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# Three boxes of supplies have an average weight of 7 kgs and

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Three boxes of supplies have an average weight of 7 kgs and [#permalink]

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28 Sep 2007, 11:18
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Question Stats:

50% (01:45) correct 50% (00:47) wrong based on 147 sessions

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Three boxes of supplies have an average weight of 7 kgs and a median weight of 9 Kgs. What is the maximum possible weight, in kilograms, 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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Re: Three boxes of supplies have an average weight of 7 kgs and [#permalink]

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28 Sep 2007, 11:28
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varunk wrote:
Three boxes of supplies have an average weight of 7 kgs and a median weight of 9 Kgs. What is the maximum possible weight, in kilograms, of the lightest box?

1. 1
2. 2
3. 3
4. 4
5. 5

good one

x, 9, y --> in ascending order thus 9 is median
y is equal or greater than 9

x+9+y=21
x+y=12
in order for the lightest X to be max weigh heaviest Y should be 9 thus the lightest weighs then 3
C

Last edited by Ravshonbek on 28 Sep 2007, 11:30, edited 1 time in total.
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Re: Three boxes of supplies have an average weight of 7 kgs and [#permalink]

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28 Sep 2007, 11:35
varunk wrote:
Three boxes of supplies have an average weight of 7 kgs and a median weight of 9 Kgs. What is the maximum possible weight, in kilograms, of the lightest box?

1. 1
2. 2
3. 3
4. 4
5. 5

It's 3.

Avg: [A + B + C]/3 = 21
Median = 9 ==> B = 9 ==> A + C = 12

Max value of A can be : 3
and the boxes are : 3, 9, 9
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Re: Three boxes of supplies have an average weight of 7 kgs and [#permalink]

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28 Sep 2007, 11:43
Thanks folks, but I am confused...why is the the third number in ascending order is equal to 9...shouldn't it be 10 i.e. one more than the median...?
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Re: Three boxes of supplies have an average weight of 7 kgs and [#permalink]

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28 Sep 2007, 11:45
varunk wrote:
Thanks folks, but I am confused...why is the the third number in ascending order is equal to 9...shouldn't it be 10 i.e. one more than the median...?

yep it should be 10 but if we assume it is 10 then we end up with 2,9,10 but the only max it can get is 3 and 3,9,9 and the order is still in ascending form
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Re: Three boxes of supplies have an average weight of 7 kgs and [#permalink]

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28 Sep 2007, 12:30
varunk wrote:
Three boxes of supplies have an average weight of 7 kgs and a median weight of 9 Kgs. What is the maximum possible weight, in kilograms, of the lightest box?

1. 1
2. 2
3. 3
4. 4
5. 5

For lightest to have maximum weight , the third one should have the same weight as the middle one ( 9 )
that gives x + 9 + 9 = 3 * 7 => 3 answer
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Re: Three boxes of supplies have an average weight of 7 kgs and [#permalink]

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28 Sep 2007, 15:33
Ravshonbek wrote:
varunk wrote:
Thanks folks, but I am confused...why is the the third number in ascending order is equal to 9...shouldn't it be 10 i.e. one more than the median...?

yep it should be 10 but if we assume it is 10 then we end up with 2,9,10 but the only max it can get is 3 and 3,9,9 and the order is still in ascending form

Yes, this is the logic behind....

-Brajesh
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Re: Three boxes of supplies have an average weight of 7 kgs and [#permalink]

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28 Sep 2007, 19:10
varunk wrote:
Three boxes of supplies have an average weight of 7 kgs and a median weight of 9 Kgs. What is the maximum possible weight, in kilograms, of the lightest box?

1. 1
2. 2
3. 3
4. 4
5. 5

S/N=A

7=S/3 ---> S = 21.

So max weight will be 21-9+9 = 3.

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Re: Three boxes of supplies have an average weight of 7 kgs and [#permalink]

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24 Nov 2014, 19:41
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Re: Three boxes of supplies have an average weight of 7 kgs and [#permalink]

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25 Nov 2014, 04:41
OPEN DISCUSSION OF THIS QUESTION IS HERE: three-boxes-of-supplies-have-an-average-arithmetic-mean-105819.html
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Re: Three boxes of supplies have an average weight of 7 kgs and   [#permalink] 25 Nov 2014, 04:41
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