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An empty wooden vessel weighs 10% of its total weight when

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An empty wooden vessel weighs 10% of its total weight when [#permalink]

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New post 05 Jun 2014, 02:23
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An empty wooden vessel weighs 10% of its total weight when filled with paint. If the weight of a partially filled vessel is one half that of a completely filled vessel, what fraction of the vessel is filled.

A. 3/5
B. 5/9
C. 1/24
D. 4/9
E. 2/5
[Reveal] Spoiler: OA

Last edited by balan88 on 05 Jun 2014, 03:14, edited 3 times in total.

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Re: An empty wooden vessel weighs 10% of its total weight when [#permalink]

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New post 05 Jun 2014, 02:45
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balan88 wrote:
An empty wooden vessel weighs 10% of its total weight when filled with paint. If the weight of a partially filled vessel is one half that of a completely filled vessel, what fraction of the vessel is filled.

A. 3/5
B. 5/9
C 1/24
D. 4/9
E. 2/5


An empty wooden vessel weighs 10% of its total weight when filled with paint:
Vessel = 0.1(Vessel + Paint);
10V = V + P (so the weight of completely filled vessel is 10V)
P = 9V (so the weight of the paint when the vessels is completely filled is 9V).

The weight of a partially filled vessel is one half that of a completely filled vessel:
V + P' = 1/2*10V;
P' = 4V (so the weight of the paint when the vessels is partially filled is 4V).

What fraction of the vessel is filled?
So, we need to find the ratio of the weight of the paint when the vessel is completely filled to the weight of the paint when the vessel is partially filled:

P'/P = 4V/9V = 4/9.

Answer: D.
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Re: An empty wooden vessel weighs 10% of its total weight when [#permalink]

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New post 05 Jun 2014, 03:15
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Empty.................. Paint............... Total

Say total weight when completely filled with paint = 100

10....................... 90 .................. 100

Say x quantity paint is removed

10 .......................... 90-x............. 100-x

Equation would come up as

\(\frac{1}{2} * 100 = 100-x\)

x = 50

90 - x = 90 - 50 = 40

Fraction \(= \frac{40}{90} = \frac{4}{9}\)

Answer = D
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Re: An empty wooden vessel weighs 10% of its total weight when [#permalink]

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New post 05 Jun 2014, 03:17
Bunuel wrote:
balan88 wrote:
An empty wooden vessel weighs 10% of its total weight when filled with paint. If the weight of a partially filled vessel is one half that of a completely filled vessel, what fraction of the vessel is filled.

A. 3/5
B. 5/9
C 1/24
D. 4/9
E. 2/5


An empty wooden vessel weighs 10% of its total weight when filled with paint:
Vessel = 0.1(Vessel + Paint);
10V = V + P (so the weight of completely filled vessel is 10V)
P = 9V (so the weight of the paint when the vessels is completely filled is 9V).

The weight of a partially filled vessel is one half that of a completely filled vessel:
V + P' = 1/2*10V;
P' = 4V (so the weight of the paint when the vessels is partially filled is 4V).

What fraction of the vessel is filled?
So, we need to find the ratio of the weight of the paint when the vessel is completely filled to the weight of the paint when the vessel is partially filled:

P'/P = 4V/9V = 4/9.

Answer: D.



Bunuel, would you kindly update the OA to D?

Thanks
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Re: An empty wooden vessel weighs 10% of its total weight when [#permalink]

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New post 06 Jun 2015, 05:42
Hello from the GMAT Club BumpBot!

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An empty wooden vessel weighs 10% of its total weight when [#permalink]

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New post 04 Nov 2015, 18:44
An empty wooden vessel weighs 10% of its total weight when filled with paint. If the weight of a partially filled vessel is one half that of a completely filled vessel, what fraction of the vessel is filled.

A. 3/5
B. 5/9
C. 1/24
D. 4/9
E. 2/5

v=weight of empty vessel
p=weight of paint in full vessel
v+p=10v=total weight of full vessel
p=9v
let x=fraction of p remaining after total weight of full vessel is halved
v+9vx=5v
x=4/9
D

Last edited by gracie on 12 Aug 2017, 12:06, edited 1 time in total.

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Re: An empty wooden vessel weighs 10% of its total weight when [#permalink]

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New post 12 Aug 2017, 04:46
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: An empty wooden vessel weighs 10% of its total weight when   [#permalink] 12 Aug 2017, 04:46
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