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Three boxes have an average weight of 7 kg and a median

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Three boxes have an average weight of 7 kg and a median [#permalink]

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New post 26 Apr 2006, 01:28
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Three boxes have an average weight of 7 kg and a median weight of 9 kgs. What is the maximum possible weight of the lightest box?

A. 1
B. 2
C. 3
D. 4
E. 5

OPEN DISCUSSION OF THIS QUESTION IS HERE: three-boxes-of-supplies-have-an-average-arithmetic-mean-105819.html
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New post 26 Apr 2006, 01:48
Answer is 2..


Average is 7 x 3 = 21
Median is 9, so the sum of the other two box = 12! (21-9)

Now, the heavier box shud be more than 9 (as 9 is the median)

Assuming all weights are INTEGERs!

The min weight of the hevier box wud be 9+1 = 10!

Hence the max weight of the lightest box = 12-10 =2!
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New post 26 Apr 2006, 01:49
What is the source?
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New post 26 Apr 2006, 06:47
sm176811 wrote:
Answer is 2..


Average is 7 x 3 = 21
Median is 9, so the sum of the other two box = 12! (21-9)

Now, the heavier box shud be more than 9 (as 9 is the median)


Assuming all weights are INTEGERs!

The min weight of the hevier box wud be 9+1 = 10!

Hence the max weight of the lightest box = 12-10 =2!


Why can't it be equal to 9?
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New post 26 Apr 2006, 06:58
the answer is 3.

21-9=12

we could have the serie 3 9 9.
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New post 26 Apr 2006, 09:20
Can u have 3,9,9 and yet have 9 as the median? I am not sure!
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New post 26 Apr 2006, 09:53
3.

I think the weights would be 3, 9 and 9.
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Re: Average Weight [#permalink]

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New post 27 Apr 2006, 20:37
getzgetzu wrote:
Three boxes have an average weight of 7 kg and a median weight of 9 kgs. What is the maximum possible weight of the lightest box?

1
2
3
4
5


The ans has to be 3.
Since the avg of 3 boxes is 7 the sum is 21. we know the median is 9, therefore the 3rd number is atleast 9. 21-(9+9)=3.
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New post 27 Apr 2006, 20:39
sm176811 wrote:
Can u have 3,9,9 and yet have 9 as the median? I am not sure!


Yes. If there are odd #s the median is the middle #. So we can have 3,9,9.
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New post 27 Apr 2006, 23:52
Agree it should be 3, median of 3,9,9 is 9.
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New post 28 Apr 2006, 00:20
shampoo wrote:
sm176811 wrote:
Can u have 3,9,9 and yet have 9 as the median? I am not sure!


Yes. If there are odd #s the median is the middle #. So we can have 3,9,9.


Thats good to know!!

Everyday u learn something new! :roll:
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Re: Three boxes have an average weight of 7 kg and a median [#permalink]

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New post 05 Mar 2013, 06:09
Is the answer 1? to this question
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Re: Three boxes have an average weight of 7 kg and a median [#permalink]

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New post 05 Mar 2013, 06:14
Re: Three boxes have an average weight of 7 kg and a median   [#permalink] 05 Mar 2013, 06:14
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