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If set Z has a median of 19, what is the range of set Z? (1) [#permalink]
 21 Jan 2006, 01:49
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If set Z has a median of 19, what is the range of set Z?
(1) Z = {18,28,11,x,15,y}
(2) The average (mathematical mean) of the members of the set Z is 20.
Standard choices: A to E.
I got this one right, but wasted a lot of time - I am looking for a quick fix soln to this though I am not sure if there is one.
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Re: DS question on median - beautiful one [#permalink]
21 Jan 2006, 01:59
watever wrote: If set Z has a median of 19, what is the range of set Z?
(1) Z = {18,28,11,x,15,y}
(2) The average (mathematical mean) of the members of the set Z is 20.
Standard choices: A to E.
I got this one right, but wasted a lot of time - I am looking for a quick fix soln to this though I am not sure if there is one.
I think answer is C.
Main Stem: Median = 19
St1: either of x or y is 20 and other number is greater than or equal to 28. So Range cannot be found out. INSUFF
St2: Clearly INSUFF
Combined:
28+18+15+11+20(This is x) + y = 20
So y 30. Hence range is 30-11 = 19. SUFF
I did this in under 1 and half minutes.
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SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008
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I am not sure if this is a short cut but this is how I worled out ,
taking 1 --> we have two unknown but we know median is 19 and so either x or y = 19 --> Z { 11 , 15 , 18, 19 , x/y , 28} not suffi
taking 2 --> Sum/6=20 not suffi
taking 1 & 2 --> (11+15+18+19+28+y)/6 = 20 ==> y = 29 and thus u can get median
so C , OA ?
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1)
We have six numbers and a median of 19, thus the median has to be between 18 and x or y, which is egally.
The stem tells us that the median is 19 so either x or y has to be 20.
We know nothing about the other value, therefore can't determine the range
2) The average is 20, but we can't decide what the biggest number is, because we don't know the smallest; x or y could be smaller than 11
1+2) Either x or y is 20, see statement 1
The other value has to be greater than 18 and greater than 28 (since the smallest number 11 and the greatest number 28 don't support an average of 20)
The remaining value has to be 29
C
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Used pure intuition and got (C) in under 10 seconds.
1. Remaining variable can be anything ---> range unknown ---> INSUFF
2. Could be any # of numbers ----> range unknown ---> INSUFF
Together, knowing the mean and median we can narrow down and solve.---> range can be calculated ---> SUFF
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A very good real world illustration of mean and median [#permalink]
21 Jan 2006, 09:37
Ten people are riding on a bus in Redmond, Washington. The mean income of those riders is $50,000 a year. The median income of those riders is also $50,000 a year.
Joe Blow gets off the bus. Bill Gates gets on.
The median income of those riders remains $50,000 a year. But the mean income is now somewhere in the neighborhood of $50 million or so. A source now could say that the average income of those bus riders is 50 million bucks. But those other nine riders didn't become millionaires just because Bill Gates got on their bus. A reporter who writes that the "average rider" on that bus earns $50,000 a year, using the median, provides a far more accurate picture of those bus riders' place in the economy.
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Good job people, the OA is "C". GMATT73, its interesting to note your approach, I am just wondering if it will work all the time! The remaining explanations are more of less the standard way of solving it; prash_c - nice story to explain a concept 
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