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Median problem

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by nubu » Tue Jul 05, 2011 4:32 pm
My friend asked me a GMAT question but she does not remember the source so I am not really sure about its validity. Here is the question:

A set : a , b , c.
"a" is the smallest
Mean = 7
Median = 9

What the max of "a" could be?

OA: [spoiler]3. I believe that median must be smaller than the biggest, am I wrong?[/spoiler]

Thank you very much!
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by Buix0065 » Tue Jul 05, 2011 4:57 pm
I get 2.

a + 9 + c / 3 = 7
a + c = 12

since b is the median at 9, and a is the smallest, a<b<c
c must be 10, 11, or 12 and a must be 0, 1, or 2

so max a = 2 and c = 10
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by artistocrat » Tue Jul 05, 2011 6:09 pm
Buix0065 wrote:I get 2.

a + 9 + c / 3 = 7
a + c = 12

since b is the median at 9, and a is the smallest, a<b<c
c must be 10, 11, or 12 and a must be 0, 1, or 2

so max a = 2 and c = 10
L=lowest: (L + 9 + 9)/3=7; L+18=21; L=3.
The set is: {3,9,9} (you can see the median is 9}

Never assume that values are different unless explicitly stated.

Good luck!
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by amit2k9 » Tue Jul 05, 2011 9:39 pm
using weighted average,
since mean is lesser than median meaning the gap between smallest number and median is more than the gap between largest number and the median.

so for max value of the smallest number, we make the median = the max number in the set = c

thus making C=9 we get 9*2=18. thus 21-18 = 3

hence a = 3.
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by Anurag@Gurome » Tue Jul 05, 2011 10:00 pm
nubu wrote:A set : a , b , c.
"a" is the smallest
Mean = 7
Median = 9

What the max of "a" could be?
(a + b + c) = 21

Now to maximize a, we have minimize the other two, i.e. b and c as their sum is constant. As the median of the three number is 9, b and c cannot be smaller than 9. hence, minimum value of b and c is 9.

Therefore, maximum value of a = 21 - (9 + 9) = 3
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by nubu » Wed Jul 06, 2011 12:08 am
I presumed that in a set, the median must be smaller than the the biggest and bigger than the smallest. I had a wrong perception.

Thank you very much for your help!
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by MBA.Aspirant » Wed Jul 06, 2011 12:33 am
nubu wrote:My friend asked me a GMAT question but she does not remember the source so I am not really sure about its validity. Here is the question:

A set : a , b , c.
"a" is the smallest
Mean = 7
Median = 9

What the max of "a" could be?

OA: [spoiler]3. I believe that median must be smaller than the biggest, am I wrong?[/spoiler]

Thank you very much!
b=9 sum= 21 a+b = 21 -9 = 12

max a = 12-9 = 3
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