]

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07 Mar 2009, 22:14
Well said mrsmarthi
mrsmarthi wrote:
ritula wrote:
I think there is something missing in the statement otherwise it shld be E

Nope the question is absolutely fine. It is just a trap to overlook one critical word COULD BE.

Set S consists of the following unique integers: -2, 17, 3, n, 2, 15, -3, and -27; which of the following COULD BE the median of set S?

When could be is asked, need to check for the possibilities. This can best be solved by the Process of Elimination method.

When the numbers are arranged in the order, we have

-27, -3, -2, 2, 3, 15, 17 and n. In total there are 8 terms. Median will be the avg of the two middle terms. One of the middle terms is 2. The other could be based on what the value of n is.

case 1 - N could be greater than 2 in which case median will avg(2 and 3) that is 2.5(There can't be any other integers between 2 and 3). So B, C and D are out of the race.
case 2 - N could be between -2 and 2. If n > -2 and < 2 ie -1,0,1 then n will occur betwee -2 and 2 and will be the other term for median calucation. In these cases, median can be 0.5 or 1 or 1.5 1 is one of the ans choices. Hence it is the ans.
case 3 - N could be less than -2 in which case median will be avg(-2,2) that is 0.

GMAT is all about trapping us. How well can we escape the trap and find the solution is what that proves our score.

Kudos [?]: 527 [0], given: 0

Manager
Joined: 27 Feb 2009
Posts: 58

Kudos [?]: 28 [0], given: 0

Re: the median [#permalink]

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08 Mar 2009, 00:18
Hey thats exactly how I did...Sorry for not posting the detailed steps...I backsolved the problem...one thing what i found regarding problem solving is, you have very very less chances of choosing cannot be determined...

ritula wrote:
Well said mrsmarthi
mrsmarthi wrote:
ritula wrote:
I think there is something missing in the statement otherwise it shld be E

Nope the question is absolutely fine. It is just a trap to overlook one critical word COULD BE.

Set S consists of the following unique integers: -2, 17, 3, n, 2, 15, -3, and -27; which of the following COULD BE the median of set S?

When could be is asked, need to check for the possibilities. This can best be solved by the Process of Elimination method.

When the numbers are arranged in the order, we have

-27, -3, -2, 2, 3, 15, 17 and n. In total there are 8 terms. Median will be the avg of the two middle terms. One of the middle terms is 2. The other could be based on what the value of n is.

case 1 - N could be greater than 2 in which case median will avg(2 and 3) that is 2.5(There can't be any other integers between 2 and 3). So B, C and D are out of the race.
case 2 - N could be between -2 and 2. If n > -2 and < 2 ie -1,0,1 then n will occur betwee -2 and 2 and will be the other term for median calucation. In these cases, median can be 0.5 or 1 or 1.5 1 is one of the ans choices. Hence it is the ans.
case 3 - N could be less than -2 in which case median will be avg(-2,2) that is 0.

GMAT is all about trapping us. How well can we escape the trap and find the solution is what that proves our score.

Kudos [?]: 28 [0], given: 0

Re: the median   [#permalink] 08 Mar 2009, 00:18
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# the median

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