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Milkman problem

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Milkman problem

by nidhis.1408 » Sun Sep 30, 2012 5:31 pm
A milkman's vessel can hold maximum how many liters of milk?

(1) The vessel contains 7 liters of milk currently.

(2) If 4 liters of milk are added to the vessel when it is half full of milk, the amount of milk in the vessel will increase by 1/4.
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Source: — Data Sufficiency |

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by Mike@Magoosh » Sun Sep 30, 2012 7:12 pm
nidhis.1408 wrote:A milkman's vessel can hold maximum how many liters of milk?

(1) The vessel contains 7 liters of milk currently.

(2) If 4 liters of milk are added to the vessel when it is half full of milk, the amount of milk in the vessel will increase by 1/4.
Hi, there. I'm happy to help with this. :-)

The prompt is simply asking for the volume, V.

Statement #1: This tell us how much milk the vessel currently holds, but we have no idea how close that is to capacity. All we could say is V ≥ 7 liters. We cannot determine the volume. This statement, by itself, is insufficient.

Statement #2: "If 4 liters of milk are added to the vessel when it is half full of milk, the amount of milk in the vessel will increase by 1/4." This one links proportional amounts with real amounts --- any statement of that form is automatically sufficient.
Specifically, it says that if we start at (1/2)*V, and add 4 L more, then volume will increase by (1/4) --- in other words, 4 L is (1/4) of (1/2)*V -----

4 = (1/4)*(1/2)*V

4 = V/8

32 = V

So the capacity of the vessel is 32 liters. This statement, by itself, is sufficient.

Answer = B

Does all this make sense?

Mike :-)
Magoosh GMAT Instructor
https://gmat.magoosh.com/
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