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Marcia's bucket can hold a maximum of how many liters of wat

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Marcia's bucket can hold a maximum of how many liters of wat [#permalink] New post 26 Dec 2012, 05:03
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Marcia's bucket can hold a maximum of how many liters of water?

(1) The bucket currently contains 9 liters of water.
(2) If 3 liters of water are added to the bucket when it is half full of water, the amount of water in the bucket will increase by 1/3.
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Re: Marcia's bucket can hold a maximum of how many liters of wat [#permalink] New post 26 Dec 2012, 05:09
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Marcia's bucket can hold a maximum of how many liters of water?

(1) The bucket currently contains 9 liters of water. This implies that the bucket can hold at least 9 liters of water. Not sufficient.

(2) If 3 liters of water are added to the bucket when it is half full of water, the amount of water in the bucket will increase by 1/3 --> x/2+3=x/2+x/2*1/3 --> we can find x. Sufficient.

Answer: B.
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Re: Marcia's bucket can hold a maximum of how many liters of wat [#permalink] New post 12 Jan 2013, 06:47
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Bunuel wrote:
Marcia's bucket can hold a maximum of how many liters of water?

(1) The bucket currently contains 9 liters of water. This implies that the bucket can hold at least 9 liters of water. Not sufficient.

(2) If 3 liters of water are added to the bucket when it is half full of water, the amount of water in the bucket will increase by 1/3 --> x/2+3=x/2+x/2*1/3 --> we can find x. Sufficient.

Answer: B.


I didn't understand that part.
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Re: Marcia's bucket can hold a maximum of how many liters of wat [#permalink] New post 12 Jan 2013, 10:09
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fozzzy wrote:
Bunuel wrote:
Marcia's bucket can hold a maximum of how many liters of water?

(1) The bucket currently contains 9 liters of water. This implies that the bucket can hold at least 9 liters of water. Not sufficient.

(2) If 3 liters of water are added to the bucket when it is half full of water, the amount of water in the bucket will increase by 1/3 --> x/2+3=x/2+x/2*1/3 --> we can find x. Sufficient.

Answer: B.


I didn't understand that part.


(2) If 3 liters of water are added to the bucket when it is half full of water, the amount of water in the bucket will increase by 1/3
Say the bucket contains (x/2) water. If 3 liters are added, then amount of water (which is x/2) will increase by 1/3 (i.e. 33.33%)
That means (1/3) of (x/2) corresponds to 3 liters -> x/6=3
Hence x = 18.

You can double check your answer -> half the capacity is 9 liters. If 3 liters are added, the water will increase from 9 to 12, i.e. increase by (1/3) or 33.33%.

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Re: Marcia's bucket can hold a maximum of how many liters of wat [#permalink] New post 02 Sep 2013, 19:58
Let x be the total capacity of the bucket.

1. insufficient

2. sufficient. x/2+3 is the volume of water when 3 liters are added
when the bucket is half full.

x/2 + 3 = x/2 * 4/3
x=18

So B
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Re: Marcia's bucket can hold a maximum of how many liters of wat [#permalink] New post 18 May 2014, 10:09
from the first statement clearly we cannot conclude.
From second statement ,
let x be the amount of water when it is half full
the amount of water in the bucket will increase by 1/3 'of its original volume' when 3 litters is added

so x/3=3 or x=9 hence capacity is 2x=18L HenceB
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Re: Marcia's bucket can hold a maximum of how many liters of wat [#permalink] New post 06 Oct 2014, 23:44
Quote:
(2) If 3 liters of water are added to the bucket when it is half full of water, the amount of water in the bucket will increase by 1/3 --> x/2+3=x/2+x/2*1/3 --> we can find x. Sufficient.


Can any one please explain the 2nd statement more clearly. I used real numbers and got the answers but still can't get around this equation and I don't want to miss out on an important concept by not clearly understanding how this equation was formed. Thanks.
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Re: Marcia's bucket can hold a maximum of how many liters of wat [#permalink] New post 07 Oct 2014, 00:24
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aj0809 wrote:
Quote:
(2) If 3 liters of water are added to the bucket when it is half full of water, the amount of water in the bucket will increase by 1/3 --> x/2+3=x/2+x/2*1/3 --> we can find x. Sufficient.


Can any one please explain the 2nd statement more clearly. I used real numbers and got the answers but still can't get around this equation and I don't want to miss out on an important concept by not clearly understanding how this equation was formed. Thanks.


The second statement basically says that 3 liters comprise 1/3 of the bucket when it is half full of water: 1/3*x/2 = 3.
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Re: Marcia's bucket can hold a maximum of how many liters of wat [#permalink] New post 07 Oct 2014, 01:17
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aj0809 wrote:
Quote:
(2) If 3 liters of water are added to the bucket when it is half full of water, the amount of water in the bucket will increase by 1/3 --> x/2+3=x/2+x/2*1/3 --> we can find x. Sufficient.


Can any one please explain the 2nd statement more clearly. I used real numbers and got the answers but still can't get around this equation and I don't want to miss out on an important concept by not clearly understanding how this equation was formed. Thanks.


Dear aj0809

Since this is a DS question, you don't need to SOLVE it. You need to know, whether you can find its value. Since this is a quadratic equation of degree 1, the chances of getting two / more values of x are next to nil. Once you get the equation, it should be clear that we can get the value of x, thus this is sufficient.

Still, to give you a clarity, here's my take:

Let the water be X.
When 3L is added, the quantity = 3 + X,
The second question stem says that the water will increase by 1/3, i.e. it would be 4X/3
3+X = 4X/3
X = 9

When 3L is added, the bucket becomes half full.
Thus 9 + 3 = 12 = Half the capacity of bucket

Bucket's capacity = 24L

Hope this helps you... :-)
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Re: Marcia's bucket can hold a maximum of how many liters of wat [#permalink] New post 07 Oct 2014, 01:56
Thanks a lot Bunuel and Thoughtosphere for the quick help :)
Re: Marcia's bucket can hold a maximum of how many liters of wat   [#permalink] 07 Oct 2014, 01:56
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