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

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

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26 Apr 2006, 02:28
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25% (medium)

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62% (01:36) correct 38% (00:41) wrong based on 114 sessions

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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
[Reveal] Spoiler: OA
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26 Apr 2006, 02:48

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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26 Apr 2006, 02:49
What is the source?
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26 Apr 2006, 07:47
sm176811 wrote:

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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26 Apr 2006, 07:58

21-9=12

we could have the serie 3 9 9.
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26 Apr 2006, 10:20
Can u have 3,9,9 and yet have 9 as the median? I am not sure!
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26 Apr 2006, 10:53
3.

I think the weights would be 3, 9 and 9.
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27 Apr 2006, 21:37
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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27 Apr 2006, 21:39
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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28 Apr 2006, 00:52
Agree it should be 3, median of 3,9,9 is 9.
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28 Apr 2006, 01:20
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!
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Re: Three boxes have an average weight of 7 kg and a median [#permalink]

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05 Mar 2013, 07:09
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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05 Mar 2013, 07:14
fozzzy wrote:
Is the answer 1? to this question

The correct answer is C (3). Check here: three-boxes-of-supplies-have-an-average-arithmetic-mean-105819.html

Hope it helps.
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Re: Three boxes have an average weight of 7 kg and a median   [#permalink] 05 Mar 2013, 07:14
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